In the Original Series, according to the Star Trek episode writer's guide, warp factors were supposedly converted to multiples of light speed with the cubic function s(w) = w3c. With that being said, that means the table for the Original Series warp speed is as follows: See Chart http://en.wikipedia.org/wiki/Warp_speed under heading Warp Velocities However, this cannot possibly be the whole story, as it would make the Enterprise far too slow for the voyages depicted in the television series. These speeds do not even correlate with solid facts and figures in some of the episodes, for example in That Which Survives the Enterprise travels at warp 8.4 for 11.33 hours and traverses 990.7 light years (as indicated in Spock's dialogue), which makes the speed more than 600,000 times the speed of light, which is two orders of magnitude larger than even warp 15. There is also the fact that the Enterprise could quite easily travel to and from the edge of the galaxy at will (Is There in Truth No Beauty and By Any Other Name), a journey which should take years at the typical warp 8, if warp 8 is merely a cube of the warp factor. This discrepancy between the behavior of warp speeds in the show and the simple formula of the warp factor cubed was picked up by fans in the 1970's and 80's who published books like Star Trek Maps (all published material is considered non-canon, even if it is by Paramount-approved Pocket Books) where the idea of an additional factor, referred to as the Chi factor or the Cochrane factor, was used in the warp calculations. The idea was that since warp drive pulls in space, you get higher speeds in areas where there is high density of mass, and lower speeds in areas of low density. If we take a warp factor and cube it, we take that product and multiply it by the number 1292.7238 (the Chi or Cochrane factor), to get the actual speed that the ship travels at (this is the number that was factored out of the factoids from That Which Survives). The Cochrane factor represents an "average" density of space in the UFP. Other areas of space will have different values for it. This is one way to explain the relationship between stated warp factors and actual calculable speeds as given in the dialogue in the episodes. Although it is not actually canon, it at least explains how the ships behaved as they did, without having to find higher exponents to factor the warp base numbers by, as Star Trek artist Michael Okuda did later for TNG (which nobody on the show ended up paying attention to anyway). The new warp scale and power usageFor the later series, Okuda devised a formula based on the older one but with important differences. For warp 1â??9, if w is the warp factor, s is the speed in km per second, and c is the speed of light, then . 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. Here is a table with new-style warp factors and their approximate values in kilometers per second and multiples of c: See Chart http://en.wikipedia.org/wiki/Warp_speed under heading Warp Velocities Here is a table of the times it would take to cover a number of distances. Since warp 1 is c, the distances for warp 1 (in years) is the light year distance. Earth's solar system is approximately 1.2x1010 km wide, measured as the diameter of the Oort Cloud. See Chart http://en.wikipedia.org/wiki/Warp_speed under heading Warp Velocities The later series were better at keeping to these speeds than the original; however, they were still far from perfect. Later episodes of Star Trek: The Next Generation (such as "Descent") contradicted these speeds and Star Trek: Deep Space Nine depicted Federation Starfleet strategic operations (fleet movements) which would have been impossible under the Okuda scale. Star Trek: Voyager, though its premise was generally based on the Okuda scale, had several notable instances, such as in the episode "Parallax" or "The 37's", where the stated warp velocities varied wildly from the Okuda standard. In general, the farther away a Star Trek show is in production date from the publish date of the Star Trek Technical Manual, the more likely a ship would be to travel at the "speed of plot". For example, in the Star Trek: Enterprise pilot episode they give a time and speed to Neptune that accords with the original series' formula, but then they estimate a trip to the Klingon Homeworld at warp 5 as a four-day journey, placing it just one light-year away from Earthâ??far closer than the nearest stellar system, Alpha Centauri. This plot hole has later been wrapped up by various sources that suggest that there is a spatial rift that allowed the Enterprise to arrive at the Klingon homeworld in such a short length of time, and that it was the Vulcans who provided Enterprise with the whereabouts of this shortcut. It should be noted, however that such a high speed for warp 5 is consistent with the extremely high speed given for warp 8.4 in That Which Survives, which has the speed at over 600,000 times lightspeed (therefore warp 5 would be 161,500 times lightspeed). In those terms, four days travel at warp 5 places the Klingon homeworld at 1,772 light years (or 536 parsecs) away from Earth. This is why any theory matching a warp factor to a specific speed is inconsistent with the show. Imagine driving on a highway under ideal weather conditions: it is quite possible to order a speed of 100 km/h and expect the order to be executed. Try leaving the highway and driving on diverse terrain, and maintaining a specific speed is no longer meaningful. All one cares about is keeping the engine intact, which in Star Trek terms is equivalent to maintaining a safe warp factor and estimating travel times based on the properties of the area of space. Newer engines may allow a greater cochrane output per warp factor and have no minimum beyond warp nine. Finally, many kinds of engines could be built over the years with different limitations and different cochrane-levels per warp factor. Source: Wikipedia

It is true that E=mc^2, however that calculation has no reference on the warp speed equation. Vmax in Star Trek has been arbitrarily established at the level of Warp Factor 10 by the ST:TNG writers. There is no calculation for Warp Factor 10, at that speed you are literally at everywhere in the universe at the same time. >>The Star Trek: Voyager episode "Threshold" agreed with this, in that the characters said attaining the velocity of warp 10 was impossible — but then they achieved it anyway. In this episode, Tom Paris describes that, while travelling at warp 10, he is concurrently in every part of the universe. [Source: Wikipedia] The highest speed (from a canon source) that follows the calculation above [s=c*(w^(10/3)). where s = speed; c = speed of light; w = warp factor] is Warp 9.975. This equates out to a speed of 2.3 trillion km/hour. By rearranging E=mc^2 to c=(m/E)^1/2 then you can substitute c in s=c*(w^(10/3)) so the final equation is s=(m/E^(1/2))*(w^(10/3)). However, this equation will not solve for Vmax.