star trek warp factor chart

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Star trek: how fast warp speed is (& how it compares to hyperspace).

Warp speed is the key to making Star Trek work - but just how does this fictional form of travel work, and how does it compare to Star Wars?

Here's how fast  Star Trek 's warp speed actually is, and how it compares to other forms of travel in science-fiction, such as  Star Wars ' Hyperspace. When Gene Roddenberry began to work on  Star Trek , he was faced with a thorny problem: he wanted the show to have some semblance of scientific accuracy, but at the same time, he also needed the Starship Enterprise to be able to move at incredible speeds.

The solution was the warp drive (or, as it was actually called in  Star Trek 's pilot episode, the hyperdrive). This brings matter and antimatter into collision in order to generate a phenomenal amount of power, and the reaction is regulated by a rare mineral called dilithium . The matter/antimatter reaction allows the starship to travel faster than light - several multiples faster.

Related:  Star Trek: How Stardates Are Calculated (& What They Really Mean)

But just how fast is warp speed? The original  Star Trek series was unclear, but over time the franchise has established clear rules. Let's explore them.

Warp Speed In The Original Series

The original  Star Trek series was wildly inconsistent in its portrayal of warp speed, with the concept basically used as a plot device to get from A to B at whatever speed an episode's writer wanted. Warp speeds of 10 or higher were treated as unsafe, at least until the Enterprise was refitted in  Star Trek: The Motion Picture , when it gained the ability to safely travel up to warp 12. The fastest warp speed shown on-screen was an alien vessel that could actually reach warp 35. All these inconsistencies clearly bugged Gene Roddenberry, and as a result warp speed was recalibrated for  Star Trek: The Next Generation in order to create something a little more well-structured.

Warp Speed In The Next Generation Era

According to the Star Trek Encyclopedia , in simple terms, the new warp speed factor 1 is the exact speed of light, 299,792,458 m/s. Each factor above is a multiple of that warp speed, although what those values are vary depending on the show in question.

• Warp Factor 1 - 1x lightspeed
• Warp Factor 2 - 10x lightspeed
• Warp Factor 3 - 39x lightspeed
• Warp Factor 4 - 102x lightspeed
• Warp Factor 5 - 214x lightspeed
• Warp Factor 6 - 392x lightspeed
• Warp Factor 7 - 656x lightspeed
• Warp Factor 8 - 1,024x lightspeed
• Warp Factor 9 - 1,516x lightspeed
• Warp Factor 9.99 - 7,912x lightspeed
• Warp Factor 10 - Infinity

In theory, a ship traveling at warp 10 is moving so fast that it essentially exists in all places and all times simultaneously. It's only known to have been achieved once in the entire history of  Star Trek , in the  Star Trek: Voyager episode "Threshold". There, Tom Paris successfully traveled at warp 10, but the experience proved to have a transformative, evolutionary effect upon any organic matter. The crew of Voyager wisely ditched the idea, concerned about the consequences. It's worth noting that warp speeds seem to have been re-calibrated again in the future timeline glimpsed in "All Good Things," where two vessels are said to travel at warp 13. Presumably as technology became more efficient, Starfleet saw the value in creating a new scale with a wider range. In a technical note, science adviser Andre Bormanis suggested that in this future timeline, warp 15 would be the Threshold limit.

In truth, warp travel is usually little more than a plot device to help the Federation's starships jump across the galaxy at speed. Almost every sci-fi series has its own equivalent, simply because the alternative is to slow your story down for quite a while as the crew jumps from one star-system to another.

How Warp Speed Compares To Hyperspace

In  Star Wars , for example, ships that break the speed of light are able to access another dimension called hyperspace . This is essentially another plane of reality, one where the laws of physics operate differently. By accessing hyperspace, a spaceship can move at a phenomenal speed; there are different classes of hyperdrive, which allow different speeds.

It's important to note that a journey through hyperspace can be disrupted; if a vessel encounters the gravity shadow of a stellar mass, such as a planet, star, or black hole, they are ripped out of hyperspace. That's why the trip from Tatooine to Alderaan in  Star Wars took 16 hours, which is actually pretty slow for a 10,000 light year journey in a ship with an illegal class 0.5 hyperdrive, and is roughly equivalent to Star Trek 's warp 7. The dream scenario would be to acquire a hyperdrive of class 0.0, which would be analogous to Star Trek 's warp 10.

More:  Picard Isn’t The First Star Trek Captain To Say “Engage”

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Star Trek Warp Calculator

27 August 2017

Select warp scale: The Original Series (before 2312) The Next Gegeration (after 2312)

Description

For Star Trek: The Original Series, the warp equation is generally accepted to be (\(v\) — velocity through space, \(c\) — the speed of light (\(3·10^8\) m/s) and \(w\) — the warp factor):

For Star Trek: The Next Generation, the warp scale has changed. Gene Roddenberry stated that he wanted to avoid the ever-increasing warp factors used in the original series to force added tension to the story, and so imposed the limit of warp 10 as infinite speed.

Scale change occurred in 2312. Warp factors were established to be based upon the amount of power required to transition from one warp plateau to another. For example, the power to initially get to warp factor 1 was much more than the power required to maintain it; likewise warp 2, 3, 4, and so on. Those transitional power points rather than observed speed were then assigned the integer warp factors.

Warp Speed Calculator

Table of contents

Omni Calculator's warp speed calculator is a tool that allows you to determine the speed of your favorite Star Trek ship . You can also compute the distance covered and the time of travel .

In the text below, we will explain the fundamental aspects of the warp propulsion system, warp factors, and how we can compute the speed of our starship. The starship speed can be calculated using three different equations: TOS (The Original Series) and two versions of TNG (The New Generation) .

Read on if you want to learn about the warp factor, the Cochrane scale , and how Star Trek ships can overcome the speed of light. Let us move to our calculator and live long and prosper🖖!

⚠️ Disclaimer: We try our best to make our Omni Calculators as precise and reliable as possible. However, this tool can never replace the professional advice of a starship's Chief Engineer.

Warp propulsion and warp factor

As it is known by any Star Trek fan or by anyone who eventually watched the USS Enterprise exploring the frontiers of space, the warp propulsion system (WPS) is the tool that allowed Captain James T. Kirk and his crew to access deep space. The WPS is a fictional technology that makes a starship move in space with superluminal speeds (speeds faster than the speed of light). The system uses a warp drive device, distorting spacetime and enabling a starship to cross several light-years in seconds!

We know it seems non-practical or strange that the spacetime can be distorted. However, this is the mechanism behind the propagation of the gravitational waves . These waves are generated by cataclysmic events in the Universe, such as the collision between supermassive black holes or neutron stars. Before their final collision, these objects are orbiting each other, and this spiral movement distorts the spacetime among them. This distortion is propagated in spacetime in the form of waves. The phenomenon was predicted by Einstein's general relativity in 1916 and observed for the first time in 2015 by LIGO detectors — Laser Interferometer Gravitational-Wave Observatory .

Back to Star Trek, the advent of the WPS is credited to a scientist called Zefram Cochrane , whose surname is used as the scale to measure the speed of a starship in multiples of the speed of light . This means that the light in a vacuum moves at one cochrane . Meanwhile, a star cruiser may reach 2450 cochranes . These superluminal speeds depend on the value of the so-called warp factor. The warp factor is a parameter that scales the starship's velocity due to the warp drive.

The warp factor formula has two main definitions: The Original Series (TOS) and The New Generation (TNG) equations. These equations are going to be discussed deeply in the following sections.

🙋 If you wish to know more about the physical limits of the speed and energy of an object, access Omni Calculator's relativistic kinetic energy calculator .

The original series equation — Cochrane Scale

The original series equation is presented in Star Trek: Star Fleet Technical Manual written by Franz Joseph, and its form is:

• v v v — Warp speed;
• w w w — Warp factor; and
• c c c — Speed of light in vacuum ( c = 299 , 792 , 458   m / s c = 299{,}792{,}458\rm \ m/s c = 299 , 792 , 458   m/s ).

The TOS equation is also known as the Cochrane scale among the community of Star Trek fans. From the previous formula, we can observe that for w = 2 w = 2 w = 2 , our ship is moving with v = 8c or 8 cochranes .

The Next Generation equations for superluminal speed

The Next Generation equations are a set of theoretical formulae based on the values for the warp factor presented by Rick Sternbach and Michael Okuda in the Star Trek: The Next Generation Technical Manual . There, the authors introduced the following table:

The data shown in the table above were used to define both TNG-1 and TNG-2 equations for w ≤ 9 w \leq 9 w ≤ 9 , whose formula is:

You can compare the speeds for the TOS with the TNG-1 and TNG-2 equations and see how the new generation starships are faster than the original series ones.

Would you like to know why we use two names for the new generation warp speed equations? Keep reading, and you will find the answer.

The technical manual for the new generation starships also talks about the physical limit for the warp factor, known as Eugene limit . The Eugene limit establishes that the maximum warp factor is w = 10 w = 10 w = 10 and that even if a civilization could reach the energy boundary of such a warp factor, an object traveling at warp factor 10 would occupy all the points of the Universe simultaneously .

You can find below a table containing the warp factor predictions for w > 9 w > 9 w > 9 :

The conjectured values are part of a warp factor chart and were approximately derived by two different equations built by fans .

This is why we use two different equations for the Next Generation starships. The TNG-1 formula for w > 9 w > 9 w > 9 is:

And the TNG-2 equation for w > 9 w > 9 w > 9 has the following form:

The numerical parameters shown in the last equations were carefully chosen to fit the warp factor chart prediction in the superluminal regime. Besides, both TNG-1 and TNG-2 go to infinity at warp factor 10, recovering the Eugene limit for superluminal velocities.

We still do not have a final answer for a warp speed equation that recovers the Eugene limit, so you can choose your favorite proposal and explore the behavior of traveling close to infinity .

Now, it is time to play with our calculator and find the speed of your favorite starship. Enjoy exploring the power of your warp drive!

How to use the warp speed calculator

Using our warp speed calculator is simple and intuitive . Just type the warp factor of your starship and then click on the name of the equation you wish to use. You will see the warp factor converted to the superluminal velocity as a multiple of the speed of light (or in cochranes).

You can also include the distance you would like to travel, and you will obtain the time necessary to complete your journey instantly. Remember that our Omni calculators work in the inverse direction, so you may enter the time interval of your space trip and derive the traveled distance in the blink of an eye.

Do you know what value to choose for the warp factor? You do not need to worry; we provide a table with the maximum warp factor for some Star Trek ships.

Searching for a new planet — an example

The Universe is so vast and full of interesting places that it is difficult to decide a destination for our starship. A potential target recently discovered by the James Webb Space Telescope is a planet known as LHS 475b .

This Earth-size planet orbits the star LHS 475, localized in the constellation of Octans. You can find more information about other fascinating new worlds in our exoplanet discovery calculator .

So, let us consider the USS ENTERPRISE D as our starship to explore this new world. Then, by taking warp factor 9.3 and 41 light years as the distance between Earth and LHS 475b in our warp speed calculator, the TOS, TNG-1, and TNG-2 equations give us:

v = 804   c v = 804\,c v = 804 c , t = 447   hours t = 447 \, \text{hours} t = 447 hours ;

v = 1713   c v = 1713\,c v = 1713 c , t = 210   hours t = 210 \, \text{hours} t = 210 hours ; and

v = 1693   c v = 1693\,c v = 1693 c , t = 212   hours t = 212 \, \text{hours} t = 212 hours , respectively.

🔎 Now, you can compare these results with those derived in our exoplanet travel planner calculator and check the power of the warp propulsion system!

How fast is Star Trek warp speed?

In Star Trek, the warp speed is a velocity scaled by the warp factor . The warp factor formula is inconsistent throughout the series . In the original series, for instance, warp factors were described using the formula v = w³⋅c , where c is the speed of light in a vacuum. Therefore, a Star Trek ship may travel faster than light , allowing the civilizations to explore the Universe.

