# dB Gain Calculator

Created by Joanna Śmietańska
Reviewed by Wojciech Sas, PhD and Adena Benn
Last updated: Jan 03, 2023

Whether you're learning to record music, be a mixing engineer, or play with your first guitar pedals, check out this dB gain calculator to 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.

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 generated sound. If you are analyzing circuits in the frequency domain, it will be more convenient to compare the ratio of output to input values on a logarithmic scale than on a linear scale. Check out our power converter to learn more about units of power.

Using the logarithmic ratio of two quantities will give you a new quantity that can be represented by 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. If you need to find sound intensity levels in decibels, look at our dB calculator.

💡 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:

$\small \text{dB} = 10 \log_{10} (P_2/P_1)$

where:

• $\text{dB}$ - Decibel gain in dB;
• $P_2$ - Final power level (output) in watts; and
• $P_1$ - 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 = 10log₁₀(100 W/0.1 W) = 10log₁₀(1000) = 30 dB.

🙋 Are you looking for a material to mute loud noises in your environment? Then this sound absorption coefficient calculator will be helpful. You can also check the speed of sound in air and other mediums.

## Voltage gain in dB

When calculating the voltage gain in dB, you can also use the input ($V_1$) and output ($V_2$) voltages:

$\small \text{dB} = 20 \log_{10} (V_2/V_1)$

As you can see, the only difference between the power and voltage gain calculations in dB concerns the constants 10 and 20 in the equation. It is also essential that the dB ratio is correct in all instances, so both quantities must have the same units, such as watts or volts.

## How to convert gain to dB? - example

Let's say we have an amplifier that delivers 2 W at the input and 400 W at the output. We can use this dB gain calculator to easily find the power gain in dB:

1. Enter the value of 2 W into the field "Initial power".
2. Choose the value of 400 W and put it in the field "Final power".
3. Read the power gain value in dB: 23.01.

In another case: input and output values are the same, but the power level is expressed in volts.

1. Enter the initial voltage of 2 V and the final voltage of 400 V into the appropriate fields of the db gain calculator.
2. Check the value of voltage gain in dB: 46.02.

Note that it is twice the power gain, as we simply used a factor of 20 rather than 10 in the equation.

## FAQ

### What does dB mean?

A dB or decibel is a dimensionless unit that measures the ratio between two numbers. We use decibels to show the ratio of changes in power (increasing or decreasing). It is commonly defined as ten times the Base-10 logarithm of two power levels. Note that 1 watt to 10 watts is the same power ratio as 9 watts to 90 watts, or 1:10, although there is a big difference in the number of watts.

### Can dB gain be negative?

Yes. This situation occurs if the ratio of powers P₂/P₁ or voltages V₂/V₁ in the formula for gain in dB is less than 1. This means that there is an input power loss in the system. If the ratio of power or voltage is equal to 1, the gain is 0 dB, and therefore the circuit does not produce any gain or loss between the signals.

### What will be the input power if dB gain is 20 and output is 150 W?

1.5 W. Calculate it easily as follows:

1. Put P₂ = 150 W and dB = 20 in the equation:
10log₁₀(150 W/P₁) = 20.
2. Use the antilog to find the P₂:
150 W/P₁ = 1020/10 = 102 = 100.
3. Find that:
150 W/P₁ = 100, and
P₁ = 150 W/100 = 1.5 W.
4. Compute the maximum initial (input) power as 1.5 W.

### What will be the output voltage when dB is -10 dB and input voltage is 12 V?

The output voltage is 3.79 V. You can solve this by knowing how to convert gain to dB:

1. Use the formula for voltage gain in dB: dB = 20log₁₀(V₂/V₁).
2. Insert V₁ = 12 V and dB = -10:
-10 = 20log₁₀(V₂/12 V)
-0.5 = log₁₀(V₂/12 V)
3. Use the antilog of the base 10:
100.5 = V₂/12 V
0.3162 = V₂/12 V
V₂ = 0.3162×12 V = 3.79 V.
Joanna Śmietańska
Power gain in dB
Initial power in watts (P₁)
W
Final power in watts (P₂)
W
dB gain
dB
Voltage gain in dB
Initial voltage in volts (V₁)
V
Final voltage in volts (V₂)
V
dB gain
dB
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