dB Gain Calculator

For power: dB = 10 × log10(Pout / Pin). For voltage (or current): dB = 20 × log10(Vout / Vin). The 10-log form is the original definition of the decibel (a power ratio); the 20-log form is the same physics rewritten for voltage, because power is proportional to voltage squared. This calculator applies both forms automatically.

Divide the output voltage by the input voltage to get the voltage ratio, then multiply the base-10 logarithm by 20: dB = 20 × log10(Vout/Vin). For example, a voltage gain of 10 becomes 20 × log10(10) = 20 dB. A voltage gain of 2 becomes 20 × log10(2) ≈ 6.02 dB. Use this calculator's voltage mode to do the math instantly.

Divide the output power by the input power to get the power ratio, then multiply the base-10 logarithm by 10: dB = 10 × log10(Pout/Pin). For example, a power gain of 10 becomes 10 × log10(10) = 10 dB. A power gain of 2 becomes 10 × log10(2) ≈ 3.01 dB. Use this calculator's power mode.

Raise 10 to the power of dB divided by 20: voltage ratio = 10^(dB/20). For example, 20 dB converts to 10^(20/20) = 10, so the output voltage is 10 times the input voltage. 6 dB converts to 10^(6/20) ≈ 2. This calculator's dB-to-ratio mode does the conversion in one step.

Raise 10 to the power of dB divided by 10: power ratio = 10^(dB/10). For example, 10 dB converts to 10^(10/10) = 10, so the output power is 10 times the input power. 3 dB converts to 10^(3/10) ≈ 2, the classic doubling of power. Use this calculator's dB-to-ratio mode with power selected.

Because power is proportional to voltage squared (P = V²/R). Taking 10 × log10 of a squared quantity moves the exponent out front: 10 × log10(V²) = 2 × 10 × log10(V) = 20 × log10(V). So 20 log for voltage and 10 log for power are the same physical definition of the decibel, just expressed in different units.

3 dB gain means the power has doubled: 10 × log10(2) ≈ 3.01 dB. In audio, a +3 dB change is a small but noticeable increase in loudness. In RF engineering, a 3 dB attenuator (pad) cuts power in half.

6 dB gain means the voltage (or current) has doubled: 20 × log10(2) ≈ 6.02 dB. For power, +6 dB means roughly four times the power (10 × log10(4) ≈ 6.02 dB). In audio, +6 dB sounds clearly louder; in mixers it is the classic doubling of a fader level.

10 dB gain means the power has increased by a factor of 10: 10 × log10(10) = 10 dB. For voltage, +10 dB means the voltage ratio is 10^(10/20) ≈ 3.16. Psychoacoustically, +10 dB is perceived as roughly twice as loud.

dBm is decibels relative to 1 milliwatt: dBm = 10 × log10(P / 1 mW). To convert dBm to watts, compute P = 10^(dBm/10) milliwatts, then divide by 1,000. For example, 30 dBm = 10^3 = 1,000 mW = 1 W; 0 dBm = 1 mW; -30 dBm = 0.001 mW. This calculator's dBm/dBW mode converts dBm to watts, milliwatts, microwatts, and dBW instantly.

Add 30: dBm = dBW + 30. This is because 1 watt = 1,000 milliwatts, and 10 × log10(1,000) = 30 dB. So 0 dBW (1 W) = 30 dBm, and 20 dBW (100 W) = 50 dBm. Subtract 30 to go the other way (dBW = dBm − 30).

Yes — negative dB means attenuation (loss) rather than gain. A ratio of 0.5 converts to 10 × log10(0.5) ≈ −3 dB (power) or 20 × log10(0.5) ≈ −6 dB (voltage). A ratio of 1 is exactly 0 dB (unity gain), and ratios between 0 and 1 always give negative dB values.

Add the gains in dB: total gain = G1 + G2 + G3 + ... in decibels. This works because multiplying ratios is the same as adding logarithms. For example, a 12 dB preamp followed by a 6 dB line amplifier gives 18 dB total, which is a voltage ratio of 10^(18/20) ≈ 7.94. This calculator's cascade mode adds any number of stages and shows the total as a voltage and power ratio.

dB is a relative ratio with no fixed reference — it only makes sense between two values. dBm, dBW, and dBV are absolute because they reference a fixed unit: dBm = relative to 1 mW (power), dBW = relative to 1 W (power), dBV = relative to 1 V (voltage). 0 dBm = 1 mW, 0 dBW = 1 W, and 0 dBV = 1 V RMS.

In gain terms, 0 dB means unity gain: the output equals the input (ratio of 1). It is not silence. Confusingly, 0 dB SPL means something different — it is the reference threshold of human hearing in acoustics — and 0 dBFS is the maximum level in digital audio. For amplifier gain, 0 dB simply means no change.

Yes. This dB gain calculator is free, runs 100% in your browser, and sends nothing to any server — no sign-up, no tracking, no data leaves your device. It converts voltage gain to dB, power gain to dB, dB to ratios, dBm and dBW to watts, and sums cascade gains.