How do I calculate the warp speed of a starship?

You can calculate the warp speed in Star Trek using two formulae: The Original Series (TOS) and The Next Generation (TNG) equations. In both cases, the speeds are given as multiples of the speed of light c . To do that, let us suppose that your starship has a warp factor w = 5 , then follow the steps below:

Input the warp factor in the TOS equation v = w 3 ⋅c .

Input the warp factor in the TNG equation v = w 10/3 ⋅c .

That is it! You will find that the warp speeds are v = 125⋅c and v = 214⋅c , for the TOS and TNG equations, respectively.

How long it takes for a starship to leave the solar system?

The most distant object made by humanity is Voyager 1 , which will take more than 30,000 years to reach the outer edge of the Oort Cloud , whose distance is estimated at 100,000 AU from the sun. The USS Enterprise D, flying in cruise mode ( w = 6 ), could reach this distance in 35 hours . To find this result:

Input the warp factor in the formula v = w 10/3 ⋅c .

Compute the warp velocity v = 392⋅c .

Isolate the time in the velocity formula t = d/v .

Input the distance d = 100,00 AU and c = 299,792,458 m/s in the last formula.

Convert the units properly.

That is it! You found that t = 35 hours .

Is a warp drive possible?

With the present science and technology, the answer is no . However, some theoretical models allow the creation of a warp bubble in flat spacetime, which can move faster than the speed of light. The most famous theoretical proposal in this direction was introduced by Miguel Alcubierre in 1994 , also known as the Alcubierre metric or Alcubierre drive .

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ol{padding-top:0px;}.css-ykr2zs ul:not(:first-child),.css-ykr2zs ol:not(:first-child){padding-top:4px;} Warp Factor

Input the warp factor and open sections of the calculator to compute the speed of your starship using different equations.

Warp factor

TOS: The Original Series

TOS is the first equation to compute the speed of a starship scaled by the warp factor.

TNG-1: The Next Generation version 1

TNG-1 combines the new speed scaled by the warp factor with the first proposal to map the Eugene Limit.

TNG-2: The Next Generation version 2

TNG-2 combines the new speed scaled by the warp factor with the second proposal to map the Eugene Limit.

Warp Speeds Chart

Note: warp 10 is meaningless -- a starship traveling at warp 10 would occupy all points in the universe simultaneously.

6 Warp Speed Measurement

The Physics and Technology of Warp Propulsion

6.1 Concept of Warp Factors 6.2 TOS Scale (23rd Century) 6.3 TNG Scale (24th Century) 6.4 Possible Future Scale

6.1 Concept of Warp Factors

• Introduction
• Chapter 1 - Real Physics and Interstellar Travel
• Chapter 3 - Subspace
• Chapter 6 - Warp Speed Measurement
• Chapter 7 - Appendix

A warp factor is a unitless figure that represents the speed of a starship or of a signal traveling faster than light. There is a non-linear dependence between the warp factor and the effective FTL speed. In every known variant of the warp scale the speed rises exponentially with the warp factor, meaning that from Warp 1 to Warp 2 the speed more than doubles. The exponent is subject to vary between the scales.

There is no common canon symbol or abbreviation for warp factors, although "WF" or "wf" are sometimes used in textbooks. In spoken language they are referred to as "Warp X" (written with a capital "W") or, now rather antiquated, "warp factor X" during the time of TOS.

In all known warp scales "Warp 1" corresponds to the speed of light. The warp scale is continuous, meaning that real numbers such as "Warp 8.179" are possible, although it seems that starships most often travel at integer warp factors 7, 8, 9, etc.

Warp factors below Warp 1 are occasionally mentioned in Star Trek, mostly in the scope of the 24th century scale. Consequentially these refer to sublight speeds. The question whether something like Warp 0.5 exists has some relevance. Warp 0.5 could either mean that the warp drive also operates at sublight speeds, without a need to activate the impulse engines, or that the warp scale is simply extrapolated below Warp 1, even if only the impulse drive is on. With the note in the TNG Technical Manual [Ste91] that the impulse drive makes use of subspace driver coils the latter makes sense also technically, because if the warp factor generally describes the formation of a subspace field, it may as well apply to the field generated by the driver coils at sublight speed.

Bearing in mind that the speed of light c is already as high as 3*10^8m/s, it is obvious that with conventional units such as meters per second or kilometers per hour as they are used for the speeds of today's planes or spaceships we would end up with unreasonably large and unhandy figures when describing FTL motion. Generally, it may have been possible to switch to something like light years per day or similar manageable time and distance units. The reason why Starfleet introduced the apparently abstract and strangely non-linear warp factor must lie in the physical principle and/or the technical implementation of the propulsion system. In other words, the function of speed vs. warp factor most likely reflects how strong a warp field must be to achieve a certain speed.

Side note Gene Roddenberry may have originally conceived warp factors for the sake of the dramatic impression of Kirk's commands. "Mr. Sulu, ahead Warp factor two." is more precise than "half speed ahead", and it sounds much more to the point than "increase to three light years per day". Moreover, with warp factors obscuring the real speed of the ship, calculation errors between speeds, times and distances mentioned on screen were less likely to occur. It was as late as in TNG that a correlation between all of the three figures was routinely made on screen (most often by Data), revealing the "true" significance of warp factors.

The sawtooth curve of the power expenditure vs. warp factor as shown in Fig. 6.1 and discussed in 3.3 Subspace Fields and Warp Fields is canon since it appeared on screen in ENT: "First Flight". The tips of the sawtooth are the so-called peak transitional thresholds, the points at which the power expenditure rises steeply because there is supposedly a physical threshold (in one possible interpretation, the transition to the next subspace layer) to be crossed. These peak transitional thresholds are located at the integer warp factors 1, 2, 3, and so on. Their existence is evidence that something significant happens at integer warp factors, justifying that the scale is based on these prominent points. In other words, the scale is designed in a way that the warp factors count up certain events that occur as the warp field is being expanded and intensified, which corresponds with an increase in speed.

Fig. 6.1 also shows a reason why ships customarily travel at integer warp factors or slightly above but never slightly below. We have to bear in mind that warp propulsion is non-Newtonian and a constant power supply is required to maintain a constant speed. If we imagine for a moment that the peaks are smoothed out, the power consumption (yellow sawtooth curve) overall increases stronger with the warp factor than the speed v/c (white for the TNG scale) does. In other words, the faster a ship goes, the higher is the energy consumption for the trip.

However, as we take into account the peak transitional thresholds, the power consumption per cochrane rapidly drops to a much lower value on the right side of each peak. More precisely, the drop happens slightly above the integer warp factor, but for the sake of simplicity we may assume that "increase speed to Warp 6" means to cross the sixth threshold, after which the ship may be actually at Warp 6.01. Here the power consumption is a lot lower than at Warp 5.99. It is obvious that staying slightly below Warp 6 would be very disadvantageous.

We can also see that a bit above Warp 6 the power consumption per cochrane is the same as at Warp 5.6. Since the cochrane value is equivalent to v/c, the effective increase of power consumption between Warp 5.6 and Warp 6.01 is the same as the speed increase. So the total energy consumption for a trip at Warp 6.01 is the same as at Warp 5.6 but the ship is some 25% faster. Hence, Warp 5.6 is some sort of break-even point, above which it is advantageous to speed up even further to Warp 6.01.

6.2 TOS Scale (23rd Century)

During the era of The Original Series (TOS) a warp scale was in use where the warp factor was described with:

So the warp factor equals the cubic root of the ship's achieved speed ratio v/c, with v being the effective ship speed and c being the speed of light. Warp 1 corresponds to the speed of light.

Side note The TOS scale is often referred to as "Cochrane scale" in fandom, but this is conjecture and, like the underlying formula, was never mentioned in the series.

Strictly speaking, the warp scale used in the TOS era is conjectural. There is no reference that would allow us to relate a warp factor stated on screen to a distance and a time. The now widely accepted scale, however, must have been established behind the scenes in a kind of writer's guide. David Whitfield, who had access to essential documents of Roddenberry's staff mentions the scale in his book The Making of Star Trek [Whi68] as soon as 1968. In his reproduction of the warp scale, Warp 1 denotes the speed of light, Warp 3 is 24c, Warp 6 is 216c and Warp 8 is 512c. Actually Warp 3 should be 27c, but with the other values following exactly the third-power law of Eq. 6.1 we have a confirmation that the scale was really being used at least as a guideline.

The continuous curve of the TOS scale (teal in Fig. 6.1) insinuates that warp factors below 1 and fractional values were well possible in this measurement system. Warp factors below 1, however, were not mentioned once in TOS, and fractions occurred only occasionally. As late as in "Star Trek: The Motion Picture" (TMP) warp factors lower than Warp 1 appeared for the first time, when Sulu carefully activated the untested warp drive and slowly accelerated to warp speed. More precisely, the ship was already at Warp 0.5 but was only running on impulse drive when the warp drive was engaged. So it appears that impulse speeds can be measured with warp factors as well, the scale is uninterrupted. Since we shouldn't assume that the measurement system has changed between TOS and TMP, we can assume that warp factors below 1 already existed in TOS. In TOS, it often seemed like Kirk ordered to go to warp, a switch was flipped and the ship's speed immediately jumped up to Warp 1, but perhaps we should ascribe this immediate effect to dramatic license.

Warp factors higher than 10 are possible in the TOS warp scale. We know of a few incidents where the Enterprise was said to have achieved such high speeds that are well beyond the nominal top speed of Warp 8. The first one is in TOS: "The Changeling", where Nomad improved the Enterprise's engines to achieve speeds of up to Warp 11. Another one is in TOS: "That Which Survives", where a modification to the engines by Losira accelerates the Enterprise to as much as Warp 14.1. This is also one of very few examples of fractional warp factors. On another occasion, in TOS: "By Any Other Name", the Enterprise was tampered with by the Kelvans crossed the Galactic Barrier at Warp 11. The Kelvans were going to reach the Andromeda Galaxy, 2.3 million light years away, in three centuries. This gives us an indirect speed reference of as much as Warp 19.7. Yet, a definite figure was not mentioned for the warp factor during the long trip.

As already mentioned above in Section 6.1 , the warp factors likely reflect the physical principle and/or the technical implementation of the warp drive. The peak transitional thresholds and the corresponding prevalence of integer warp factors is a reason why the structure of the warp field and/or of subspace is most likely a layered one, as outlined in 3.3 Subspace Fields and Warp Fields . So in the TOS warp scale "Warp 1" may simply mean that the subspace field extends just into the first layer of subspace, having crossed the first peak transitional threshold. This may go on for Warp 2, 3, and so on. In the TOS scale there is no theoretical limit for warp factors and for the according submersion of the warp field into subspace. Only the power available on a ship imposes a limit to crossing the peak transitional thresholds of always deeper layers.

In TOS: "That Which Survives" one of the following two things may have happened when the ship attained Warp 14.1. The first possibility is that actually 14 subspace layers were subsequently crossed by tuning the warp field accordingly, although this has never been attempted before. The other possibility is that the Enterprise's engines were never built to penetrate more than eight layers (Warp 8 was said to be the maximum safe speed), and that simply so much power was pushed into the first to the eighth layer, overstressing these layers, that the equivalent warp factor was 14.1. In other words, in the latter case the Enterprise's instruments would not have registered further thresholds and may have been off scale anyway, so the equivalent warp factor would have been calculated from the actual speed.

Use in Star Trek Enterprise

For the sake of plausibility, we should assume that the 22nd century (Star Trek Enterprise) uses the same warp scale as in the 23rd century (TOS), rather than the one of the 24th century (TNG). Enterprise NX-01 has a top speed of Warp 5, which in the TOS scale is reasonably slower than the max. speed of the Enterprise NCC-1701 (Warp 6) or its max. emergency speed (Warp 8). If Enterprise used the TNG scale, NX-01 would be almost as fast as the NCC-1701.

