A warp factor is a term indicating velocity in the subspace realm where faster-than-light (FTL) speeds are possible. Starfleet and the Federation has used a scale using cochrane units to measure the distortion potential of a warp drive. An original (OCU) scale was used up until the early 24th century, whereupon a revised scale (MCU) was put into effect when a more complete understanding of the nature of subspace was reached. (ST reference: Starship Spotter)

Original cochrane unit

In the 22nd and 23rd centuries, the relationship between warp factor (WF) and speed in multiples of the speed of light (Xc) was defined as:

Xc = WF3

This gives a speed of 1c for Warp 1, 512c at Warp 8, 1000c at Warp 10, and so on.

Modified cochrane unit

In the 24th century, the relationship between warp factor (WF) and speed in multiples of the speed of light (Xc) was defined as:

For WF 1–9, Xc = WF10/3
For WF >9, the WF exponent approaches infinity as the WF approaches 10.

This gives a speed of 1c for Warp 1, 1024c at Warp 8, and speeds above 1516c at Warp Factors between 9 and 10. Warp 10 is understood to be infinite speed and thus theoretically impossible to achieve.

The relationship between Transwarp and high Warp Factors is ambiguous.

Speed comparison

1 1 1     
2 8 10.08
3 27 38.94
4 64 101.59
5 125 213.75
6 216 392.50
7 343 656.14
8 512 1024     
9 729 1516.38
10 1000 Infinite
11 1331 Undefined
12 1728 Undefined
13 2197 Undefined
14 2744 Undefined
15 3375 Undefined

The table to the right compares speed in multiples of the speed of light for the two scales.


The production crew behind The Next Generation simply used a hand-drawn curve for decimal Warp Factors between WF 9 and 10, and thus there is no correct formula for those speeds in the TNG/DS9/Voyager era.

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