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This question already has an answer here:

There is a major difference in the warp scales used in Star Trek TOS and TNG onwards (or am I wrong in this?). I was wondering if there was a conversion system out there to see what the equivalent of, say, warp 8 in TOS era was in TNG era?

marked as duplicate by Valorum, The Fallen, neilfein, James Sheridan, Ward Mar 2 '14 at 5:26

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Per Aramis' answer;

 OWF = Old Scale Warp Factor
 NWF = New Scale Warp Factor
   C = Speed in multiples of the speed of light
D/LY = Days per Light year 

 OWF:  1   2    3    4    5    6    7    8    9    10    11    12    13    14    15
   C:  1   8   27   64  125  216  343  512  729 1,000 1,331 1,728 2,197 2,744 3,375
D/LY: 365 45.6 13.5 5.7  2.9  1.7 1.1  0.7  0.5   0.4   0.3   0.2   0.2   0.1   0.1

Post Movies

TNG, DS9 and Voyager use about WF^(10/3) through warp 9.0...

 NWF:    1   2     3      4      5      6      7       8       9
   C:    1  10.1  38.9  101.6  213.7  392.5  656.1  1024.0  1516.4
 OWF:    1   2.2   3.4    4.7    6.0    7.3    8.7    10.1    11.5
D/LY:  365  36.2   9.4    3.6    1.7    0.9    0.6     0.4     0.2

Above 9.0, between 9.0 and 10, the exponent increases dramatically, and warp 10 is theoretically infinite speed.

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