There are some cases in which the original Enterprise must have traveled at extremely high speeds, even without alien modifications to the engines. The first example is Pike's line in "The Cage" that his ship comes from "a stellar group at the other end of this galaxy" . Also, in TOS the Enterprise crosses the Galactic Barrier no less than three times, which is supposedly at the very least a thousand light-years from Federation space. Finally, in "Star Trek: The Final Frontier" the Enterprise-A explicitly travels to the center of the galaxy, which is some 25,000 light-years away, a journey that would take a lifetime at Warp 8. Enterprise NX-01 too is occasionally much faster than Eq. 6.1 would allow. The most blatant case is in ENT: "Broken Bow" when the travel time to Qo'noS is said to be "Four days there, four days back." , which would place the Klingon homeworld only 1 light-year away from Earth, considering that Enterprise's top speed at the time is merely Warp 4.5.

There are occurrences in other Trek series too where the starships are effectively many times faster than they should be, or travel to destinations that should be far out of reach. See also the examples in Section 6.3 . These are most often fundamental plausibility problems of the stories, rather than of the warp speed measurement. Yet, it has been suggested that the actual speed of a starship at a given warp factor depends on environmental conditions.

The TNG Technical Manual [Ste91] states: "The actual values [of the cochrane value and hence of the speed attainable at a warp factor] are dependent upon interstellar conditions, e.g., gas density, electric and magnetic fields within the different regions of the Milky Way galaxy, and fluctuations in the subspace domain. Starships routinely travel at multiples of c, but they suffer from energy penalties resulting from quantum drag forces and motive power oscillation inefficiencies." In order to explain away warp speed inconsistencies along these lines, we need a correction factor k to give us the actual relation between warp factor and speed, modifying Eq. 6.1 for the TOS scale to WF=k*(v/c)^(1/3). While some regions of space may allow only below average speeds, most importantly there have to be other regions in which a much higher speed is attainable at a certain warp factor (known as "warp highways" in fandom). In these regions k has to be considerably lower than 1 and in extreme cases (travel across the whole galaxy) close to 0. There are a couple of problems with this assumption, however:

If there is a coefficient k (x,y,z) of spatial conditions that locally influences the warp speed at a given warp factor, this k ought to play a role in the stories. It is totally implausible that it was never mentioned in any form. Well, we know of the low-warp Hekaras Sector in TNG: "Force of Nature", but here the problem is to maintain a stable warp field in the first place; there is no hint that in this region warp factors may correspond to lower speeds. The whole series Star Trek Voyager makes no sense under the assumption that there are warp highways everywhere. The crew was seeking wormholes and other rare phenomena all the time, not on-ramps and exits of warp highways. Well, thanks to Seven's work in the astrometric lab five years could be shaved off as mentioned n VOY: "Year of Hell, Part I", but on the display it looks like Seven, with the more accurate Borg technology, just plotted a straighter course than the previous one (or one with fewer obstacles to be avoided). A ship's captain (sea or space) orders a course and a speed. If a captain has to take into account the gradient of an additional coefficient along the flight path that strongly influences the speed, he either has to be a genius in mental calculus, or he doesn't really care how soon the ship actually arrives. Well, there is always the possibility of asking the computer to calculate the course and the travel time in advance, but in Star Trek offhand ETA calculations and swift orders to go to a certain course and warp factor are commonplace. These would be pointless if the travel time to the same destination could vary between minutes and months, and the best course would not be a straight line. Well, we may expect that realistically the interstellar conditions don't vary too strongly, with a factor of perhaps 2 between the highest and the lowest possible speed at a given warp factor, which would alleviate the preceding point. Moreover, on very long journeys the varying conditions in the flight path will average out. But then the theory of fluctuating conditions couldn't explain phenomena such as the Enterprise's journey to the center of the galaxy at all. Eq. 6.1 and Eq. 6.2 give us quite simple relations between warp factor and speed, without a correction factor (or with k=1) or any other coefficients in it. If anything, these formulae look like they describe a "basic" or "optimum" condition of space (without interstellar dust, without interfering fields, etc.), rather than an average. And if they really describe an average as hinted at in the TNGTM , there is the question of the averaging method, the size of the sample, the sampling region and how frequently such an average would need to be updated.

Summarizing, there may be regions in which warp travel is facilitated, meaning that less power is required to achieve and/or maintain a certain warp factor. There may be other regions where the contrary is true (such as the Hekaras Corridor). But while the peak transitional thresholds may be lowered, they rather wouldn't shift with the natural inhomogeneity of space, because this would make the concept of warp factors pretty useless. And even if they do shift, it may not suffice to explain anomalous warp speeds.

6.3 TNG Scale (24th Century)

Definition up to warp 9.

Some time between the TOS Movie era (late 23rd century) and the TNG era (mid-24th century) the warp scale changed. The new scale is valid in all series set in the 24th century (TNG, DS9, Voyager). In this new TNG scale Warp 1 still denotes the speed of light. But above Warp 1 the speed corresponding to a certain warp factor is generally higher than in the TOS scale. The discrepancy slowly grows between Warp 1, where the curves intersect, to Warp 9, where the speed is 729c according to the TOS scale but 1516c for the TNG one (see Fig. 6.1). The exact equation for speeds up to Warp 9 in the TNG scale is:

So the exponent increased from 3 to 10/3=3.333..., accounting for the higher speed at a given warp factor.

Definition between Warp 9 and 10

The difference between TOS and TNG scale, however, becomes dramatic above Warp 9. The warp speed table was changed in accordance with Roddenberry's wish that Warp 10 should be the absolute maximum speed.

Side note The TNG Technical Manual [Ste91] states about the real-life rationale for the recalibration: "Figuring out how 'fast' various warp speeds are was pretty complicated, but not just from a 'scientific' viewpoint. First, we had to satisfy the general fan expectation that the new ship was significantly faster than the original. Second, we had to work with Gene's recalibration, which put Warp 10 at the absolute top of the scale. These first two constraints are fairly simple, but we quickly discovered that it was easy to make warp speeds TOO fast. Beyond a certain speed, we found that the ship would be able to cross the entire galaxy within a matter of just a few months. (Having the ship too fast would make the galaxy too small a place for the Star Trek format.) Finally, we had to provide some loophole for various powerful aliens like Q, who have a knack for tossing the ship millions of light-years in the time of a commercial break. Our solution was to redraw the warp curve so that the exponent of the warp factor increases gradually, then sharply as you approach Warp 10. At Warp 10, the exponent (and the speed) would be infinite, so you could never reach this value. (Mike used an Excel spreadsheet to calculate the speeds and times.) This lets Q and his friends have fun in the 9.9999+ range, but also lets our ship travel slowly enough to keep the galaxy a big place, and meets the other criteria. (By the way, we estimate that in 'Where No One Has Gone Before' the Traveler was probably propelling the Enterprise at about Warp 9.9999999996. Good thing they were in the carpool lane.)"

In the TOS scale the speed continued to increase with the third power as in Eq. 6.1, with Warp 10 being as "slow" as 1000c. In the TNG scale, beyond Warp 9, the exponent rises in a way that at exactly Warp 10 the speed (as well as the power expenditure) becomes infinite. In other words, the TNG scale ends at Warp 10. The recalibration compresses the whole range from about Warp 9 to infinite Warp factor in the TOS scale into the Warp 9..10 interval of the TNG scale.

A table in the Star Trek Encyclopedia III [Oku99] lists selected TNG warp factors and the corresponding speeds above Warp 9. But these figures don't seem to originate in Mike Okuda's Excel sheet mentioned in the TNGTM . In an e-mail from January 1995 Mike Okuda states, "Between 9 and 10, I gradually increased the exponent so that it approached infinity as the warp factor approached 10. Lacking knowledge of calculus, I just drew what looked to me to be a credible curve on graph paper, then pulled the points from there." So there does not seem to be an "official" underlying formula for the range between Warp 9 and Warp 10.

Side note There are some fan-made approximations, notably the formula by Graham Kennedy at DITL and the ones on Joshua Bell's site for TNG warp factors beyond 9.

The following table compares the two warp scales:

Tab. 6.1 Comparison of TOS and TNG warp scales

As the TNGTM explains, the real-world reason for changing the warp scale was to put a limit to the warp factors that otherwise may have continued rising indefinitely (in a similar unfortunate fashion as the amounts of quads that can be stored in the computer did on Voyager).

Making up a fictional explanation for the recalibration is not so easy, however. Speed measurements can be expected to be very accurate, their improvement certainly wouldn't lead to a factor of 2 at Warp 9 between the TNG and the TOS scale. Likewise, the peak transitional thresholds that define the integer warp factors wouldn't shift just because the measurement of the ship's power consumption is improved. We have to seek the explanation in a better understanding of subspace physics, one that allowed to refine the working principle of a ship's warp engines in a way that the peak transitional thresholds and hence the warp factors could be moved to higher speeds. In other words, the warp engines were improved in a way that less power was necessary to attain the same speed. This modification must have been so successful and universally applicable that it was decided to change the warp scale. For older ships without this modification the new scale would give us just an equivalent warp factor, meaning that an old ship with the true power expenditure of Warp 6 (TOS scale) is rated with an equivalent warp factor 5 (TNG scale). The same equivalent rating may apply to alien ships whose propulsion system may work differently than that of the Federation, and perhaps not even based on conventional warp fields.

This theory still doesn't explain the dramatic speed increase between Warp 9 and 10 in the TNG scale though. But we could imagine that, as part of the refinement of the propulsion system, at least on Federation vessels, it was recognized that submerging the warp field more than nine layers into subspace was not practically possible or at least inefficient. We have to bear in mind that, as seen in Section 6.2 , the maximum possible speed of the TOS era was Warp 8, and that the warp factor 14.1 attained by the Enterprise in TOS: "That Which Survives" may have been just an equivalent figure. So it may have been discovered some time between TOS and TNG that there are other, more efficient methods to attain high speeds than crossing the tenth subspace barrier. And since the peak transitional thresholds 10, 11, etc. don't exist any longer, the scale was changed to reflect this, effectively compressing the whole range from warp factor 9 to infinite warp factor into the new range between Warp 9 and 10. We may even speculate that the refinement of the warp scale has something to do with the Excelsior transwarp experiment, and that "transwarp" here merely means that the principles that would be commonplace in the TNG era were tested for the first time, rather than "transwarp" being something akin to "Borg transwarp" or even Tom Paris's alleged Warp 10 engine.

In TNG, DS9 and Voyager there are various statements by crew members such as Data that allow to correlate warp factors, distances andtravel times. Sometimes they correspond to Eq. 6.2, sometimes they are significantly off. Overall, however, there are no gross violations of the concept of limited speed, because the ships don't travel to regions of space that should be out of reach, unless the ship's warp drive was explicitly accordingly modified. In Star Trek Voyager it is even a key concept of the series that the ship would need 75 years at maximum warp to travel the 70,000 light-years back to Federation space. This corresponds to about Warp 9.8, going by the figures in Tab. 6.1.

There are three incidents that conflict with the TNG scale more fundamentally because they call the Warp 10 limit into question. The first is in TNG: "Where No One Has Gone Before". During Kosinski's experiment Geordi says at one point: "We're passing Warp 10." This should be absolutely impossible considering that Warp 10 means infinite speed, and there can be nothing equal to or even faster than infinite speed. But there is an explanation for Geordi's line. A few moments later Data states that the speed is off the scale. This could mean that Geordi was reading some sort of overflow on the speed display, which was simply leaving the valid range up to Warp 9.9something, so he didn't mean "infinite speed" or even "more than infinite speed" although he effectively said it. Still later, however, Kosinski claims that the "warp barrier" has become meaningless thanks to his work. This seems to corroborate the wrong notion that Warp 10+ might be possible. On the other hand, Kosinski may simply mean the peak transitional thresholds that have shifted or were lowered thanks to his work (or actually, thanks to his assistant, the Traveler).

