How this calculator works
Headphone sensitivity says how loud the headphones get for a known electrical input, and impedance says how much voltage is needed to drive a given current through them. Together they answer the practical question for an amplifier: how much power, voltage and current does the pair demand at the loudness you want. Decibels are logarithmic, so every 10 dB of extra loudness means ten times the power, and every 20 dB means ten times the voltage. The 1/8 rule for output impedance comes from damping: an amplifier whose output impedance is below one eighth of the headphone impedance controls the driver well enough that the frequency response does not shift.
Formula
From dB per mW: power in mW = 10^((target loudness - sensitivity) / 10), then voltage RMS = square root of (power in mW / 1000 x impedance). From dB per V: voltage RMS = 10^((target loudness - sensitivity) / 20), then power in mW = voltage squared / impedance x 1000. Current RMS = voltage / impedance in both cases.
Worked example
A 32 ohm headphone rated 110 dB per mW needs exactly 1 mW to reach 110 dB. That is 0.001 W, so the voltage is the square root of 0.001 x 32 = 0.179 V, or 179 mV, and the current is 179 mV / 32 ohm = 5.59 mA. The amplifier output impedance should stay below 4 ohm.
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Frequently asked questions
Why do high impedance headphones need more voltage?
Ohm law. At the same power, a higher impedance needs more voltage and less current, so an amplifier with a limited output voltage runs out of headroom first. This is why 300 ohm headphones often need a dedicated amplifier.
Is sensitivity quoted per mW or per volt?
Both conventions exist. Per milliwatt sensitivities compare how efficient the driver is; per volt sensitivities compare how loud the headphones go for a given amplifier output voltage. The two are related through the impedance, so pick whichever your specification uses.
What loudness should I target?
Music peaks of 100 to 110 dB SPL leave a sensible margin. Sustained listening above 85 dB is a hearing risk, and headphone loudness figures are normally quoted for a 1 kHz tone rather than for music.
What is the 1/8 rule?
It says the amplifier output impedance should be at most one eighth of the headphone impedance. Higher output impedance changes the damping and can tilt the frequency response, most noticeably on low impedance headphones.