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Power Amplifier Gain Calculator

Calculate power amplifier voltage gain (V/V and dB) and power gain from input/output voltage and power measurements.

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Formula

Av_dB = 20·log₁₀(V_out/V_in)

Av— Voltage gain (V/V or dB)
Ap— Power gain (W/W or dB)

How It Works

Amplifier gain describes how much the output signal is larger than the input signal. Voltage gain (Av) is the ratio of output to input RMS voltage: Av = V_out / V_in. In decibels: Av_dB = 20·log₁₀(Av). Power gain (Ap) is the ratio of output to input power: Ap = P_out / P_in. In decibels: Ap_dB = 10·log₁₀(Ap). For a power amplifier, the input power refers to the power consumed by the amplifier input stage (a small signal power), while output power is the acoustic power delivered to the speaker load. Power amplifiers are characterised by their sensitivity (the input voltage required to produce rated output power), typically 0.775 V (0 dBu) or 1.0 V for professional equipment. Voltage gain of professional power amplifiers is typically 20–40 dB (10× to 100× voltage gain), while power gain can be 60–80 dB or more.

Worked Example

Power amplifier: 1 V RMS input, 28 V RMS output, input power = 0.1 mW, output power = 100 W. Voltage gain: Av = 28 / 1 = 28 V/V Av_dB = 20·log₁₀(28) = 28.9 dB Power gain: Ap = 100 W / (0.1 × 10⁻³ W) = 1,000,000 W/W Ap_dB = 10·log₁₀(1,000,000) = 60 dB Amplifier sensitivity check: At 1 V RMS input → 28 V RMS output → P = 28²/8 = 98 W into 8 Ω ≈ 100 W rated power. Sensitivity = 1.0 V (the input level for rated output) — standard for professional power amps. For a 0.775 V (0 dBu) input standard: Av needed = 28 / 0.775 = 36.1 V/V = 31.2 dB

Practical Tips

  • ✓When cascading amplifier stages, add voltage gains in dB: a preamplifier at +20 dB followed by a power amplifier at +29 dB gives +49 dB total voltage gain. For V/V ratios, multiply: 10 × 28 = 280 V/V total.
  • ✓Power amplifier datasheets may specify 'sensitivity' (input level for rated power output) rather than gain. Convert: Av_dB = 20·log₁₀(V_rated_output / V_sensitivity). For a 1 V sensitivity amp with 100 V output into 8 Ω: Av_dB = 20·log₁₀(100) = 40 dB.
  • ✓Real amplifier gain is not perfectly flat across frequency. Check the frequency response graph in the datasheet — most audio power amplifiers are ±0.1 dB flat from 20 Hz to 20 kHz, but some budget designs show rolloff at the frequency extremes that reduces gain by 1–3 dB.

Common Mistakes

  • ✗Using voltage gain dB for power calculations — voltage gain uses the factor 20·log₁₀, while power gain uses 10·log₁₀. 28 dB voltage gain is not 28 dB power gain. The 10 vs 20 factor difference is the most common decibel calculation error.
  • ✗Comparing amplifier gain specs without considering input impedance — the power consumed by the input depends on both input voltage and input impedance. An amplifier with 10 kΩ input at 1 V draws P = 1²/10000 = 0.1 mW. An amplifier with 600 Ω input at 1 V draws P = 1²/600 = 1.67 mW. Same voltage, very different power gain numbers.
  • ✗Confusing amplifier gain with signal level — a 30 dB gain amplifier takes a −20 dBu input and produces +10 dBu output. The gain is fixed; the output level depends on the input level. Do not confuse gain (a ratio) with output level (an absolute measurement).

Frequently Asked Questions

Professional power amplifiers typically have voltage gain between 23–40 dB (14× to 100× V/V). A 26 dB gain (20× V/V) amp produces 20 V RMS output from 1 V RMS input, delivering about 50 W into 8 Ω. A 40 dB amp produces 100 V from 1 V, delivering ~1250 W into 8 Ω — typical for large-format touring amplifiers.
dBV references 1 V RMS (0 dBV = 1 V). dBu references 0.7746 V RMS (0 dBu = 0.7746 V, the voltage that delivers 1 mW into 600 Ω). A 0 dBu input is 2.21 dB below 0 dBV. When comparing amplifier sensitivity specs, confirm whether the manufacturer uses dBu or dBV to avoid a 2.21 dB systematic error.
Because power gain uses 10·log₁₀ and voltage gain uses 20·log₁₀, a voltage ratio of 28× gives Av_dB = 28.9 dB but translates to Ap_dB = 60 dB power gain when the input impedance (10 kΩ) is much higher than the output load (8 Ω). The power gain includes both the voltage gain and the impedance transformation effect.

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