Warp 1 is c (the speed of light) and is 186,240 mps...
Also you should know that it doesn't scale up. Warp speeds increase on a curve, so Warp 9 isn't 9 times faster than Warp 1
It seems roughly (at least on the old scale) that warp 1 is the speed of light, warp 2 is about 10c, 3 is 100c, 4 is 1000c, etc. At least, that's hinted on in Enterprise (as they mention how fast they're travelling in km/h, and it's 1000 times the speed of light if I remember correctly)
Kitface 10:46, June 14, 2011 (UTC)
It should be noted that 'warp' was redefined at some point between the 23rd and 24th centuries. In TOS (and so, presumably, ENT) the scale increased at a lower rate than in TNG and onward. In TNG and onward, warp 10 represented infinite speed. This was made explicit in an episode of Voyager. It was not so in the TOS timeperiod.
I believe the Warp scale in the TOS timeframe was logarithmic, but was later redefined using the TNG scale of Warp 10 being infinite velocity or "existing in all places simultaneously" (Voyager: Threshold).
There may also be the possibility that warp factors (at least in TNG) are not directly translatable to specific velocities. It may refer to the degree of the "warping" of space/subspace that is occurring within the warp-field encapsulating the ship. There are several instances where distances and travel time are mentioned, and the numbers vary wildly. One such example is the TNG episode "Clues" where the Enterprise crew is rendered unconscious, their memories are wiped, and the ship is moved just over a parsec away in order to protect the secrecy of an extremely xenophobic race. Riker exclaims that they were moved "over a day's travel" in seconds, while in other episodes (not counting those where the ship experiences extraordinary engine performance, such as "Where No One Has Gone Before") the helmsman reads out that the ship has covered over a parsec in just a few minutes. (The episode with the "hole" in space, and the "experimenter" Nagilum trapped the ship and wanted to kill 1/3 to 1/2 the crew in order to fully understand "death". It was a second-season episode, because when they first contacted the being, Dr. Pulaski was on the bridge, and it "grabbed" her and threw her against a wall as it said "this one is different" meaning female, and then asked for a demonstration of procreation.)
From TNG on warp 1 equals the speed of light while warp 10 means infinite speed, with an exponential curve in between. __
Although everything I have read over the years pegs warp 1 at or around light speed (give or take), there is a measurement used over and over that is interesting. In Voyager as well as several episodes of TNG, they reference that they are 75000 light years and say that that will take them 75 years to get home at maximum warp. Max warp for Voyager is pretty fast so I have to assume they are scaling it down to Warp 9. Sorry, I am a history teacher, not a math teacher so I cannot do that bit of physics algebra. But it stand that at warp nine, you can do 1000 light years per year (that makes my head hurt). But that still doesn't add up given that Vulcan is only a few light years away and it doesn't take but a few hours to get there. Or am I really confused?
Infinite speeds and time dialation may or may not apply to definitions of warp depending on your particular show of the moment, but that's not to say that warp is ever TV-packaged in conventional speed terms, because cannon sources I know of generally keep the methods of calculation of arrival times at warp speeds a mystery. For the purposes of TNG, perhaps warp speeds are greater than c, and impulse are "sub-warp." To venture a guess, Warp 1 is 671,000,000 MPH, the approximate speed of light.
188.8.131.52 19:13, October 4, 2011 (UTC)
Just wanted to say that although it would take 75 years to travel 75 000 light years, that is at the normal/most efficient warp which is, I think, warp 6.2. Voyager hardly ever travels at warp 9 on their trip to the alpha quadrant.