Warp factor

"They say gossip travels faster than warp speed."
 * - The Doctor in 2375

Warp factor (or time warp factor) was the primary means of measuring speeds attained using warp drive. The term was often shortened to warp when followed by its value so that saying "warp six" is the same as saying "warp factor six." Faster-than-light travel began after warp one, whereas lower fractional values were sometimes used to measure sublight speeds. ( display graphic) Spacecraft ordinarily traveled at a higher integer warp factor.

In the mid to late 24th century, infinite velocity was designated as warp factor ten. It was considered to be unattainable by conventional means. Because of this, extremely high warp factors were indicated with fractional values between nine and ten, such as warp 9.975. 

Multiwarp speeds
In the 23rd century, warp factors of 10 and higher were known as generally unsafe velocities. They were called multiwarp speeds. 


 * Warp factor 10. In 2267, the USS Enterprise (NCC-1701) engaged an Orion scout ship capable of warp 10, if not higher speeds, since crew safety was of no concern to them, prompting Spock to remark that it was "interesting." The ship was too fast for the Enterprise to hit it with phasers or photon torpedoes. In 2268, Bele, upon commandeering the engine and directional controls of the Enterprise, propelled the starship faster than warp 10 towards Cheron.


 * Warp factor 11. In 2267, the Nomad probe improved efficiency in the antimatter input valve and energy release controls on the Enterprise, allowing the ship to achieve at least warp 11. When this happened, Montgomery Scott was in disbelief. Captain James T. Kirk ordered Nomad to reverse the modifications though, as the structure of the Enterprise was not designed to handle the stress of that much power output. In 2268, the Kelvans who commandeered the ship made similar modification. At that time the ship could maintain warp 11 without danger.


 * Warp factor 14. In 2268, the Enterprise achieved a speed of warp 14.1 when the engine of the ship was sabotaged to overload by a Kalandan planetary defense system. At that velocity the ship came within moments of destroying itself.


 * Warp factor 15. In 2267, the Nomad probe was armed with a weapon system capable of firing energy bolts that traveled at the speed of warp 15.


 * Warp factor 22. In 2270, the Enterprise was accelerated to speeds in the excess of warp 22, while being linked to Karla Five's vessel with a tractor beam.


 * Warp factor 36. In 2270, the Enterprise encountered Karla Five's vessel, that was about to enter the Beta Niobe nova. At maximum speed, the ship was traveling at approximately warp 36.

Infinite velocity
In 24th century warp theory, warp factor 10 had been redesignated to correspond with infinite velocity. A vessel traveling at warp 10 occupied all points in the universe simultaneously. Warp 10 was also known as the transwarp threshold. Warp 10 had also become a slang term referring to anything extremely fast. Kathryn Janeway made the observation in 2376 that on USS Voyager rumors traveled fast. Chakotay agreed with Janeway, quipping at "warp 10." 


 * Warp factor 10-. In 2364, the Traveler used the energy of his thoughts to move the USS Enterprise (NCC-1701-D) through space at a speed that registered on instruments as exceeding warp factor 10 and going off the warp scale.


 * Warp factor 10. 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 a transwarp drive and an extraordinarily rare form of dilithium discovered earlier that year. After it was discovered that such travel induced hyper-evolution, this technology was discontinued after the initial test.


 * Warp factor 10+. It was possible to travel backwards in time by surpassing warp 10. In 2365, Captain Jean-Luc Picard and Commander William Riker speculated on what phenomenon could have thrown the El-Baz back through time. While Riker knew the shuttlepod didn't have warp drive, he still suggested the theory that it could have somehow accelerated beyond warp 10. Picard suggested this could have been achieved by a warp-powered slingshot using the gravitational pull of a star.

Alternate timelines
In an alternative future, around the turning point of the 24th to 25th century, warp factor values beyond warp 10 were again used to describe extremely fast speeds. 


 * Warp factor 13. The Enterprise-D traveled at warp 13 in the incident concerning the temporal anomaly in the Devron system.