The second mention of breaking the Warp 10 barrier is in TNG: "Time Squared", where Riker notes that accelerating beyond Warp 10 would enable time travel. More precisely, he states that this constitutes the only known method of going to the past, which is not true for all we know from the countless time travel episodes. Anyway, if we believe him and anything beyond Warp 10 is equivalent to time travel, we may interpret it in a way that achieving exactly Warp 10 may be still impossible. Beyond Warp 10 the speed of a ship becomes undefined within the bounds of our space-time, because speed as a physical quantity always requires a fixed time frame that doesn't exist during a time travel.

The third problem with the Warp 10 limit occurs in the infamous episode VOY: "Threshold". There are many problems and errors with this story, the most pressing of which is how Tom could possibly attain a speed of Warp 10 with his shuttle. As correctly stated in this very episode by Harry Kim: "Nothing in the universe can go warp ten. It's a theoretical impossibility. In principle, if you were ever to reach warp ten, you'd be traveling at infinite velocity." We could argue that, just as in Geordi's case, the speed of the shuttle was simply off scale and hence may have registered as Warp 10, although it was actually slower. The dilemma is that the very intention of Tom's flight was to "break the warp barrier" as already Kosinski expressed it, and explicitly to speed up to Warp 10 and not to Warp 9.999something. Also, the speed was later confirmed to have been infinite, unlike it was the case in the TNG episode. This Voyager episode only makes sense if we ignore many statements and essentially major parts of the story.

6.4 Possible Future Scale

The warp scale changed yet again in the late 24th century, albeit just for the TNG series finale "All Good Things", part of which is set in the year 2395. In this new AGT scale, starships such as the three-nacelled Enterprise-D and the Pasteur routinely achieve Warp 13.

There is no official formula to calculate the speed corresponding to the revised warp factors. In the October 1995 issue of the Omni magazine, science advisor Andre Bormanis states: "I raised that question in a TECH note. Basically, the idea there was that they recalibrated the warp scale. I don't think that ended up in the final draft teleplay, but the idea there was that if you've got ships that can routinely travel at speeds in excess of Warp 9, then maybe it makes sense to recalibrate your speed scale so that Warp 10 is no longer infinite velocity. Maybe Warp 15 will be the ultimate speed limit, and Warp 13 in that scale will be the equivalent of warp 9.95 or something like that."

See Fig. 6.7 for an illustration of Bormanis's proposal (yellow). Here AGT Warp 13 corresponds to 5200c, which is about the same as TNG Warp 9.95 just as Bormanis reckoned.

The only thing really known about the AGT scale is that it permits warp factors higher than 10 that, as fans are well aware of, were not allowed in the TNG scale. The obvious real-world reason to switch to this new scale for this one episode was to emphasize that a lot has changed from 2370 to 2395 - just like the additional nacelle on the Enterprise or the new uniforms.

The in-universe explanation may be just as Bormanis suggested. At some point it would be tiresome for the crews of always faster ships to speak out warp factors in the TNG scale with always more decimal places. "Go to Warp 9.9996." and "Go to Warp 9.99996." are unhandy, and they look and sound so much alike to a human crew member that it is likely to become a source of confusion. If, however, the scale was only changed to decompress the warp factor range of high warp speeds for the sake of convenience, the question arises why it was compressed in the first place and if the move of the limit to to Warp 15 or something wouldn't just postpone the problem yet again.

Perhaps, rather than being a totally arbitrary recalibration along the lines of "We think Warp 10 is too low a limit, let's move it up to Warp 15", the new AGT scale reflects a change in the propulsion principle yet again. As already explained for the TNG scale in Section 6.3 , the highest possible warp factor may denote the deepest possible subspace layer boundary that the ship's warp field penetrates. If, in the year 2395, warp engines are generally modified in a way that they reach down to the the 13th layer, the AGT scale makes sense again. And if 14 subspace layers instead of previously 9 is a commonly accepted limit, the limit of the scale may be located at Warp 15 just as Bormanis suggested, only that the rationale would be different one.

Alternatively, we could imagine that the perhaps impractical warp factor limit was dropped altogether. In Fig. 6.7, the orange curve shows the TNG warp scale without the asymptotic behavior at Warp 10 (TNG scale) or at Warp 15 (AGT scale as suggested by Bormanis).

It is even possible that the warp factors up to Warp 10 are still exactly the same as in the TNG scale, denoting conventional operation of the warp drive, but that a completely new and independent AGT scale begins above Warp 10, denoting a new propulsion system such as transwarp or quantum slipstream drive. In this case, the new warp factors may as well have been named "Transwarp I, II, III, etc." Anyway, the two scales wouldn't be compatible, but we could imagine a transition from one scale to the other. The ship naturally wouldn't go up to Warp 10 with conventional warp drive, but may accelerate up to the break-even point at something like TNG Warp 9.5 and then activate the new propulsion system. After a short transition phase in which both engines (or both working principles of the same engine) are active, the ship may end up at AGT Warp 10, which is perhaps the equivalent to TNG Warp 9.6.

Power & Propulsion - about the right intermix ratio, warp inside a star system, how to stop a starship etc.

A Close Look at 22nd Century Technology - with considerations about the speed of Enterprise NX-01

Voyager Inconsistencies - with a rant about Tom's "Warp 10" flight

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Fleet Yards

Warp Speed Chart

The use of warp speed is commonplace in the 24th century, and is the major form of travel within the Federation. This chart identifies the relationship between Warp speeds and 20th century standard units of speed. With the discovery and deployment of the Warp XV project across the fleet after Project Capstone , a new warp factor chart was introduced.

Below is a Chart linking Warp Factor to energy and speed.

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Last modified: Friday, 27 August 2004 03:07 AM -0700 Maintained by: Joshua Bell , [email protected] Archive site (WWW): http://www.calormen.net/Star_Trek/ FTP site (text versions): ftp://ftp.cc.umanitoba.ca/startrek/minifaqs/

Copyright � 1994-2003, Joshua Bell. Not in the public domain. Permission to distribute this document, unedited and including this copyright notice is granted, provided no fees are charged for access beyond charges for downloading or connection time from a commercial information service. Publication of this document in a magazine or journal (in any media format) must be approved by the author.

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This FAQ does not discuss subspace or the mechanics of warp travel. See the Warp and Subspace FAQ for discussions of the how warp drive works, and what subspace actually is.

• TOS-era: The Original Series
• TNG-era: The Next Generation, Deep Space Nine, and Voyager
• AGT-era: "All Good Things..." (TNG final episode)
• VOY-era: Transwarp Frogs In Spaaaaaaace!
• Speed Limits
• Contributors

In all of the formulas in this FAQ, the following hold:

"Who the heck is Mike?"

Mike is Michael Okuda, a member of the Star Trek television production crew as a scenic artist and technical advisor. He designs the computer displays and alien writing seen in TNG, DS9 and VOY. He is also co-author of the TNG Technical Manual, which mentions that the the TNG Warp formula exists in a Excel spreadsheet on his Macintosh. Thus, when it comes to warp calculations, Mike is god. At the very least, a patron deity. He is also co-author of the Encyclopedia and Chronology.

"So who's Rick?"

Rick is Rick Sternbach, the "other" author of the TNG Technical Manual, and the main writer of the DS9 Technical Manual. He is also a member of the Star Trek television production crew, designing most of the ships and props seen in TNG and VOY.

1. TOS-era: The Original Series

The original series warp equation is generally accepted to be:

But this has never appeared in any episode. However, it has such wide acceptance that it has pretty much stuck. It's even in the Encyclopedia.

Boris S. writes:

The equation is almost certainly the work of TOS producers. Stephen Whitfield extensively researched the show in the period of 1967-68 and published the information in his book The Making of Star Trek (1968). He states that Warp 1 is the speed of light, Warp 3, 24 times the speed of light, Warp 6, 216c and Warp 8, 512c. With the exception of the value for Warp 3 (which should be 27c), the W^3*c formula holds. Whitfield almost certainly obtained the numbers from the TOS writer's guide which contained a small technical manual.

This chart compares TOS-era Warp speeds with the speed of light:

It is also generally accepted that the TOS scale was also used for the first few movies. Since speeds are rarely quoted in the movies, however, that's only speculation.

Joe Chiasson, describing Star Trek Maps , a map and manual combination by Bantam Books from 1980, offers:

The booklet contains quite a lot of written information on the development of warp drive systems and how warp travel is affected by matter density in a given area of space. The above formula was written as v = Wf^3 * c . This was further modified to include the Greek letter chi ( X ), which was a variable denoting the local density of matter, which changed depending on where you happened to be. So the proper formula for TOS level warp drive is v = c * Wf^3 * X where Wf was the warp factor, and c was the speed of light. Included was a table of corrected warp speed for a given average value of X . Wf Wf^3 X * Wf^3 Time per parsec hrs min sec 1 1 1,292.7238 22 05 29 2 8 10,341.7904 02 45 41 3 27 34,903.5426 00 49 05 4 64 82,734.3232 00 20 43 5 125 161,590.4750 00 10 36 6 216 279,228.3407 00 06 08 7 343 443,404.2634 00 03 52 8 512 661,874.5856 00 02 35 9 729 942,395.6502 00 01 49 10 1000 1,292,723.8    00 01 19

This correction factor does make a lot of sense, given that v = W ^ 3 by itself is almost ludicrously slow given the speeds quoted by TOS. Joe also suggests that by the time of TNG warp fields have been refined to the point that the chi factor is dropped from the formula. I think that the numbers are a little too high, however, when compared to TNG speeds.

As a side note, wf(n) = n * c appears in James Blish's TOS script adaptations, which have been widely read, so you may see that formula cropping up from time to time as well. Those speeds would be ridiculously slow, so that formula isn't really worth considering. (Thanks to Taki Kogoma for pointing that out.)

John "Eljay" Love-Jensen points out that in "By Any Other Name" [TOS] the Kelvans were using there technology to propel the Enterprise "to Andromeda, 300 years of travel". Andromeda is 2.3 million light-years away. For 300 years of travel, that translates into Warp 19.7! They probably intended to accelerate to that speed once they made it outside the galaxy, and the Enterprise didn't end up going that fast during the episode, but it means they thought it was possible for the ship to make it.

2. TNG-era: The Next Generation, Deep Space Nine, Voyager

By the time of Star Trek: The Next Generation, the warp scale has changed. Warp 1-9 are roughly the same, but Warp 10 is infinite speed. Going Warp 10 or faster is hogwash on the TNG scale. It isn't a speed barrier that can be or needs to be broken, but an energy barrier.

At least, that's what the Tech Manual says. Many fans disagree, saying that this has been contradicted on air, most clearly by the episode "Where No One Has Gone Before" [TNG] where someone says "We are passing Warp 10." See the Warp and Subspace FAQ for more discussion of this.

Here's the graph of warp vs. speed and warp vs. power consumption from the Technical Manual:

This chart was compiled with data from episodes, the Encyclopedia, and the TNG Technical Manual:

The Tech Manual (on page 111) says that a subspace radio signal travels at Warp 9.9997, and takes 45 minutes to reach 17 light years, which works out to 198696c.

As an interesting anomaly, Pete Carr also points out the following tidbit from the Tech Manual:

... the TM goes on to say that TNG Warp 9.7 is about 14.1 on the TOS scale. So [TNG Warp] 9.7 ~= 14.1^3 [c] and 14.1^3 [c] = 2803 [c]. I went and graphed the new value with our current values. Unfortunately the new value doesn't fit into the exponential curve ... it should be lower.

I suspect Mike made a rounding error; TOS Warp 14.1 is much closer to TNG Warp 9.8 by all of the accurate formulas that have been found or sheer reckoning off the graph.

