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[]
| WF | OCU | MCU |
|---|---|---|
| 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.
Background[]
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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