Only infrequently a distance is directly given in a Star Trek episode, but quite often sentences are used like "travelling this distance will take us 23 days at warp 8, and only about 15 days at warp 9". Because we have a warp formula confirmed on screen, we can calculate distances very easily by using these indirect statements.
However, there are great discrepancies above warp 9.6, therefore inputs above that speed are invalid.
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