I don't know what the most cursed unit conversion factor out there is but I think a strong contender has to be American Wire Gauge, in which the ratio between any two consecutive gauges is defined to be the thirty-ninth root of ninety two.
Apparently they defined gauges 1 and 40 (ok, 0000 and 36), and since 0000 is 92 times wider than 36, yeah, ³⁹√92 it is 🤷
This is fine because (³⁹√92)⁶ is basically 2.
It is all very silly, I assume there was some reason it seemed like a good idea at the time.
