This page contains: The two different formulae used in Star Trek to calculate warp factors, illustrated by animations/Flash movies of USS Voyager jumping to warp or in warp flight Warp factor chart Behind-the-scenes information Real-life background

Warp factor is the unit of measure for faster-than-light warp velocities generated by warp drive. Warp factor one is c, the speed of light, while higher speeds are computed geometrically under one of two different formulae. USS Voyager's warp capability is computed under the second formula.

1. The Constitution-class U.S.S. Enterprise NCC-1701 had a cruising speed of warp factor 6, and could reach warp 8 only with significant danger to the ship itself [TOS: Arena], but it nevertheless attained warp 11 in 2267 when modified by the Nomad device [TOS: The Changeling]. The Kelvans also modified the ship's engines to reach warp 11 [TOS: By Any Other Name]. The ship reached warp 14.1 in 2268 when the warp engines were sabotoged [TOS: That Which Survives].

   It is not known whether warp 5 which could be attained by NX-01 Enterprise, captained by Jonathan Archer in the 2150s, was calculating warp factor speed by that or another method [Enterprise].
    

2. By the 24th century, a new warp factor scale was in use that employed an asymptotic curve, placing warp 10 as an infinite value.

Under the new scale, the Galaxy-class U.S.S. Enterprise NCC-1701-D had a normal cruising speed of warp 6 (392 times light speed, about warp 7.3 under the old system), and a maximum normal velocity of warp 9.2 (about 1649 times light speed, equivalent to about warp 11.8 in the 'old' system).

In 2370, following the formation of a massive subspace rift within the Hekaras Corridor, the Federation Council agreed that the use of warp fields posed a significant threat to some areas of space. Therefore the Council decreed that some areas would be limited to essential travel only. Furthermore, the Council imposed a Federation-wide 'speed limit' of warp 5, which could only be exceeded in times of extreme emergency [TNG: Force of Nature]. Later advances in Federation warp drive technology permitted the use of speeds exceeding warp 5. One of the first ships to be so equipped was the Intrepid-class U.S.S. Voyager, whose variable-geometry warp drive nacelles prevented damage to the subspace continuum [#1 and #2 Caretaker]. See Detailed Exterior Tour: Variable Geometry Warp Nacelles for information about the warp nacelles.

The Type-12 shuttlecraft, called Cochrane after Zefram Cochrane the inventor of warp drive technology, and piloted by Tom Paris, exits Voyager's shuttlebay. As it jumps to warp, Voyager does the same. (pop-up window) [#31 Threshold]	Voyager in warp flight. (Stock footage seen in several episodes. Screenshots from [#166 Author Author].)
USS Voyager travels at warp speed. (pop-up window)	As the moon pans left, creating eclipse and flare, Voyager is revealed flying out of the light. Voyager passes a planet and heads toward a distant nebula. The ship's nacelles fold down and Voyager jumps to warp speed. (opens in a pop-up window) [opening credits]

Voyager in flight
[#166 Author Author]

above 8 screenshots: Voyager passes a planet and heads toward a distant nebula, and jumps to warp
opening titles

The relative translation scale of warp factor was recalibrated by the time of the 24th century, with warp factor 1 being the lowest speed and warp 10 believed to be impossible to attain. U.S.S. Voyager has a sustainable cruise velocity of warp factor 9.975 [#1 and #2 Caretaker]. Even the U.S.S. Prometheus NX-59650 of 2374 [#82 Message In A Bottle], which was designed to be the fastest ship in Starfleet, could travel only at warp 9.9, fractionally slower. Warp 9.9 is about 4 billion miles per second [#20 The 37's].

Warp 10, or transwarp, was considered impossible until Paris' historic flight in the upgraded Type-9 shuttlecraft Cochrane (the upgrade was known as Type-12). The breaking of the transwarp threshold had the unexpected side-effect of causing cellular mutation on Paris and later in addition Janeway [#31 Threshold].

