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Headphone Amplifier Power

Calculate the amplifier output power, voltage, and current required to drive headphones to a target SPL.

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Formula

P = 10^((SPL − S)/10) mW, V = √(P × Z)

S— Headphone sensitivity (dB/mW)
Z— Headphone impedance (Ω)

How It Works

Headphone amplifier power requirements depend on the headphone's impedance (Z, in Ω) and sensitivity (S, in dB SPL per milliwatt). Unlike speaker sensitivity which is rated at 1 W/1 m, headphone sensitivity is referenced to 1 mW delivered to the headphone. The required power in milliwatts to reach a target SPL is: P_mW = 10^((SPL_target − S) / 10). From this, the required RMS voltage and current follow from Ohm's law: V_rms = √(P_W × Z) and I_mA = (V_rms / Z) × 1000. High-impedance headphones (150–600 Ω) need higher voltage swings, while low-impedance IEMs (8–32 Ω) need higher current. This is why desktop headphone amplifiers with high voltage rails drive planar-magnetic and high-impedance dynamic headphones better than smartphone DAC outputs.

Worked Example

Headphone: 300 Ω impedance, 100 dB/mW sensitivity. Target SPL: 110 dB. Required power: P_mW = 10^((110 − 100) / 10) = 10^1.0 = 10 mW P_W = 10 / 1000 = 0.010 W Required RMS voltage: V_rms = √(0.010 × 300) = √3.0 = 1.73 V Required current: I_mA = (1.73 / 300) × 1000 = 5.77 mA A typical smartphone output maxes at ~1.0–1.5 V RMS, so it can drive these headphones to about 107–108 dB — adequate but with minimal headroom. A dedicated amplifier providing at least 2 V RMS into 300 Ω is recommended for peaks.

Practical Tips

  • ✓For most home use at comfortable volume (~85 dB SPL), power requirements are tiny (under 1 mW). Focus amplifier selection on achieving low noise floor and adequate voltage swing rather than maximum power.
  • ✓Rule of thumb: 100× the required power to reach target SPL gives you 20 dB of headroom — enough for transient peaks without clipping. If you need 1 mW for 90 dB, a 100 mW amplifier gives comfortable headroom.
  • ✓Planar-magnetic headphones (e.g., HiFiMAN, Audeze) are typically 20–60 Ω but have low sensitivity (90–95 dB/mW), requiring both current and voltage — they benefit most from dedicated headphone amplifiers.

Common Mistakes

  • ✗Mixing up sensitivity units — headphone datasheets may quote sensitivity as dB/mW or dB/V (at 1 V RMS). Converting: if sensitivity is given as dB/V, then dB/mW = dB/V − 10·log₁₀(1000/Z). For 300 Ω: dB/mW = dB/V + 10·log₁₀(Z/1000) = dB/V − 5.2 dB.
  • ✗Targeting SPL that risks hearing damage — 110 dB SPL at the ear is safe for only ~1 minute per NIOSH guidelines. 85 dB for 8 hours is the recommended limit. Use the calculator to ensure your amplifier can reach 100–105 dB with headroom, not to maximise output.
  • ✗Ignoring output impedance of the amplifier — a high-output-impedance amp (>10 Ω) forms a voltage divider with the headphone, reducing power delivery and altering the frequency response because headphone impedance is not flat.

Frequently Asked Questions

Smartphones typically output 1–1.5 V RMS into high-impedance loads. For a 300 Ω headphone at 100 dB/mW, 1 V provides P = 1²/300 = 3.3 mW, giving 100 + 10·log₁₀(3.3) ≈ 105 dB — which sounds moderate but leaves almost no headroom. A dedicated amplifier with a higher voltage rail resolves this.
Impedance (Ω) determines how much voltage and current the headphone requires for a given power level. Sensitivity (dB/mW) determines how loudly that power is converted to sound. A high-impedance, high-sensitivity headphone and a low-impedance, low-sensitivity headphone can require the same amplifier power but very different voltage levels.
Yes. A balanced output effectively doubles the voltage swing versus a single-ended output, quadrupling the delivered power into the same load impedance. This is especially beneficial for high-impedance headphones that need high voltage to reach listening levels.

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