Unlike TOS (where we have a formula but no scale), for TNG we have a scale but no formula! The reason for this is that the graph was drawn by Mike Okuda rather than calculated, as is related in the following:

On June 22, 1995, Jeff Reinecke forwarded the following letter from Michael Okuda to rec.arts.startrek.tech :

Date: Fri, Jan 27, 1995 02:09 AM EST From: MOkuda Subj: Re: Star Trek Warp To: Yar of Spit The warp factors we've used in ST:TNG were computed in an arbitrary way to fit some specific characteristics we needed. First, the speed for any given warp factor had to be greater than it was in the original Star Trek series. This was primarily to satisfy fan expectations. Second, the new warp speeds couldn't be TOO much faster, or it would be possible for the ship to cross the galaxy in a fairly brief time. (In a way, maintaining this restriction made Voyager's story situation possible. If we hadn't done this, Voyager could have gotten home too quickly.) We used an exponent of (I think) 3.33 or 3.33333... for warp factors less than 9. Between 9 and 10, I gradually increased the exponent so that it approached infinity as the warp factor approached 10. Lacking knowledge of calculus, I just drew what looked to me to be a credible curve on graph paper, then pulled the points from there. I think I re-created the curve fairly accurately in the Star Trek: The Next Generation Technical Manual . Hope this helps. -Mike

So it looks like there isn't a grand formula to end all formulas after all!

On May 29th, 1996, Dominic Berry wrote:

Since Mike calculated the speeds for the various warp factors up to 9 simply using the exponent 10/3, it is more sensible to use a piecewise function for the speeds that gives an exponent of 10/3 for W<9 and gives higher exponents for higher warp factors. My suggestion is n ( 10/3 + u(W-9) * A * (-ln(10-W)) ) v = W where u is the step function, i.e. u(x)=0 for x<0 and u(x)=1 for x>0 . Note that the term multiplying the step function is zero at W=9, so the step function introduces no discontinuity in the formula. If the value of n used is greater than 1, then both the function and its derivative are continuous at W=9. (In order to have continuous higher order derivatives a function like c(w) could be used.) [ Martin Shields amends that with: There is a better alternative to the step function as follows: / 0 ; x <= 0 | u(x) = < | \ e ^ ( -1 / (bx^2)) ; x > 0 Where b is a constant whose value remains to be determined. This function is "infinitely smooth" (that is, no matter how many times you differentiate it, the value of the differential is 0 at x=0 ). As b approaches infinity, the function approaches the pure step function.

I take A and n as

I then get the correct warp factors for W<9, and for the warp factors above 9 I get

[* Martin Shields offers A = 0.036528749373 and n = 1.79522947028 which are slightly better for some values. ]

My formula agrees with the values for warp factors of 9.2, 9.9, 9.99 and 9.9999 to within 0.6%, though it is about 6% out at 9.6 and it is way out at 9.9997. If you calculate the exponents for the data points at 9.9997 and 9.9999, however, you get 5.29826 and 5.30000, suggesting that the exponent 5.3 was used to calculate the speed at both of these warp factors. Since the exponent should be increasing with the warp factor, one of these data points should be ignored. Ignoring the data point for W=9.9997, my formula is perfect for W<9, and is slightly better than that of Tahk for W>9.

Now the exponent corresponding to the speed given for W=9.2 was about 3.33810. If we linearly extrapolate this to W=9.6 then the exponent should be about 3.34763. The exponent corresponding to the speed for W=9.6 is 3.34002, which is slightly less! This means that a formula for the exponent that gives values similar to the given values for warp factors of 9, 9.2 and 9.6 must have a derivative that decreases. (This means that the function for the exponent would have to curve downwards between 9.2 and 9.6.) Since this is not a desirable property if we want an exponent that gradually increases, I also left out the data point for W=9.6 in fitting the curve.

I mentioned before that the speeds for W=9.9997 and W=9.9999 seemed to have both been calculated using an exponent of 5.3. If you calculate the exponents corresponding to the other warp factors above 9, you get:

The speeds for warp factors of 9.6, 9.9 and 9.99 were obviously calculated using exponents of 3.34, 3.5 and 3.9 respectively, and the speed for a warp factor of 9.2 was probably calculated using an exponent of 3.338. Therefore it is not reasonable to ascribe any greater accuracy to the warp factors given than is implied by the number of significant digits in the exponents used to calculate them. By this criterion my formula gives speeds well within the uncertainty for warp factors of 9.9, 9.99 and 9.9999, although it gives an exponent of about 3.336 for W=9.2, which is a little low. Since the points were originally taken off a hand drawn curve, this is still reasonable accuracy.

I used to have a bunch of formulae in here from various posters who made some pretty good attempts at finding the Holy Grail of an accurate formula. However, due to length considerations I'm only going to keep the current best. Older formulae (basically an excised chunk of this FAQ) can be found at http://www.calormen.net/Star_Trek/FAQs/warp_formulae.html , but that page will probably never look too pretty.

Do any of these values actually match up with what we've seen on the show? There are often claims that these speeds are much to slow to allow the kind of adventuring that the Star Trek series portrays. But amazingly enough, when they do quote numbers and we can time things without cuts (wherein we may miss hours of ship-time), the numbers do match up:

Ges Seger offers:

The numbers I remember were about how far a ship doing warp 3 for 23 hours would travel, and the answer they came up with was 0.102 light-years. I worked the math just now and got 0.1022 light-years.

Riker calculated in his head the time required for the Enterprise to travel 300 billion kilometers at Warp 9, and gets 20 minutes:

Warp 9 = (300e12 m) / (20 min * 60s/min) ~= 2.5e11 m/s

From the chart: Warp 9 = 1516c ~= 4.548e11 m/s

The Enterprise jumped to Warp 7.3, and traveled 30 billion kilometers in a couple of minutes.

c/o Boris S.:

Wesley gives the ETA of the Enterprise to Lonka Pulsar as 34 minutes at Warp 7. When Picard orders Warp 2 instead, he comments that at that speed it would take 31 hours to get there. Using the first two data points, 34 minutes at Warp 7, I calculated a distance of 4.012e14 m. At Warp 2, it would take the Enterprise 37 hours to travel that distance. This clearly shows that the TNG production staff used the established warp scale when they calculated the travel time, and the 6-hour discrepancy can be explained by the use of a less accurate value for the speed of light.

the Enterprise is transported 0.54 parsecs by the Paxans. Riker says something like "nearly a day's travel in 30 seconds" (I cannot give you the exact quote since I am watching TNG on German TV). At Warp 6 (Enterprise cruising speed), the Enterprise would need 1.6 days to travel that distance. Given that Riker calculated the travel time without a computer in a couple of seconds, you can allow for the deviation. On the other hand, if you calculate the travel time at Warp 7, you get 23.5 hours, which fits the quote.

Kim states the ships speed as 2 billion km/s, which is 2*10^12 m/s, which is roughly 6667c. This is in the same ballpark as what Warp 9.975 (Voyager's top cruise speed), it turns out.

B'Elanna gives the distance to Rakosan system as more than 10 light-years. A day or so later Chakotay states that the vessel has resumed its journey at Warp 9 and will reach Rakosan V in 51 hours, which works out to a distance of 8.8 light-years.

Counter Evidence

There have been several times where the warp velocities proposed don't match what we see on-screen. The most blatant example of this kind is a call by the captain to head somewhere at Warp 1, or some other ridiculously slow speed. This happened several times in TOS, but does crop up from time to time. Here are some examples:

Roger M. Wilcox offers:

The Enterprise-D gets sucked into a black nebulous void. Before Nagilum announces his/her/its presence to our intrepid crew, they find an opening in the void "1.3 parsecs away". (1.3 parsecs would be 4.243 light-years.) Picard orders the crew to head for the opening at Warp 2.

It may be best to just pretend that these didn't happen, or rationalize them on a case by case basis (going Warp 1 until outside of the solar system, then switching to a higher speed "off camera").

A bigger problem which crops up on rec.arts.startrek.tech is the size of the Federation. Sizes of up to 10,000 LY across have been quoted as diameters, and this corresponds to the occasional graphic displayed on screen showing the Federation's size and position within the galaxy. Other evidence points to a somewhat smaller size, but such questions as the distance from Earth to Bajor appear to present a paradox: some routes between Federation locations which are known to be far apart are traveled much more quickly than the TNG formula appears to allow.

The leading speculation on the newsgroup is a concept called "Warp Highways". Distinct from wormholes, these "highways" represent either natural (pre-existing) or artificial (thanks to heavy traffic) pathways where warp travel is much faster than the TNG formula, which represents a baseline.

The highways do not require additional technology beyond warp drive. Highways are not easily detectable in unknown space. This means that an exploration ship, such as the Enterprise, or a ship in unknown territory, such as Voyager, will travel between two arbitrary points at the nominal velocities presented in the TNG formula. A well-known region of space - such as the route from Bajor to Earth - would probably contain several well-known warp highways and allow less powerful ships to make the route in weeks rather than years, and top-of-the-line Starfleet ships to make the trip in mere days. Contact with local civilizations would allow Voyager to take shortcuts through the Delta Quadrant - which they frequently seem to.

Perhaps the Hekaras Corridor in "Force of Nature" [TNG] is one such route, explaining the frequent travel in that area. The whole notion of starship travel affecting local subspace properties in a permanent way supports the notion that at least some warp highways are created by frequent warp travel - that is, as a route is used it becomes more efficient. Other speculation includes the notion that gaseous anomalies are indicators of the presence of warp travel. Why else would Excelsior - one of Starfleet's latest ships - be engaged in charting such anomalies in Star Trek IV ?

This is strongly reminiscent of the X (chi) factor first presented in Star Trek Maps , where the warp equation varies with local spatial conditions.

(Other speculation or comments?)

Why did it change?

• In terms of a real-world "Star Trek is just a TV show" reason, Gene Roddenberry himself put Warp 10 at infinite speed, according to the TNG Tech Manual. To keep the scale fluid, Mike and Rick made it asymptotic at Warp 10, while starting off similar to the TOS scale.

Looking at the graph, you can see that the energy costs for cruising at integral Warp values are much lower than for non-integral Warp factors. The first explorers to travel past Warp 1 must have realized this. Since for Warp values in the 1-3 range follow the v = (W ^ 3) * c formula, it makes sense that a scale based on the formula would come into use.

When ships started cruising at Warp values larger than 5, the difference between what v = (W ^ 3) * c predicted to be the most energy efficient speeds and what actually were must have become noticeable. It may have taken a long time for a new, accurate scale based on new observations came into use. (Look at the USA and SI, for an example of a large sociopolitical body taking a long time to adopt a more useful, universally used scale.)

3. AGT-era: "All Good Things..." (TNG final episode)

Quoted in the final episode of Star Trek: The Next Generation, in a possible or imaginary future, is the speed Warp 13. Both Admiral Riker and Captain Beverly Picard call for this speed, and at another point in the episode, Admiral Riker calls for "maximum warp", which is either Warp 13 or greater.

While we haven't a clue how fast this is, they're presumably faster than Warp 9 on the TNG scale, and necessarily slower than Warp 10 on the TNG scale (since TNG Warp 10 is infinite speed). A few possibilities present themselves:

• Just another technical muck-up. (But that won't stop this intrepid FAQ maintainer!)
• Warp 10-13+ are shorthand for Warp 9.x. One possibility is that 9.90 is called Warp 10, 9.91 is called Warp 11, etc.
• New warp technologies provide at least 13 power usage minima between c and infinite speed, instead of the 9 possible with old warp technologies.
• Further research revealed that there were more than 9 minima accessible with traditional drives, and that they simply required more power to attain than had been previously attempted, but less power to maintain than 9.x values.
• The Federation switched back to the TOS scale.

The last one is demonstrably incorrect (see below). Among the others, there's no way to tell which is correct. Sharp-eyed Boris S. found the following explanation by Andre Bormanis, Star Trek's science advisor:

I raised that question in a TECH note. Basically, the idea there was that they recalibrated the warp scale. I don't think that ended up in the final draft teleplay, but the idea there was that if you've got ships that can routinely travel at speeds in excess of Warp 9, then maybe it makes sense to recalibrate your speed scale so that Warp 10 is no longer infinite velocity. Maybe Warp 15 will be the ultimate speed limit, and Warp 13 in that scale will be the equivalent of warp 9.95 or something like that. OMNI , October 1995.