Related topics

 * Bessel function
 * Cochrane
 * Cochrane equation
 * Maximum warp
 * Time warp
 * Slingshot effect
 * Warp equation
 * Warp barrier
 * Time barrier
 * Transwarp threshold
 * Warp 2 barrier
 * Warp theory

Variations in relative speed
Although formulas to calculate a relative speed from a warp factor have existed in the writer's guides, these were rarely used for reference in the episodes and films. To explain the apparent discontinuities of relative speed equivalents for warp factor speeds, reference sources have given several explanations:


 * Star Trek: The Next Generation Technical Manual (pg.55) states the actual speed values of a warp factor are dependent upon interstellar conditions, for example gas density, electric and magnetic fields in different regions of the galaxy, and fluctuations of the subspace domain. Also quantum drag forces and motive power oscillation cause energy penalties to a ship using warp drive.


 * Star Trek Maps (pg.6) introduced a similar concept as the Cochrane's factor, that influences the actual speed by multiplying it. It can be as high as a multiplication of 1500 to the relative speed within the curvature of space caused by the interstellar dust and gas of a galaxy, and as little as 1 in the empty intergalactic void. In the vicinity of massive objects it is so high that disproportionately high speeds are created when approaching them, and they tend to result in the slingshot effect. Between the galaxies there is only the empty void, so the speed follows only the basic cubic formula. (see below) Within the interstellar medium of Federation space the average value for the Cochrane's factor has been calculated to be 1292.7238.

The effect of gravity to the relative speed has been well established in canon. For example in, the Enterprise is at maximum warp but is not moving in space at all, due to the gravity of a black hole behind it. In, a starship moving away from a star system at a speed better than warp 6 is actually moving slower than the speed of light. In some areas of space with unstable or disrupted subspace, it is impossible to use warp drive at all, as was established in such episodes as and.

Many examples of more subtle variations exist. For example, in "By Any Other Name", the Kelvans modified the USS Enterprise (NCC-1701) to accelerate to a speed of warp 11 in order to safely cross the galactic barrier. If this was also meant to represent the velocity of travel to the Andromeda Galaxy, a travel time of 300 years would indicate a far greater speed than can be derived from the cubic scale from the writer's guide. Warp 8.4 was stated to be much faster in "That Which Survives" than warp 9.9 in "The 37's". In, warp 7 was stated to be about 55 times faster than warp factor 2, again confirming that fluctuations in the relative speeds exist that are not covered by the basic formula.

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 6,400 c (equivalent to TOS warp 18.57, and approximately TNG warp 9.98).

The original warp scale was described in the writer's guide, The Star Trek Guide, third revision, dated April 17. 1967 (pg. 8) and first appeared in widespread print in 1968 in The Making of Star Trek (pg. 191). The book also states a shift in relative time occurs while traveling at warp, an hour might equal to three hours experienced outside the ship. (pg. 198) In 1975, the warp scale given a more technical gloss in Franz Joseph's Star Fleet Technical Manual, now extended to include warp factors below 1. In 1977 Roddenberry again adopted the scale for the abortive Star Trek: Phase II series, but abandoned it for The Next Generation series. It was not until the the episode  of Star Trek: Enterprise, that the warp factor scale made an official on screen debut. Warp factors from 1 to 5 were depicted with their corresponding relative speed values on a large computer graphic.

The scale used by Starfleet in the 22nd and 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 warp factor was calculated as follows:
 * $$wf=\sqrt[3]{\frac{v}{c}}$$
 * with
 * v being the speed of the signal or starship
 * c being the speed of light (3.0 &times; 108 m/s) and
 * wf being the resulting warp factor

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


 * $$v=wf^{3}c$$

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

Using this scale:

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 Original Series. Rather than a simple geometric progression based on relative speed, 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. These transitional points were established to apply to the original warp scale as well in the canonical warp chart presented in "First Flight".

According to a Star Trek: The Magazine article by André Bormanis, this scale change occurred 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.

For warp factors up to 9, the revised formula became:
 * $$wf=\sqrt[{\frac{10}{3}}]{\frac{v}{c}}$$
 * with
 * v being the speed of the signal or starship
 * c being the speed of light (3.0 &times; 108 m/s) and
 * wf being the resulting warp factor

Or, to calculate speed in terms of c (up to warp 9), the formula would be:


 * $$speed=wf^{\frac{10}{3}}c$$

In this case, warp 1 is equivalent to c (as it was in the 23rd century scale), but above warp 9 the exponent was increased exponentially, approaching infinity as the warp factor approaches 10.

