dB Gain Calculator — Power & Voltage Gain in Decibels (10·log and 20·log)

Whether you're learning to record music, working as a mixing engineer, or playing with your first guitar pedals, this dB gain calculator helps you adjust the loudness of the sound you create. Think of gain as the difference in signal strength in your audio system or processor. Here you can specify the dB gain as a power or voltage change ratio and calculate power or voltage gain in dB — or work backwards from a decibel value to the underlying ratio.

Understanding what gain is can be the key to changing the way your mixes sound for the better. Don't worry if it sounds a bit complicated at the moment! Read on to find out how you can create better mixes through the proper use of gain.

What is gain?

Generally, gain in audio describes the amount of amplification applied to a signal — or, simply, the loudness of the generated sound. If you are analyzing circuits in the frequency domain, it is more convenient to compare the ratio of output to input values on a logarithmic scale than on a linear scale.

Using the logarithmic ratio of two quantities gives you a new quantity that can be represented in decibels (or dB for short). In the name decibel, 'deci' means one-tenth (1/10) of a Bel; hence there are 10 decibels (10 dB) per Bel, or 1 Bel = 10 decibels.

To understand what dB means, remember that it is a ratio used to compare and calculate levels of power change. Unlike voltage or current, which are measured in volts and amperes respectively, the decibel is a dimensionless quantity. Because gain is a ratio, the units of the two signals cancel out — so the dB result is identical whether you enter your values in the metric system (watts, volts) or with American units such as horsepower.

💡 The 'Bel' term in "decibel" comes from the famous inventor of the telephone, Alexander Graham Bell.

Formula for gain in dB

We can use the decibel gain to compare and calculate the levels of change of two power quantities. This dB gain calculator uses the following equation to find power gain:

dB = 10 × log₁₀(P₂ / P₁)

where:

• dB — Decibel gain in dB;
• P₂ — Final power level (output), in watts; and
• P₁ — Initial power level (input), in watts.

For example, use an input signal of 100 mW to power a speaker and get a 100 W signal at the output. The formula for gain in dB will be:

dB = 10 × log₁₀(100 W / 0.1 W) = 10 × log₁₀(1000) = 30 dB

Voltage gain in dB

When you work with voltage (or any field quantity such as current or sound pressure) rather than power, the multiplier in the formula changes from 10 to 20. This is because power is proportional to the square of the voltage (P ∝ V²), and squaring inside the logarithm doubles the coefficient:

dB = 20 × log₁₀(V₂ / V₁)

where:

• V₂ — Output voltage; and
• V₁ — Input voltage.

This is why a voltage ratio of 2× equals about 6 dB, while a power ratio of 2× equals only about 3 dB. Doubling the voltage quadruples the power.

How to convert gain to dB? – example

Let's walk through the 100 mW → 100 W example step by step:

1. Pick the calculation mode. Select "Power Gain" because we know the input and output power.
2. Enter the input power. Type 100 and choose the unit mW (milliwatts) for P₁.
3. Enter the output power. Type 100 and choose the unit W (watts) for P₂.
4. Read the ratio. The calculator converts both values to watts: P₁ = 0.1 W, P₂ = 100 W, so the power ratio P₂/P₁ = 1000.
5. Read the gain. dB = 10 × log₁₀(1000) = 30 dB.

You can also run the calculation in reverse: choose the "dB → Power Ratio" mode, enter 30 dB, and the calculator returns a power ratio of 1000× (or use "dB → Voltage Ratio" to get the corresponding voltage ratio of 31.6×).

Quick reference: common gain values

FAQs

What is the difference between power gain and voltage gain in dB?

Power gain uses the factor 10 (dB = 10·log₁₀(P₂/P₁)), while voltage gain uses the factor 20 (dB = 20·log₁₀(V₂/V₁)). The factor of 20 appears because power is proportional to the square of voltage. For the same dB value, the voltage ratio is the square root of the power ratio.

Why is a 3 dB gain often called "double the power"?

Because 10 × log₁₀(2) ≈ 3.01 dB. So every +3 dB roughly doubles the power, and every −3 dB roughly halves it. For voltage, doubling happens at +6 dB instead.

Can gain in dB be negative?

Yes. A negative dB value means attenuation (loss) — the output is smaller than the input. A positive value means amplification, and 0 dB means the signal is unchanged (unity gain).

Do the units of measurement matter?

No — because gain is a ratio, the units cancel as long as both signals use the same kind of quantity (both powers or both voltages). You may enter values using metric units (watts, volts and their prefixes) or American units such as horsepower; the resulting gain in dB is exactly the same.

What does 0 dB gain mean?

0 dB means the output equals the input (a ratio of 1). The signal passes through without being amplified or attenuated. This is also called unity gain.