Tom Bagwell writes:

I timed the interval in AGT between when Data reported the second Klingon ship to be disengaging and when Riker's helmsman reported it to be a "half a light year away" at about 22 seconds, so I calculated the speed assuming 20 seconds to reach 1/2 a light year and assuming 30 seconds to reach 1/2 a light year. At 30 seconds, the velocity would be approximately 525,960c which equates to roughly Warp 9.97244 on the TNG scale and approx. Warp 81 on the TOS scale. At 20 seconds, the velocity would be approximately 788,940c which equates to roughly Warp 9.97535 on the TNG scale and approx. Warp 92.4 on the TOS scale.

Martin Shields updates that with:

Assuming 30 seconds to travel 1/2 a light year, v = 525,960c which he estimates is Warp 9.97244 on the TNG scale. However, the Tech Manual and Encyclopedia tell us that Warp 9.9999 (a higher warp factor) is set at 199,516c (less than half the speed calculated). This figure comes from the M = -11/3 equation. My equation gives the TNG warp factor of 9.999974 (approx.) which better fits the known data.

If a damaged AGT-era Klingon ship can limp home at TOS Warp 81, while a Federation ship trying to be sneaky can only manage TOS Warp 13, the Klingons have nothing to worry about. I consider this adequate evidence that the TOS scale was not returned to use in the AGT future.

4. VOY-era: Transwarp Frogs In Spaaaaaace!

As you may have guessed, the .tech community was less than impressed with "Threshold" [VOY] in which Voyager - a ship running low on supplies, with half its crew dead, stranded away from repair or research facilities, on the other side of the Galaxy from the Federation - manages to upgrade one of its never-ending supply of shuttles to make a Transwarp flight, something that has defied the best minds in the Federation for a century. Things go higglety-pigglety after that, and many people (including some of the production crew) just pretend it didn't happen.

Forgiving that, however, the episode's technobabble isn't too bad. The Voyager crew mention how Warp 10 = Infinite Speed = being everywhere at once. An interesting tidbit is that once Transwarp drive is active, the shuttle's speed registers at Warp 10.

5. Speed limits

"What's this about a Warp 10 barrier?"

In the TNG scale, Warp 10 is infinite speed. As you approach a position on the graph corresponding to Warp 10, your power requirements increase astronomically compared to your increase in speed. But you can keep speeding up forever, unlike the light barrier, which keeps you from getting to the speed of light.

In other words, keep piling on the 9s. Warp 9.99 is a lot faster than Warp 9.9, while Warp 3.99 is only marginally faster than Warp 3.9. The barrier is only one of energy, not velocity.

Once again, in case you missed it, TNG Warp 10 is not a speed barrier; it cannot be broken like the sound barrier. Any warp factor greater than 10 must be on a different scale than the TNG scale (either TOS or AGT or something else), since a speed faster than infinite speed is nonsensical.

"But in "Is There in Truth no Beauty?" [TOS] and "That Which Survives" [TOS], the old Enterprise went over Warp 14!"

Yes, but that's on the old scale. By the new scale, that translates to about Warp 9.7 (TM), which the Enterprise-D can do for brief periods. The original Enterprise was being shaken apart. Voyager can cruise at that speed without blinking.

"But in "Where No One Has Gone Before" [TNG] they went past Warp 10!"

Chalk this one up to instrument failure. While Geordi did say they'd passed Warp 10, later in the episode they were booting along at some outrageously huge speed, while the instruments only read Warp 1.5. So there's canonical evidence that the Traveler's tweaking of the warp drive and the Enterprise's speedometer don't get along well.

Daryle Walker points out that the real-world explanation for this is probably that the Warp 10 rule hadn't been established yet - this was an early first-season episode.

"This new Warp 5 speed limit - what's up with that?"

In "Force of Nature" [TNG] it is discovered that in the Hekaras Corridor, a region of space where warp travel is hindered except for a narrow path the intense use of warp drives in an already sensitive area can (over time) cause subspace rifts to form, where subspace manifests itself in real space on a macroscopic scale. This is not a good thing.

"Does this take effect everywhere?"

Yes. In "The Pegasus" [TNG] an Admiral Pressman gives Picard permission to travel faster than Warp 5 for the duration of the mission. Ditto in "Eye of the Beholder" [TNG] , when Picard is given permission to exceed the speed limit to delivery needed medical supplies. The Encyclopedia concurs as well, naming Warp 5 as the new cruising speed for starships. Overkill? Probably. Typical bureaucratic overcompensation? Yep.

"So what about in "All Good Things..." [TNG] and post-TNG shows?"

It's safe to say that the U.S.S. Pasteur and U.S.S. Enterprise, cruising at Warp 13, were able to ignore the Warp 5 limitation enforced by Starfleet. While the limitation was mentioned in a few later TNG episodes, it was ignored in DS9 and VOY episodes set only a few years later. There are a few possible explanations. The first is that Starfleet simply repealed the ruling, and is allowing ships to muck up subspace. That isn't what we'd expect in the eco-friendly Star Trek Universe, however.

Another is that changes to warp technology allow warp travel without the nasty side effects. Rumors abound that Voyager's folding nacelles and/or warp core design mitigate the effect, although Rick Sternbach (the designer of Voyager) isn't so sure. The most probable explanation is that internal technological changes allow warp drive without damaging subspace.

Franz Joseph's "Field Restoration" nacelle end-cap, anyone? ( Star Fleet Technical Manual )

6. Q & A

"What causes fractional warp speeds?"

As you can see from the above chart, travelling at integral Warp factors is much more energy efficient. But there are times when a fractional value must be used - for example, staying a certain distance from another ship, or keeping pace with some phenomenon. Also, beyond Warp 9, only fractional speeds are possible. (Modulo "All Good Things..." [TNG] , of course.)

"Why not use impulse drive within the warp field to create a higher velocity?"

There's no reason to think that a Newtonian drive (Impulse) would augment a non-Newtonian drive (warp). Also, consider that the maximum velocity attainable with a Newtonian drive is c. At Warp 2, which is ~= 10c, this gives you a whole 11c at maximum (overloading, fuel wasting) impulse. Warp 2.1 is about 12c anyway, so overloading the impulse drive doesn't get you much.

"What about "The Corbomite Maneuver" [TOS] or The Voyage Home ?"

Kirk and Sulu use a combination of warp drive and Impulse to break free of the First Federation pilot craft. The combination of a tractor beam, impulse drive, and warp drive would be very strange, and many explanations come to mind, such as the warp field causing the tractor effect to "slip" away, while the impulse provides propulsion, or the impulse fighting the tractor beam inertially while the warp drive provides propulsion, etc.

In The Voyage Home , for the trip back to the future, thrusters are used by Spock to get the last burst of speed just before entering time warp. Also, during both trips, the ship is brought out of time warp by braking thrusters. The H.M.S. Bounty is visibly moving slower than the speed of light toward the sun and certainly slower than the Warp 8 quoted by Sulu, so the time warp slingshot (in an intense gravity well) may be one case where Impulse drives are useful to augment warp drives.

"Whoah! Hold on! They must be moving faster - look at the stars that shoot past while they're in warp!"

Joseph Haller offers:

The most extreme ship induced speed discussed ... is W(ST:TNG) = 9.97535, or 788,940c. This would give a characteristic angular speed for nearby stars of 1578 arc-seconds per second or 1 degree every 2.3 seconds. This is indeed verified in the simulations. Travel at high warp speeds, on the ST:TNG warp scale, does not match very well the appearance of the bridge view screen on a typical episode. Indeed, most visible stars are not nearby but are further away with correspondingly lower angular speeds. I offer no solutions to this discrepancy other than the dramatic necessity that stars go whooshing by at high warp speed.

Or should we give up so easily?

There's a lot of support on rec.arts.startrek.tech for the notion that those things aren't really stars. For one, as the Enterprise drops out of warp (with the camera tagging along for the ride) some of the "stars" do some pretty strange things, such as suddenly angling off in various directions, disappearing, etc.

Also, in Star Trek: First Contact , the Phoenix barely breaks Warp 1 and stays relatively close to Earth, but we still see the streaks. Definitely not stars.

The predominant theory is that what we're seeing are free particles in space interacting with the expanding boundaries of the warp field. As they cross the warp field, they are repeatedly accelerated to FTL velocities and then slowed to STL speeds, and start spewing out something like Cerenkov radiation, a (real!) bluish light emitted when particles moving faster than the local speed of light (in a dense medium) are forced to slow down. If not exactly Cerenkov radiation, then something similar.

Jon Mitchell tells me that in the TNG video game for the Sega Genesis console platform states the streaks are part of the visual manifestation of Einsteinian space in subspace. So people other than us .techers have noticed this problem too.

As a side note, in "The Cage" [TOS], the moving particles seen through the forward view-screen are explicitly identified as meteoroids.

7. Contributors:

8. glossary:, 9. references:.

See the Reading List FAQ for more details on the reference volumes mentioned above and below.

The question of "what is canon" has been argued for years in the Star Trek newsgroup hierarchy. In the realm of technical discussions, this can be refined to the question of "what evidence is factual, and what is apocryphal". These FAQs follow the currently dominant notion that "canon" is aired live-action material and nothing more, with the caveat that materials produced off-camera by the production crew are often (but not always) reliable predictors of the direction future canonical material will follow, and are therefore granted a special "quasi-canonical" status. Any other material falls into the realm of speculation - it may be perfectly well grounded speculation useful for building up technical arguments, or wild flights of fancy that have no rational basis.

In addition, more recently presented information is considered to supercede old information, unless the weight of the evidence supports the original data. While this may seem highly biased and may be eyed with some skepticism as a form of Orwellian "newthink", it is a more useful predictor of what those directly responsible for the creation of the series are likely to include as canonical material in the future.

For example, the excellent and groundbreaking Star Fleet Technical Manual , by Franz Joseph created in the 1970's was a very well thought out look at the technical world of Starfleet just slightly beyond what was seen in the original series. Unfortunately, and perhaps for purely arbitrary reasons, the future development of "canon" Star Trek diverged from this speculation. This in no way implies that there was anything wrong with that volume or any others, merely that due to later "evidence", it can no longer be regarded as an authoritative overview of Trek technology. On the other hand, the author performed a lot of research to create it, and therefore its speculation should not be dismissed out of hand.

That said, we are dealing with a universe in the process of being created by scores of (usually) non-technical people, aiming to provide weekly entertainment for a mass audience. There are many inconsistencies even amid the canonical material, and often times the wildest speculation on the newsgroup makes more sense than what we see in the episodes.

Canonical material:

• Star Trek: Voyager [VOY]
• Star Trek: Deep Space Nine [DS9]
• Star Trek: The Next Generation [TNG]
• Star Trek feature films
• Classic Star Trek [TOS]

Quasi-canonical material:

• The Star Trek Encyclopedia: A Reference Guide to the Future
• Star Trek Chronology: The History of the Future
• Star Trek: The Next Generation Technical Manual
• Star Trek: Deep Space Nine Technical Manual
• The Making of Star Trek
• Newsgroup postings
• Convention presentations
• Email conversations

Highly regarded, but non-canonical material:

• Star Trek: The Animated Series [TAS]
• Mr. Scott's Guide to the Enterprise
• Star Fleet Technical Manual
• Starlog's Star Trek: The Next Generation Technical Journal
• Other "reference" guides
• Novels, incl. novelizations of films and episodes
• Blueprints, drawings, photographs, models, etc.

Joshua Bell, [email protected]

“Helm, Warp One, Engage!” Calculating Warp Speed Factors

Wolfram|Alpha’s goal is to cover all things computational, from mathematics and the sciences to movies and sports. But the set of all things computable encompasses areas outside of the real world as well. With the 25th anniversary of Star Trek: The Next Generation coming up, we can now compute the relationship between warp factors and the speed of light.

