Basically, it is the Speed of Light multiplied to the factor stated. For example, Warp Factor One is the speed of light. Warp Factor Two is the speed of light times the speed of light. Warp Factor Three is the speed of light X the speed of light X the speed of light. And so on... The original USS Enterprise was stated to reach a top speed of Warp Factor Eight. This was the fastest of any Star Trek ship until USS Voyager, which claimed a top speed of Warp Factor 9.98. It was claimed in show dialog that Warp Factor Ten was "the max", meaning nothing could exist beyond that speed. However, every now and then Star Trek ships would exceed Warp Ten whenever alien intruders tampered with the engines.

The factor-cubed equation is mostly correct for warp factors stated in "TOS" and "Enterprise"; however, in the original warp spectrum there was no all-encompassing ceiling to warp speed, save what the ship was able to handle before breaking apart. We see this in the "TOS" episode "That Which Survives" when the ship reaches warp 14, or 2744 times the speed of light. Since then, for the series set after TOS, a new equation has been implemented to calculate warp factors. The new equation is similar to the old, where speed (in terms of multiples of the speed of light, 'c') equaled c * (warp factor) ^ 3. Now, the equation is speed = (warp factor) ^ (10/3), that is c * (warp) ^ 3.3333...; basically a slide of the scale to allow the ship to travel much faster without demanding absurdly high numbers. There is one caveat to this new scale. The new system DOES place a top speed of warp 10. This can't be dealt with by the w ^ 3.33 scale, so for speeds above warp 9, the power the factor is raised to increases to infinity as the numbers get closer to 10.

I believe this answer to be incorrect. He states that the fastest was on Voyager. Two times (Once on the OLD Kirk Enterprise and once on the Enterprise D, Picard's ship) they have broken Warp 10. Kirk's ship did this when a probe/computer mistakenly identified Kirk as his creater. This probe modified the ship and had it doing over Warp 11 before they shut it down. On TNG, one of the lesser engineers (Reggie) was given great mental powers by a playful and friendly alian from the far edge of the universe. With this great mental ability he was able to facilitate modifications to the warp engines producing well above warp 10 without any ramifications whatsover. Regarding the warp facter, I believe that part of the answer to be correct. Light speed is warp 1, then exponentially increased with each warp factor.

The Warp speed that you are traveling.

"Warp travel velocity in Star Trek is generally described in "warp factor" units, which - according to the Star Trek Technical Manuals - correspond to the strength of the warp field. Achieving warp factor 1 is equivalent to breaking the light-speed barrier, while the actual speed of higher factors is determined according to an ambiguous "warp formula". Several episodes of the original series placed the Enterprise in peril by having it travel at high warp factors; in "That Which Survives", this factor was as high as 14.1. However, the actual speed of any given warp factor is rarely explicitly stated on screen, and travel times for specific interstellar distances are not consistent through the various series. According to the Star Trek episode writer's guide for The Original Series, warp factors are supposedly converted to multiples of light speed with the cubic function s(w) = w^3.c . Accordingly, "warp 1" is equivalent to the speed of light, "warp 2" is eight times the speed of light, "warp 3" is 27 times the speed of light, and so on. However, this conflicts with the on-screen application of the technology, as it would make the Enterprise far too slow for the voyages depicted in the television series. These speeds do not even correlate with details presented in some of the episodes. For example, in "That Which Survives" (1969), the Enterprise travels at warp 8.4 for 11.33 hours and traverses 990.7 light years (as indicated in Spock's dialog), which makes the speed more than 600,000 times the speed of light. The Enterprise has also easily traveled to and from the edge of the Milky Way galaxy ("Is There in Truth No Beauty" and "By Any Other Name" (1968)), a journey which should take years at "warp 8" if the actual speed is merely a cube of the warp factor." "For Star Trek: The Next Generation and the subsequent series, Star Trek artist Michael Okuda devised a formula based on the original one but with important differences. For warp 1–9, if w is the warp factor, s(w) is the speed in km per second, and c is the speed of light, then s(w) = w^(3/10).c . In the half-open interval from warp 9 to warp 10, the exponent of w increases toward infinity. Thus, in the Okuda scale, warp speeds approach warp 10 asymptotically. There is no exact formula for this interval because the quoted speeds are based on a hand-drawn curve." Source and further information: http://en.wikipedia.org/wiki/Warp_factor#Warp_velocities http://en.wikipedia.org/wiki/Image:Warptable.gif