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# Warp Speed Calculator

Warp propulsion and warp factorThe original series equation — Cochrane ScaleThe Next Generation equations for superluminal speedHow to use the warp speed calculatorSearching for a new planet — an exampleFAQs

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 — .

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:

$\footnotesize v = w^3 \cdot c$

where:

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

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 $w = 2$, 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:

Warp factors lower than 9. Source: Star Trek: The Next Generation Technical Manual.

Warp factor

Cochranes

1

1

2

10

3

39

4

102

5

214

6

392

7

656

8

1024

9

1516

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

$\footnotesize v = w^{10/3} \cdot c$

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 $w = 10$ 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 $w > 9$:

Warp factors larger than 9. Source: The Star Trek Encyclopedia: A Reference Guide to the Future.

Warp Factor

Cochranes

9.2

1649

9.6

1909

9.9

3053

9.99

7912

9.9999

199516

10

Infinity

The conjectured values are part of a and were approximately derived by .

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

$\footnotesize \begin{split} v &= w^{10/3} \cdot w^{f_1} \cdot c \\[1em] f_1 &= \exp\left(-\frac{0.001}{(w - 9)^2}\right)\\[1.5em] &\quad \cdot 0.03658749373 \\[0.5em] &\quad \cdot (-\ln(10-w))^{1.7952294708} \end{split}$

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

$\footnotesize \begin{split} v &= w^{10/3} \cdot w^{f_2} \cdot c \\[1em] f_2 & = 0.00264320\\[0.5em] &\quad \cdot(-\ln(10-w))^{2.87926700} \\[0.5em] &\quad+ 0.06274120 \cdot(w-9)^5\\[0.5em] &\quad+0.32574600\cdot(w-9)^{11} \end{split}$

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.

Star trek ship's warp factors. Sources: Star Trek: Deep Space Nine and Star Trek: The Next Generation Technical Manuals

Starship

Max warp factor

AKIRA-CLASS

9.8

CARDASSIAN FIGHTER

9.5

CARDASSIAN FREIGHTER

6.5

DEFIANT-CLASS

9.982

INTREPID-CLASS

9.55

MIRANDA-CLASS

9.2

NEGHV'AR-CLASS

9.6

NEBULA-CLASS

9.9

U.S.S. ENTERPRISE D

9.3

VORC'HA-CLASS ATTACK

9.6

## 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:

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

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

• $v = 1693\,c$, $t = 212 \, \text{hours}$, 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!

FAQs

### 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:

1. Input the warp factor in the TOS equation v = w3⋅c.

2. Input the warp factor in the TNG equation v = w10/3⋅c.

3. 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:

1. Input the warp factor in the formula v = w10/3⋅c.

2. Compute the warp velocity v = 392⋅c.

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

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

5. Convert the units properly.

6. 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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