Warp factors describe the speed for a spaceship, such as the Starship Enterprise , traveling faster than the speed of light within the Star Trek universe. In the real world, even approaching the speed of light is outside of our current capabilities. To get the sense of energies involved, we can start with the mass of the space shuttle . This comparatively small spaceship turns out to weigh about 81,000 kilograms. The kinetic energy of 81,000 kilograms at 0.99999c is 1.621*10^24 joules . This in turn is about 42 times the world’s estimated fossil fuel reserves as of 2003. So, for now, even fast subluminal velocities are outside of our reach.

But in Star Trek , faster than light travel is a well developed technology. However, exact conversion of warp factor into multiples of the speed of light is somewhat complicated by the fact that the writers often neglected the established formulas in their scripts and that there are two versions of the formula used over the course of the various Star Trek series. The first formula was introduced in the original series’ writer’s guide by Gene Roddenberry, and was used for the original series. This the default formula used by Wolfram|Alpha when asked about warp factors such as warp factor 3 .

An interesting aspect of this formula is that unlike in the latter series, there is no restriction against warp factors above 10 in the original series, a fact that came up in several episodes. If we ask about 200,000c in warp factors , we see that this would be equivalent to a warp factor of over 58 in the original series.

In Star Trek: The Next Generation and series that followed it, a limit was placed on the maximum warp factor possible (even if the writers again often ignored this restriction). In this revised warp factor framework, we have a new formula that covers warp factors up to 9. Thus we can ask about Warp Factor 7 in Deep Space 9 or Voyager at Warp Factor 5 .

Above warp 9, speed is supposed to increase exponentially to infinity as one approaches warp 10. There was never a hard formula given for this, but we have tried to approximate it by interpolating over the data extracted from the hand-drawn curve used by the production team for The Next Generation series. So we can still give an approximate answer to the question of warp factor 9.5 in Next Generation .

A log plot of the interpolated data shows the speed rapidly heading to infinity as one approaches warp factor 10.

Reverse queries are also possible with this model. We might ask what warp factor is needed to cross the Milky Way. The diameter of the Milky Way is about 100,000 light years, which is similar to the distance the characters in the series Star Trek: Voyager needed to cross to return home. In that series it was estimated that it would take them 75 years to complete by normal means. That works out to an average speed of 100,000 light years / 75 years or 1334c. 1334c in warp factors for Voyager works out to be warp factor 8.661.

We hope that you enjoy using this formula and discovering the speeds that James Tiberius Kirk or Jean-Luc Picard traveled at while boldly going where no man had gone before .

Would be interesting to see the relative time calculation. So how long it ‘appears’ to take the Enterprise to travel these distances from a viewer on Earth 🙂

A nice present for the Trekkie fans. So to get to Alpha Centauri in one day , using Voyager’s warp factors, I would need a warp factor of around 9.14 . This is so cool.

@Jim I’m pretty sure relativity doesn’t apply in subspace.

Two problems I have with this function: 1. It tops out at Warp 9.999. Any faster and it falls back to 2154 c. (Warp 9.998 is 30578 c.) 2. It’s “off” compared to other calculators. For Warp 9.999, the calculator I use[1] gets 10267 c. Wolfram|Alpha gives 48839 c.

[1] http://blog.shields-online.net/?page_id=65 << Martin Shields is one of the guys who /really/ tried to determine the WF formula as seen here: http://www.calormen.com/Star_Trek/FAQs/warp_velocities-faq.htm

Voyager had a path of 75000ly.

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Warp Factor

From star trek: theurgy wiki.

Warp factor was the primary means of measuring speeds attained using warp drive. An alternative term time- warp factor was also used. The term was often shortened to warp when followed by its value, so that saying "warp six" is the same as saying " warp factor six." Faster-than-light travel began after warp one, whereas lower fractional values were sometimes used to measure sublight speeds. Spacecraft ordinarily traveled at a higher integer warp factor .

By the 24th century, infinite velocity was designated as warp factor ten. It was considered to be unattainable by conventional means. Because of this, extremely high warp factors were indicated with decimal values between nine and ten, such as warp 9.975.

Source: Memory Alpha & Star Trek: Adventures Core Rulebook

• Starfleet Information
• General Information

Star Trek : Warp (2380)

This page provides a chart with warp factor, speed, power requirements, etc.

In 2380, a team of Federation scientists and engineers (including Commander LaForge and Lieutenant Crusher) developed revolutionary new warp field configurations, calculations, and technology which have redefined Warp travel and necessitated a new warp scale.

Behind the Scenes

The new scale is a more standard exponential equation with no theoretical limit, each warp factor being several times faster than the previous factor.

The standard warp scale seen in TNG, DS9, and VOY for the purposes of travel in RPGs is rediculously slow when compared to the size of the Federation. The Federation at it's greatest diameter is between 8,000 ly and 10,000 ly. If we were to assume a crusing speed of warp 8, it would take a ship a little less than 8 years to traverse federation space.

In "All Good Things" we saw Federation ships using an alternative warp scale, so there is prescedent.

Using this new scale, a cruising warp factor of 8 would take a starship about two years to travers the federation. In addition to the warp factor and relative speed, I've included the power requirements for use with the Star Trek Adventures RPG. Speeds with a power requirement of 0 are considered cruising speeds, do not cost additional energy to sustain, and do not generate significant wear-and-tear on the warp engines. According to Memory Alpha the time a ship could maintain maximum warp varied from days to months ( Source ).

In the Star Trek Adventures RPG, have the crew/ship perform skill checks probably (Engines + Engineering). Each sucess "buys" a challenge die. (May need to take into account ship / crew talents to augment this roll). Roll challenge dice equal to the number of sucesses. The rolled challenge dice score is the number days the ship may maintain maximus warp. Each effect counts as a month.

• explore Travel Time Calculator Distance (Light Years) Warp Factor Travel Time: Power Requirement: Calculate
• border_all Table Engines Score Calculate

Warp Velocities Mini-FAQ

1. tos-era: the original series.

I'm reasonably confident that this first appeared in the old Star Fleet Technical Manual by Franz Joseph and was quickly adopted by fandom. (Note that in some of James Blish's episode transcriptions, he had WF n = n*c.)

The booklet contains quite a lot of written information on the development of warp drive systems and how warp travel is affected by matter density in a given area of space. The above formula was written as v = Wf^3 * c. This was further modified to include the greek letter chi(X), which was a variable denoting the local density of matter, which changed depending on where you happened to be. So the proper formula for TOS level warp drive is X * Wf^3 * c = v where Wf was the warp factor, and c was the speed of light. Inclued was a table of corrected warp speed for a given average value of X. Wf Wf^3 X * Wf^3 Time per parsec hrs min sec 1 1 1,292.7238 22 05 29 2 8 10,341.7904 02 45 41 3 27 34,903.5426 00 49 05 4 64 82,734.3232 00 20 43 5 125 161,590.4750 00 10 36 6 216 279,228.3407 00 06 08 7 343 443,404.2634 00 03 52 8 512 661,874.5856 00 02 35 9 729 942,395.6502 00 01 49 10 1000 1,292,723.8 00 01 19

2. TNG-era: The Next Generation, Deep Space Nine, Voyager

... the TM goes on to say that TNG Warp 9.7 is about 14.1 on the TOS scale. So 9.7 ~= 14.1^3 and 14.1^3=2803. I went and graphed the new value with our current values. Unfortunately the new value doesn't fit into the exponential curve... ...the value doesn't quite fit; it should be lower. I entered 9.7 into some of the better warp formulas. Here are the results: M = -11/3 --> 2029 M = -1.502 --> 1953 My Formula --> 1947 I graphed each value, and found that the 2029 value was the best fit. This makes sense, since the same formula was out by 1 for the value of 9.6 and the other 2 were off by 70.

Date: Fri, Jan 27, 1995 02:09 AM EST From: MOkuda Subj: Re: Star Trek Warp To: Yar of Spit The warp factors we've used in ST:TNG were computed in an arbitrary way to fit some specific characteristics we needed. First, the speed for any given warp factor had to be greater than it was in the original Star Trek series. This was primarily to satisfy fan expectations. Second, the new warp speeds couldn't be TOO much faster, or it would be possible for the ship to cross the galaxy in a fairly brief time. (In a way, maintaining this restriction made Voyager's story situation possible. If we hadn't done this, Voyager could have gotten home too quickly.) We used an exponent of (I think) 3.33 or 3.33333... for warp factors less than 9. Between 9 and 10, I gradually increased the exponent so that it approached infinity as the warp factor approached 10. Lacking knowledge of calculus, I just drew what looked to me to be a credible curve on graph paper, then pulled the points from there. I think I re-created the curve fairly accurately in the Star Trek: The Next Generation Technical Manual . Hope this helps. -Mike

Is this it?

The numbers I remember were about how far a ship doing warp 3 for 23 hours would travel, and the answer they came up with was 0.102 light-years. I worked the math just now and got 0.1022 light-years.

Why did it change?

3. agt-era: "all good things..." (tng final episode).

I timed the interval in AGT between when Data reported the second Klingon ship to be disengaging and when Riker's helmsman reported it to be a "half a light year away" at about 22 seconds, so I calculated the speed assuming 20 seconds to reach 1/2 a light year and assuming 30 seconds to reach 1/2 a light year. At 30 seconds, the velocity would be approximately 525,960c which equates to roughly Warp 9.97244 on the TNG scale and approx. Warp 81 on the TOS scale. At 20 seconds, the velocity would be approximately 788,940c which equates to roughly Warp 9.97535 on the TNG scale and approx. Warp 92.4 on the TOS scale.

Assuming 30 seconds to travel 1/2 a light year, v = 525,960c which he estimates is Warp 9.97244 on the TNG scale. However, the Tech Manual and Encyclopedia tell us that Warp 9.9999 (a higher warp factor) is set at 199,516c (less than half the speed calculated). This figure comes from the M = -11/3 equation. My equation gives the TNG warp factor of 9.999974 (approx.) which better fits the known data.

4. Speed limits

5. q & a.

The most extreme ship induced speed discussed ... is W(ST:TNG) = 9.97535, or 788,940c. This would give a characteristic angular speed for nearby stars of 1578 arcseconds per second or 1 degree every 2.3 seconds. This is indeed verified in the simulations. Travel at high warp speeds, on the ST:TNG warp scale, does not match very well the appearance of the bridge view screen on a typical episode. Indeed, most visible stars are not nearby but are further away with correspondingly lower angular speeds. I offer no solutions to this discrepancy other than the dramatic necessity that stars go wooshing by at high warp speed.

6. Contributors:

7. glossary:, 8. references:.

Star Trek: How Fast Is Warp Speed Exactly?

"Star Trek" fans are well accustomed to hearing Starfleet captains give the order to travel at maximum warp, but what, exactly, does that mean? The intergalactic storytelling in the "Star Trek" franchise is enabled by the futuristic invention of faster-than-light travel, with starships able to cross impossibly vast distances of space in the time it takes for a commercial break. But for fans who've wondered how fast warp speed actually is, things start out relatively (pun intended) simple. The way warp works is the complex part.

Basic warp speed, also referred to as warp 1, is exactly the speed of light. That's approximately 300,000 kilometers per second. Anything below that speed is described on board a Starfleet vessel as a fractional. But the scale isn't linear, which makes things tricker to calculate at any speed other than a flat warp 1. The best scale to use is the one from "Star Trek: The Next Generation," by which point there was an actual mathematical formula in use to calculate warp speeds. By that scale, a warp factor of 0.5 is only about one-tenth the speed of light, while warp 5 is 213.7 times faster than light.

As seen in many "Star Trek" episodes, the laws of space-time start to break down entirely once warp 10 is reached . Warp 10 gets defined as infinite speed, which means anything traveling at it would occupy all points in space at the same time. Even in science fiction, there must be a limit somewhere.

The science of Star Trek's warp speed

Faster-than-light travel isn't possible with current technology, and may not be possible at all. The speed of light, 300,000 kilometers per second, is thought to function as a sort of "cosmic speed limit." Nothing with mass can travel at that speed or faster, with light being the exception since it has no weight. As Einstein proved, this simple rule holds the fabric of space and time together. So how does the warp drive in "Star Trek" circumvent this apparent law of nature?