Using this scale:

Star Trek: Deep Space Nine
The Bajoran Wormhole connected Bajoran system to a region in the Gamma Quadrant 70,000 light years away. In, Sisko stated that it would take Starfleet's fastest ship over 67 years to cross the distance, suggesting the fastest ship in 2369 could travel at approximately 1044 times the speed of light on a flight of that duration. The figure was further explained in the series bible, that it is more specifically a 60 year journey at warp 9, suggesting warp 9 would be about 1167 times the speed of light.

Star Trek: Voyager
In the pilot episode of the series,, it is established that "at maximum speeds" it would take 75 years for Voyager to reach Earth, that was at that time approximated to be 70,000 light years away. In Star Trek: Voyager Technical Manual it is stated that this calculation is based on a non-stop direct journey at the speed of warp 9.6. This indicates warp 9.6 equals to approximately 933 times the speed of light.

In the episode, Captain Kathryn Janeway states that the current Starfleet starships are twice as fast to what the USS Enterprise (NCC-1701-A) and the USS Excelsior were in the 2290s. The maximum warps of the Enterprise-A and the Excelsior were established to be warp 9 in the script of. This would suggest that the maximum speed of the Voyager, warp 9.975, is twice as fast as warp 9. This would be consistent with how fast warp 9 was established to be in and how fast the Voyager was established to be in  at maximum warp.

Star Trek: Enterprise
Officially and according to the large warp chart featured in, the warp drive of the uses the TOS-scale. Speeds mentioned in of traveling at 30,000,000 kilometers per second, and going to "Neptune and back in six minutes." fit well into the ballpark of cubic warp factors between 4 and 5. In, Trip states that warp 4.8 (approximately 111 times the speed of light in the TOS-scale) is double the speed of warp 3.9 (approximately 59), which is also a close enough margin of error considering it is an offhand comment made without navigational implications.

A location was given to Archer on where to go look for the Xindi inside the Delphic Expanse in the episode. The location was stated to be a three month trip away from Earth at warp 5. In the next episode,, when the Enterprise had arrived to look for the Xindi in that region, it was said they were 50 light years away from Earth. This indicates warp 5 would equal to a speed of approximately 200 times the speed of light. This would fall closer to the TNG-scale figure for warp 5 instead of the TOS-scale figure of 125 times the speed of light presented in the canonical chart.

There are however instances in "Broken Bow" that are not compatible with any of the basic scales. Zefram Cochrane notes in his recorded speech that the warp five engine would allow a ship to travel a hundred times faster than what they could in 2119. Warp 2 is established to be the maximum warp of ships in the early-22nd century in. Warp 5 however is only 16 or 21 times faster than warp 2 in the scales. The journey from Earth to Qo'noS in four days is another. In either scale the Enterprise wouldn't even reach the closest star to Earth in four days. Qo'noS has not been given an exact canonical distance from Earth. But based on The Explored Galaxy star chart, the Klingon border is clearly not in the immediate stellar neighborhood with stars like Alpha Centauri and Vulcan, and beyond Organia, it would seem to be at least some 50 light years away.

In, it is stated that a warp three engine would allow a ship to travel ten times faster than warp factor 1.8. This doesn't work out in either of the basic formulas, unless we interpret the statement to indicate that a warp three engine would allow a speed of warp factor 3.9 in the TOS-scale or 3.6 in the TNG-scale. Warp factor 3 would be only around five times faster in either scale.

Alternate reality
In the alternate reality, seen in, USS Enterprise (alternate reality) traveled from Earth to at maximum warp. According to Vulcan is located slightly over sixteen light years away from Earth. According to background sources maximum warp of the ship was warp factor 8. Directly after the ship had accelerated to and attained maximum warp, Captain ordered  to give an announcement of the mission to the crew. At the end of the broadcast, Chekov stated that the ship would arrive within three minutes.

However, there was an unknown amount of time the ship spent accelerating to maximum velocity, so there is no accurate way to ascertain the total voyage time of the Enterprise from Earth to Vulcan, beyond the obvious implication that it was not an especially lengthy trip. By comparison to the prime reality, in, when the crew was returning to Earth from Vulcan on board the HMS Bounty, Sulu reported they would arrive in 1.6 hours.

In, the Enterprise and the three times faster USS Vengeance were capable of traveling from the Sol system, through the Neutral zone to the edge of Klingon space and back in less than a day. Co-writer Roberto Orci acknowledged 's line about his time away from the Enterprise should have been something like "one week" rather than "one day".