The headphone power math, demystified
From sensitivity to required power
For dBSPL/mW sensitivity, required power is P = 10^((target − sensitivity + crest) ÷ 10) mW. The corresponding RMS voltage drops out of Ohm's law: V = √(P × Z) with P in watts and Z in ohms.
For dBSPL/V sensitivity, required voltage is V = 10^((target − sensitivity + crest) ÷ 20), and power follows from P = V² ÷ Z.
Converting the two: dBSPL/V = dBSPL/mW + 10 × log10(Z ÷ 1000). At 300 Ω, dB/V is 5.2 dB lower than dB/mW.
Crest factor: why music needs more headroom than a sine wave
Music isn't a steady tone. Classical recordings can have 18 dB between the average level and the loudest transients; pop and rock typically 8-12 dB; modern EDM is squashed to 4-6 dB. To hear an average loudness of 85 dB without the loudest peak clipping your amp, you need the amp's clean output to reach the average level plus the crest factor.
Pick a genre above and the calculator picks the right crest factor; the requirement jumps accordingly. The math is the same as +1 dB SPL on the sensitivity figure - but the genre presets make it obvious why classical reference monitoring asks for so much more amp than EDM at the same average level.