Warp factor

The Warp factor is a unitless figure that describes the speed of a starship or signal using a warp drive, thus traveling faster than light (FTL). The warp factor is a non-linear measure of speed.

Warp factors vs. speed

Warp factor	Speed	Distance travelled	Travel time	Reference
<5	~83 c	~60 AU (Earth-Neptune and back)	6 mins	ENT: "Broken Bow"
10	∞	n/a	n/a	VOY: "Threshold"
n/a (probably >= 11)	~8,300 c	2.5 mly (to Andromeda Galaxy)	300 yrs	TOS: "By Any Other Name"

Tom Paris described Warp 9.9 as being "about 4 billion miles per second." (VOY:The 37's)

Warp 10...

In 24th century warp theory, a warp factor of 10 corresponds to an infinite velocity. Theoretically, a vessel travelling at Warp 10 would occupy all points in the universe simultaneously.

Although considered a theoretical impossibility at the time, Tom Paris of the USS Voyager reached the Warp 10 threshold in 2372, using shuttlecraft Cochrane which was equipped with an extraordinarily rare form of dilithium discovered earlier that year. After it was discovered that such travel induces hyper-evolution, this technology was discontinued after the initial test. (VOY: "Threshold")

Many fans and even Paramount staff (including Rick Sternbach and Brannon Braga) discount the events of "Threshold", due to its severe scientific flaws.

Kathryn Janeway once made the observation that rumors travel fast on board Voyager. Chakotay agreed with Janeway, quipping at "warp 10." (VOY: "The Voyager Conspiracy")

...and beyond

However, in the 23rd century, Warp factors greater than 10 seemed to denote extraordinarily fast, but not infinite, speeds. In 2268, for example, the Enterprise achieved a speed of Warp 14.1 after being sabotaged by an alien woman known as Losira, though at that velocity the ship came within moments of destroying itself. (TOS: "That Which Survives") The previous year, the Enterprise also engaged a suicide attack ship of the Orion Syndicate, which was capable of at least Warp 10 if not higher speeds, due to crew safety being of no concern. (TOS: "Journey to Babel")

In 2270, the Enterprise encountered Karla Five's ship, which was on a collision course with the Beta Niobe nova. Spock reported that the ship was travelling at a speed of "something on the order of Warp 36." As Karla Five's ship was native to the negative universe, it was undoubtedly equipped with technology completely alien to the normal universe. (TAS: "The Counter-Clock Incident")

In a possible future timeline, warp factors as high as Warp 13 were routinely achieved by Federation starships. The Enterprise-D traveled at Warp 13 in the incident concerning the temporal anomaly in the Devron system. (TNG: "All Good Things...")

Rather than denoting something "faster than infinite", these warp factors may point to either a return to the old 23rd century scale (see section "Background information") or yet another recalibration of the scale. Advancements in warp technology could mean that stating a speed of Warp 9.9997 would be much more cumbersome than Warp 13. Otherwise, it may be that these high warp factors indicate that ships of this time are equipped with transwarp or quantum slipstream drive or other advanced propulsion technology.

Another possibiliy is that there has always only been one warp scale. That would mean that the Star Trek: Voyager episode "Threshold" was in error. After all, even some members of the Paramount staff said that they discount the events of that episode due to its scientific flaws. Then again, one could still argue and say that Gene Roddenberry himself created the revised Cochrane scale, which established that Warp 10 was infinite speed.

Appendices

Related topics

• Warp Theory

Background

Although formulae to calculate speeds from warp factors existed in the writer's guides, these were not always used consistently. As an example, in "By Any Other Name" the Kelvans modified the USS Enterprise to maintain a speed of Warp 11 in order to return to their home in the Andromeda galaxy. They estimated that the journey would take less than 300 years, indicating a far greater speed than the scale would indicate.

To explain this, fans speculate that Warp factors are, in terms of their light speed equivalents, not absolute, but only relative figures, depending on the local properties of space and subspace, the multiples given are only minimum/average values. The actual speed is dependent upon interstellar conditions like gas density, electric and magnetic fields and fluctuations in the subspace domain as well as energy penalties resulting from quantum drag forces and power oscillation inefficiencies. This theory would seem to be substantiated by references in several episodes, including "Bride of Chaotica" (VOY).

Star Trek: The Original Series

During TOS, the Warp factor scale wasn't clearly defined. In his initial draft proposal, "Star Trek is...", Gene Roddenberry established the maximum velocity of the starship as ".73 of one light-year per hour". This would translate to a top speed of approximately 6,400c.

The warp scale now commonly known as "TOS scale" first appeared in widespread print in 1968 in The Making of Star Trek. It was given a more technical gloss in Franz Joseph's Star Fleet Technical Manual in 1975. In 1977 Roddenberry again adopted the scale for the abortive Star Trek: Phase II series, but abandoned it for The Next Generation series.

According to these publications, the scale used by Starfleet in the 23rd century is based on a geometric progression, where the speed of a vessel (measured in multiples of c, the speed of light) is equal to the cube of the given warp factor. The scale assumes travel through a vacuum with no gravimetric or subspace perturberances. The warp factor was calculated as follows:

$wf={\sqrt[{3}]{v/c}}$

with

• v being the speed of the signal or starship
• c being the speed of light (3.0x10⁸ m/s) and
• wf being the resulting warp factor

At Warp 1, a starship would reach c; at Warp 6, it would reach 216c. This is a much slower speed as initially proposed by Roddenberry.

Star Trek: The Next Generation

According to the Star Trek: The Next Generation Technical Manual, the warp factor scale used by Starfleet in the 24th Century was based on a recalibration of the scale used in the 23rd Century. Rather than a simple geometric progression based on relative speed, the scale was based upon the amount of power required to transition from one warp plateau to another. For example, the power to initially get to the recalibrated Warp Factor One was much more than the power required to maintain it; likewise Warp Two, Three, Four, and so on. Those transitional power points rather than observed speed were then assigned the integer warp factors.

According to a Star Trek: The Magazine article by Andre Bormanis, this scale change occured in 2312. A term was added to the above equation that caused the speed to rise slightly at lower warp factor, but to become infinite at Warp 10. The ratio v/c at a given warp factor is equal to the corresponding cochrane value that describes the subspace distortion.

The 24th Century scale was created at the start of Star Trek: The Next Generation. 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.

$wf={\sqrt[{10/3}]{v/c}}$

with

• v being the speed of the signal or starship
• c being the speed of light (3.0x10⁸ m/s) and
• wf being the resulting warp factor

Or, to calculate speed in terms of c (below Warp 10), the formula would be:

$speed=wf^{10/3}c$

In this case, Warp 1 is equivalent to c (as it was in the 23rd century scale); Warp 6 is approximately 392c.

This scale was used from TNG onwards. Note that, since Warp 10 equals infinite speed, it is physically impossible to achieve. This fundamental law has been violated in the episode VOY: "Threshold", where Tom Paris allegedly crossed the "Warp 10 Barrier".

Star Trek: Enterprise

Although it has not been directly confirmed, the Enterprise (NX-01) may use the "TOS scale". In ENT: "Broken Bow", Archer specifically stated that the ship was traveling at 30,000,000 kilometers per second, which translates to approximately 100 times the speed of light, or approximately Warp 4.6 on the 23rd Century scale.

Archer also states in "Broken Bow" that the ship travels to "Neptune and back in six minutes." Although the engine is designed for travel at speeds of up to warp 5, this particular statement translates to a speed of roughly warp 4.6 as well.