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

Warp factor
Distance	light years

Velocity	c
Time to pass that distance
Time to reach the Pluto (33.4 au ≈ 0.0005 ly)
Time to reach the Alpha Centauri (4.3 ly)
Time to reach the Ocampa planet (75000 ly)
Time to cross the Milky Way (100000 ly)
Time to reach the Andromeda galaxy (2000000 ly)

Description

TOS

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):

\[v = w^3 c\]

TNG

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.

\[v = w^{ \frac{10}{3} + f(w)} c, \\ f(w) = \begin{cases} 0, & 0 \leqslant w \leqslant 9.0 \\ -0.5 \log_{10}(10 - w), & 9.0 < w \leqslant 10.0 \\ \end{cases}\]