As astrophysicist Erin MacDonald explained on the Star Trek YouTube channel , "Just because nothing can travel faster than the speed of light on the surface of space-time, nothing says that space-time itself can't go faster than the speed of light." But how does a warp engine use that loophole in the laws of physics to accomplish FTL travel? By generating a field of energy that warps the space-time around a starship. Said MacDonald, "The idea with warp drive is that you build a bubble of space-time around your ship and then that propels you faster than the speed of light." These bubbles are called warp fields.

This is also how different warp factors can be achieved. A single warp field causes a starship to travel at warp 1, but adding an additional bubble around the first causes even more acceleration — warp 2, 3, and so on. "Eventually, you get to the point where you wrap all of space and time around your ship, and that, you can think of as warp factor 10," MacDonald said.

The history of Star Trek's warp drive

The invention of warp technology is well-documented in "Star Trek" lore. In the franchise's fictional history, Earth went through a dark period between the late 1900s and mid-21st century. First, the Eugenics Wars ravaged the planet, though its dates have been retconned. Next, starting in the early to mid-2020s, World War III broke out following a period of economic collapse. We see the beginnings of this during "Star Trek: Picard" Season 2. But in the post-atomic wastelands of the period that followed, a scientist named Zefram Cochrane managed to engineer the first warp-capable ship.

The movie "Star Trek: First Contact" tells the story of what happened next. Visited by Captain Picard (Patrick Stewart) and the crew of the Enterprise after they travel through a temporal vortex created by the Borg, Cochrane finishes his work on the warp drive. On April 5, 2063, he takes it on a maiden voyage. This triggers the attention of nearby Vulcans, who, realizing a new species has become interplanetary, visit Earth to introduce themselves to humanity.

In the "Star Trek" universe, April 5 is celebrated across the Federation as First Contact Day, and many fans join in on the fun in real life by honoring the holiday. More than a time to celebrate "Star Trek," it's a day to celebrate what the franchise represents: the hope for a future where humanity warps past our petty quarrels to unite with a shared sense of curiosity and exploration.

Maximum warp

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Maximum warp (shortened from maximum warp speed and also known as top warp speed , maximum speed , high warp speed , emergency speed ) was the maximum warp factor velocity a starship was designed for and a term whereby a bridge officer could ask the flight control officer to accelerate the ship to its highest possible velocity.

The maximum warp velocity and the time it could be maintained by a starship varied between classes. This was due to energy output limitations of the warp core and limitations of other systems, such as the warp coils , the structural integrity field , and the amount of energy the propulsion system could handle without overloading . ( ENT : " In a Mirror, Darkly "; DS9 : " The Sound of Her Voice "; TOS : " The Changeling ")

In the early days of warp drive development, the top speed capabilities took massive leaps in the mid- 22nd century after the warp 2 barrier was broken. ( ENT : " First Flight ") The invention of the warp three engine allowed early Earth starships to travel ten times faster, ( ENT : " Fortunate Son ") while ships installed with the warp five engine could travel a hundred times faster. ( ENT : " Broken Bow ") The increase in capabilities slowed down later on, as the Starfleet ships of the 2370s were only twice as fast as the ships used in the 2290s . ( VOY : " Flashback ")

Though originally rated for warp 5, by 2154 the installation of new warp injectors allowed the Enterprise NX-01 to push to warp 5.06. ( ENT : " Babel One ")

In 2268 on stardate 4843.6, it was imperative for the USS Enterprise to proceed at maximum warp speed for a period which exceeded the recommended safety margin in order to intercept an asteroid headed on a collision course with the planet Amerind . Chief Engineer Montgomery Scott noted that they couldn't maintain warp 9 for much longer as the engines began to show signs of stress . ( TOS : " The Paradise Syndrome ")

Galaxy -class ships, such as the USS Enterprise -D , could theoretically achieve warp 9.8, but the maximum warp speeds above 9.6 could be maintained for a few hours only. ( TNG : " Encounter at Farpoint ", " The Best of Both Worlds ") Intrepid -class ships such the USS Voyager , on the other hand, could maintain it from three days up to two months. ( VOY : " Workforce ", " Workforce, Part II ", " Friendship One ")

In 2370 , the Federation imposed a maximum speed limit of Warp 5 on all vessels (except for emergencies) due to concerns over high warp factors causing damage to subspace. ( TNG : " Force of Nature ", " The Pegasus ", " Eye of the Beholder ") This limit would appear to have been temporary.

The Klaestron starship that visited Deep Space 9 in 2369 was said to have a high warp capability, and was able to achieve warp 5 or better. ( DS9 : " Dax ")

The USS Carolina traveled 0.7 light years in two hours when at maximum warp. ( VOY : " Inside Man ")

Even though the Nova -class was designed to travel at a maximum speed of warp factor 8, when the USS Equinox powered its warp drive with energy derived from the corpses of nucleogenic lifeforms , an increase of 0.03% was added to the warp factor, allowing the velocity of traveling ten thousand light years in less than two weeks. ( VOY : " Equinox ")

During its time in the Delta Quadrant , the USS Voyager encountered technologies that enabled it to travel great distances at massively greater speeds than its rated maximum warp velocity, including the quantum slipstream drive , transwarp coil and Tash's catapult . The vessel had arrived in the Delta Quadrant from the Alpha Quadrant , approximately 75,000 light years, via the Caretaker's array . ( VOY : " Hope and Fear ", " Dark Frontier ", " The Voyager Conspiracy ", " Caretaker ")

• 1 Maximum warp limitations by class
• 2.1 Maximum warp requests
• 2.2 Background information
• 4 External link

Maximum warp limitations by class [ ]

• Warp 1.4 † – Arctic One -type
• Warp 1.8 † – Y-class
• Warp 2 † – Neptune -class , J-class
• Warp 3.2 – Defiant -class , USS Valiant had suffered combat damage
• Warp 4 – Whorfin -class † , type 9 shuttlecraft
• Warp 5 – Danube -class
• Warp 5.2 † – NX-class
• Warp 6 † – D5-class , Class III neutronic fuel carrier
• Warp 6 – D'deridex -class , maximum speed that can be used where the use of the Cloaking device is not detected
• Warp 6.5 † – Suurok -class ( Ti'Mur )
• Warp 7 † – Suurok -class ( Sh'Raan ) , Coridan ship
• Warp 8 † – Constitution -class
• Warp 8 – Nova -class
• Warp 8.7 – Baran's mercenary ship
• Warp 9 – Defiant -class ††
• Warp 9.3 – Nebula -class (2368)
• Warp 9.5 – Nebula -class (2370, could be pushed to warp 9.6)
• Warp 9.6 – D'deridex -class , can be exceeded in exchange for engine damage
• Warp 9.8 – Galaxy -class , Xepolite Free Trader
• Warp 9.9 – Prometheus -class
• Warp 9.97 – Protostar -class (with conventional warp drive)
• Warp 9.975 – Intrepid -class
• Warp 9.99 – Constitution III -class
• Warp 36 † – Karla Five's vessel

Appendices [ ]

Maximum warp requests [ ].

• " Where No Man Has Gone Before " (first mentioned)
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• " All Good Things... "
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• " Equinox "
• " Equinox, Part II "
• " Tinker Tenor Doctor Spy "
• " Flesh and Blood "
• " Body and Soul "
• " The Aenar "
• " In a Mirror, Darkly "
• Star Trek Generations
• Star Trek: First Contact

Background information [ ]

As noted above, the tolerance of a ship's systems for the stresses of warp travel are a primary limiting factor, so while exceeding the ship's maximum rated speed can be technically possible, it carries the risk of severe damage to the warp drive or to the ship's structural integrity.

When a ship is ordered to accelerate to maximum warp, it does not always mean the absolute highest reachable warp factor. For example, in ENT : " Affliction ", Enterprise NX-01 already travels at maximum warp, but then accelerates to warp 5.2. In both TNG : " Time Squared " and TNG : " Bloodlines ", maximum warp denoted warp 9, although the Enterprise -D was established to be capable of faster speeds in other episodes. A similar situation occurred in DS9 : " The Sound of Her Voice ", when the USS Defiant , traveling at maximum warp, accelerates to warp 9.5.

According to Star Trek Encyclopedia  (3rd ed., p. 556) updated with information up to 2375 and Star Trek: Insurrection , warp factor 9.2 was the normal maximum warp speed of Federation starships.

TNG : " Force of Nature " established Warp 5 as the maximum allowable Federation-vessel speed (except in emergencies), due to environmental concerns. Following this episode, the use of the term "maximum warp" became ubiquitous in lieu of a specific warp factor being stated. Even though later episodes and series strongly indicated that the limit was no longer in place (in particular throughout Star Trek: Voyager ), the use of the phrase "maximum warp" has continued, even in series set well before the events of "Force of Nature".

See also [ ]

• Cruising speed
• Emergency warp

External link [ ]

• Warp factor at Memory Beta , the wiki for licensed Star Trek works
• 2 USS Enterprise (NCC-1701-G)
• 3 Star Trek: The Next Generation

It’s fun to delve into the background details of Star Trek , but sometimes it’s hard to find the information you want. Check out an interactive warp speed calculator, an assortment of fonts from each series, an extensive gallery of logos and symbols, an archive of television scripts, and more.

EXCLUSIVE: Mary Wiseman talks Star Trek: Discovery season 5, the final frontier of Tilly's transformation

G et ready, galaxy trekkers, because the stars have aligned to bring us a supernova of excitement with Star Trek: Discovery 's final voyage in its fifth season.

As a huge fan of the show, I was ecstatic to get a chance to sit and chat with the stellar trio that is Wilson Cruz, Mary Wiseman, and Blu del Barrio. Their gravitational pull was simply irresistible.

Beam aboard and check out how Mary Wiseman, who plays the incredible Sylvia Tilly, talks about her portrayal of this refreshingly relatable character and what we can expect for her as the final season unfolds .

To Boldly Grow: Tilly's Cosmic Journey

First up, the indomitable Mary Wiseman, whose portrayal of Sylvia Tilly has been nothing short of a warp-speed ascent through the ranks of Starfleet and our hearts. Remember that time I penned an ode to Tilly , hailing her as the finest Star Trek character in the known universe? Well, Mary and I revisited that galaxy of thought, delving into Tilly's evolution from a starry-eyed cadet to the luminous beacon of hope and mentorship she's become.

Mary shared the riveting reversal of Tilly's journey: from a girl singularly fixated on achievement (and perhaps lacking a smidge in the social graces department) to a woman whose true north is her profound connection to community and relationships. The shift from seeking the captain's chair to finding unparalleled joy in nurturing the next generation of Starfleet officers at the Academy is a tale of self-discovery that even the Borg couldn't assimilate.

Mary's reflection on Tilly's transformation – shedding the skin of past expectations and embracing a path of genuine fulfillment – resonated like a perfect note in the symphony of the universe. It's a reminder that sometimes, to find our place in the cosmos, we must be willing to journey into the unknown parts of ourselves.

Stellar Reflections: The Heart of Discovery

As we navigated through this constellation of conversation, it was clear: the essence of Star Trek: Discovery lies not just in its thrilling explorations of space and time but in its profound examination of identity, growth, and the unbreakable bonds that form our interstellar family.

The journey of Tilly, beautifully brought to life by Mary Wiseman, stands as a testament to the enduring spirit of Star Trek: a universe where exploration is not only external but internal, where the bravest frontier is the soul, and where every star we reach for illuminates the path to discovering our true selves.

So, as we prepare to embark on this final voyage with the crew of the USS Discovery, let's strap in for a season that promises not just to chart new territories but to explore the depths of what it means to be human among the stars. Warp factor nine, anyone?

This article was originally published on bamsmackpow.com as EXCLUSIVE: Mary Wiseman talks Star Trek: Discovery season 5, the final frontier of Tilly's transformation .