# warp speed

Once upon a time when I had too much time and too little to do I decided to work out an equation which be able to reproduce the speeds used in Star Trek: The Next Generation for specific warp factors. The results are reproduced here in the form of a JavaScript calculator.

This calculator allows you to either find the speed corresponding to a certain warp factor, or the warp factor corresponding to a certain speed. Results may vary in accuracy and are limited by the precision of your software.

 Warp factor: Speed : c

To find what speed corresponds to a certain warp factor, enter the warp factor and press "Find speed." Results will be displayed in multiples of the speed of light and will always be exact.

To find what warp factor corresponds to a certain speed, enter the speed (in multiples of the speed of light) and press "Find warp." Results from this calculation may vary in accuracy due to the methods used to determine them. To check the accuracy, press "Find speed" once the warp factor has been displayed to see if the result is close to the speed you originally entered.

The calculator determines the speed according to the warp scale used in Star Trek: The Next Generation; Deep Space 9; and Voyager. Warp speeds in the original series were based on a different scale.

The speed of light in a vacuum is 299,792,458 ms-1.

The equations used to calculate the speed from the warp factor is quite complex, but here it is for those who are interested. To simplify the presentation, it takes the form of: For values of w < 9.5 (or so), the equation reduces to approximately just w to the power of 10/3. For higher values the exponent has to be determined more precisely using the product of the functions a(w), b(w), and c(w). These are:   Each of these equations provides a further refinement of the results, so including c(w) provides a better result than leaving it out, and including b(w) provides a better result than using only a(w).

Warp factors are calculated using Newton's method with up to 20 iterations. This page, its contents and code are protected by copyright. © 1998-2021, Martin A. Shields.