# Warp factor

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"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. (Star Trek: The Motion Picture; Star Trek; ENT: "First Flight" 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. (VOY: "Threshold") Because of this, extremely high warp factors were indicated with fractional values between nine and ten, such as warp 9.975. (TNG: "Encounter at Farpoint"; VOY: "Caretaker")

According to Star Trek Maps, the alternative term "time warp factor" used in TOS: "The Cage" is so called due to the time dilation effects that occur during warp travel.
Subspace communication speeds have also been given high warp factors in several reference materials.

## Warp factor vs. average speed

The following is a list of warp factor values that have been given a relativistic speed equivalent on screen. Average speeds are typically calculated from given values for travel time and distance. Some figures were depicted in charts and others given as statements in dialogue. See: Variations in relative speed for more information.
Warp factor Average speed (*c) Distance traveled Travel time Reference
.5 0.304 - 0.496 ~3.95 - 6.45 AU (Earth-Jupiter) 1.8 hours Star Trek: The Motion Picture
1 1 depicted in warp factor chart ENT: "First Flight"
2 8 depicted in warp factor chart ENT: "First Flight"
3 27 depicted in warp factor chart ENT: "First Flight"
3 39 0.102 light years 23 hours TNG: "The Most Toys"
3 487 4 light years 3 days ENT: "Damage"
4.4 100 30,000,000 km 1 second ENT: "Broken Bow"
4.5 79.7 - 87.2 ~57.5 - 62.92AU (Earth-Neptune and back) 6 minutes ENT: "Broken Bow"
5 200 50 light years (Earth-An area inside the Delphic Expanse) ~3 months ENT: "The Expanse", "The Xindi"
6+ 0.02 10,000 kilometer intervals as a Klingon D7 approached ~2 seconds per interval TOS: "Elaan of Troyius"
8.4 765,000 ~990 light years 11.337 hours TOS: "That Which Survives"
9 834 approximately 300 billion kilometers (0.032 light years) ~20 minutes TNG: "Bloodlines"
9.9 21,473 about 4 billion miles (0.0007 light years) 1 second VOY: "The 37's"
9.975 1,554 - 1,721 132 light years 1 month VOY: "Relativity", "Friendship One"
9.975 2,922 40 light years 5 days VOY: "Relativity", "Scorpion, Part II"
10 0 VOY: "Threshold"
n/a [1] 8,300 2.5 million light years (to Andromeda Galaxy) 300 years TOS: "By Any Other Name"
1. The Kelvans modified the USS Enterprise to travel at warp eleven through the Galactic barrier. They did not clarify whether the same warp factor would have been used for intergalactic travel also.

## Warp ten and above

### Multiwarp speeds

In the 23rd century, warp factors of 10 and higher were known as generally unsafe velocities. (TOS: "Journey to Babel") They were called multiwarp speeds. (TOS: "The Changeling")

• 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. (TOS: "The Changeling") In 2268, the Kelvans who commandeered the ship made similar modification. At that time the ship could maintain warp 11 without danger. (TOS: "By Any Other Name")
According to the Star Trek Spaceflight Chronology (page 180) and Mr. Scott's Guide to the Enterprise (page 14), after the refit of the Constitution-class USS Enterprise in Star Trek: The Motion Picture, the maximum speed of the ship was warp factor 12.
• 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. (TOS: "The Changeling")
In the comic book A Warp in Space set in the late-2260s, Starfleet tested the prototype Warp 15 engine on several test ships. Zefram Cochrane also devised modifications to the USS Enterprise that allowed the ship to achieve the speed, though the ship was almost torn apart at that velocity.
• 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. (TAS: "The Counter-Clock Incident")

### 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. (VOY: "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." (VOY: "The Voyager Conspiracy")

The slang term was also used in the script for DS9: "Sons and Daughters", where Alexander Rozhenko's adrenaline was described as "pumping at warp 10." [1]
According to Star Trek: Starship Spotter, the redesignation of warp 10 as infinite speed occurred in 2312. The warp factor specifications prior to 2312 were rated by Starfleet using the Original Cochrane Unit warp scale, abbreviated as the OCU. Warp factors after 2312 use the Modified Cochrane Unit warp scale, abbreviated as the MCU.
According to Star Trek: The Next Generation Technical Manual (page 55), the ship didn't actually achieve warp 10 or go beyond it, but it did travel at the extreme speed of about Warp 9.9999999996. This would be confirmed in "Threshold" where Tom Paris becomes the first Human to travel at warp 10.
• 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. (VOY: "Threshold")