WARP FACTOR CHART

BEHIND-THE-SCENES

[Star Trek: The Original Series] occasionally had ships and other objects travelling at warp 10 or faster. At the beginning of [Star Trek: The Next Generation], Gene Roddenberry, Star Trek's creator, (pictured), said he wanted to change the warp speed scale to put warp 10 at the absolute top of the scale. Presumably the warp scale has been recalibrated so that all the speeds shown in the original show are 'actually' less than warp 10. [Star Trek: The Original Series] never established actual speeds for warp factors in any episode or movie, although the old warp factor cubed formula has come to be generally accepted. The Federation-wide warp 5 speed limit established in [TNG: Force of Nature] was abandoned a couple of years later when it was assumed that newer Federation starships (like U.S.S. Voyager and the new U.S.S. Defiant) had improved with the installation of environmentally friendly warp drive systems that did not cause damage to the spatial continuum. The speed limit was actually abandoned in order to return flexibility to storylines as far as the show's writers were concerned. In [TNG: All Good Things...], the final televised episode of [Star Trek: The Next Generation], both the U.S.S. Pasteur and U.S.S. Enterprise NCC-1701-D were ordered to use 'warp 13'. This may be yet another recalibration of the warp curve, although it is not clear if this will happen in the 'real' Star Trek timeline, since that future was a fabrication of Q's. It is also possible that this alludes to some kind of implementation of transwarp drive, as seen in [#31 Threshold].

REAL-LIFE BACKGROUND

In the Star Trek universe, a brilliant but eccentric (aren't they always?) scientist named Zefram Cochrane developed the first practical FTL (faster-than-light) propulsion system, the celebrated warp drive, in 2063. Space warps have been a subject of serious scientific research since Albert Einstein (pictured) created the general theory of relativity in 1915. Einstein showed that matter warps space; in other words, space itself is not "flat" but curved. Just as we cannot directly perceive the curvature of the Earth while standing on its surface, we cannot directly perceive the curvature of space, but it is just as real. In his special theory of relativity, Einstein demonstrated that nothing can travel faster than the speed of light in a vacuum. As noted above, the nearest star beyond our solar system, Proxima Centauri, is a bit more than four light-years away. Since nothing can travel faster than light, a journey to Proxima Centauri would require at least four years (as measured by an observer on Earth-the relativistic effect known as time dilation would lead to a different reckoning of travel time among the crew of a starship traveling at near-light speed). The idea of using "warped" space as a kind of loophole to circumvent the laws of special relativity has been examined by many scientists, but no one has yet developed a practical means of creating a space warp for propulsion. According to the general theory of relativity, the presence of matter is the only thing that warps space. High concentrations of extremely dense matter (in a black hole, for example) will warp space to an extreme degree (high concentrations of energy can also warp space, since, according to relativity theory, matter and energy are different manifestations of the same thing). Black holes may also be connected to other points in space through worm holes, cosmic short cuts through the curved space-time fabric of our universe. The question of how to create and manage space warps through the application of forces we know how to control (such as the electromagnetic or nuclear force) will have to await a fundamental breakthrough in basic physics. For much of the twentieth century, theoretical physicists have struggled to achieve what many would consider the ultimate theory: a "theory of everything." Such a theory would be a single mathematical formulation that unifies all four fundamental forces in nature: gravitation, electromagnetism, and the strong and weak nuclear forces. The last three forces were combined into a single unified theory in the 1980s, but gravity has yet to be incorporated into the scheme. Understanding how gravity is one manifestation of a single, general force may provide the theoretical understanding that will eventually lead to the ability to manipulate gravitational fields through some mechanism involving the other basic forces. Or we may discover that matter is the only thing that can warp space; if this proves to be the case, "warp drive" may never be a practical means of propulsion. On Star Trek, we assert that in a starship warp engine, high energy plasma, created by a matter-antimatter reaction, is pumped through a series of warp coils cast from an artificial (and fictional) material called verterium cortenide. Verterium cortenide provides a bridge between electromagnetic and gravitational forces. By design, it has the property that when a high-energy plasma circulates through appropriately fashioned verterium cortenide castings, a "warp field" is generated. Electromagnetic interactions between waves of superhot plasma and the verterium cortenide coils change the geometry of space surrounding the engine nacelles. In the process, a multilayered wave of warped space is born, and the starship cruises off to its next destination at hundreds of times the speed of light (relative to "normal" space); within the warp field, the starship does not exceed the local speed of light, and therefore does not violate the principal tenet of special relativity. From source AB.

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