The headphone power math, demystified
From sensitivity to required power
For dBSPL/mW sensitivity, required power is P = 10^((target − sensitivity + headroom) ÷ 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 + headroom) ÷ 20), and power follows from P = V² ÷ Z.
Converting the two: dBSPL/V = dBSPL/mW + 10 × log10(Z ÷ 1000). At 300 Ω, dBSPL/V = dBSPL/mW − 5.2 dB.
Why high-impedance cans need more voltage
At the same SPL/mW figure, a 300 Ω headphone needs roughly 2× the voltage of a 75 Ω headphone, because power scales with voltage squared. Phone outputs and dongle DACs run out of voltage before they run out of current. That is why a 600 Ω DT880 stays quiet on a phone and roars on a desktop amp.
For sanity-checking an amp shop list, look at its rated output at the impedance of your headphone, not at 32 Ω. Most amps publish multiple curves; the conservative buy is one that exceeds your calculated requirement at your impedance with at least 2-3× headroom.