### 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. (TNG: "All Good Things...")

In the October 1995 issue of OMNI, science advisor Andre Bormanis stated the idea of warp factors beyond 10 in the alternative future was in a recalibration of the warp scale, as ships had gotten faster. Maybe warp 15 was set to be the transwarp threshold instead, according to Bormanis, and warp 13 in that scale would have been the equivalent of warp 9.95 of the previous scale.

## Appendices

### Background information

#### 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 Star Trek, 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 TOS: "Elaan of Troyius", a D7-class 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 VOY: "Bride of Chaotica!" and "The Omega Directive".

Many examples of more subtle variations exist. For example, in "By Any Other Name", the Kelvans modified the USS Enterprise 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 TNG: "Allegiance", 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) [2] 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 2003 episode "First Flight" 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 × 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:

Warp factor Calculated speed (*c) Distance traveled in 24 hours (*light years) Travel time from Earth to Alpha Centauri
0.5 0.125 0.0003 34.64 years
1 1 0.003 4.33 years
2 8 0.022 197.69 days
3 27 0.074 58.57 days
4 64 0.175 24.71 days
5 125 0.342 12.65 days
6 216 0.591 7.32 days
7 343 0.939 4.61 days
8 512 1.402 3.09 days
9 729 1.996 52.07 hours
10 1000 2.738 37.96 hours
11 1331 3.644 28.52 hours

#### 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 × 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:

Warp factor Calculated speed (*c) Distance traveled in 24 hours (*light years) Travel time from Earth to Alpha Centauri
0.5 0.099 0.0003 43.64 years
1 1 0.003 4.33 years
2 10.079 0.028 156.91 days
3 38.941 0.107 40.61 days
4 101.594 0.278 15.57 days
5 213.747 0.585 7.4 days
6 392.498 1.075 4.03 days
7 656.135 1.796 2.41 days
8 1024 2.804 37.07 hours
9 1516.381 4.152 25.03 hours
10 0

#### Star Trek: Deep Space Nine

According to DS9: "Emissary" and "Battle Lines", the Bajoran Wormhole connected the Bajoran system to a region in the Gamma Quadrant 70,000 light years away. In "Battle Lines", 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, [3] suggesting warp 9 would be about 1167 times the speed of light.

In "The Sound of Her Voice", the USS Defiant, traveling at warp 9, is three days away from a planet. Increasing speed to warp 9.5 took almost a full day away from the travel time. This indicates that warp 9.5 is almost 50% faster than warp 9.

#### Star Trek: Voyager

In the pilot episode of the series, VOY: "Caretaker", 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 VOY: "Flashback", Captain Kathryn Janeway states that the current Starfleet starships are twice as fast to what the USS Enterprise-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 Star Trek VI: The Undiscovered Country. [4] This would suggest that the maximum speed of the Voyager, warp 9.975, is twice as fast as warp 9.

#### Star Trek: Enterprise

Officially and according to the large warp chart featured in "First Flight", the warp drive of the Enterprise NX-01 uses the TOS-scale. Speeds mentioned in ENT: "Broken Bow" 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 ENT: "Regeneration", 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 ENT: "The Expanse". The location was stated to be a three month trip away from Earth at warp 5. In the next episode, ENT: "The Xindi", 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 ENT: "First Flight". 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 ENT: "Fortunate Son", 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 Star Trek, USS Enterprise traveled from Earth to Vulcan at maximum warp. According to ENT: "Daedalus" Vulcan is located slightly over sixteen light years away from Earth. According to background sources maximum warp of the ship was warp factor 8. [5] Directly after the ship had accelerated to and attained maximum warp, Captain Christopher Pike ordered Pavel Chekov 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 Star Trek IV: The Voyage Home, when the crew was returning to Earth from Vulcan on board the HMS Bounty, Sulu reported they would arrive in 1.6 hours.

In Star Trek Into Darkness, 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 Scotty's line about his time away from the Enterprise should have been something like "one week" rather than "one day". [6]