# dB Gain Calculator

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:

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:

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**:

- Enter the value of
`2 W`

into the field "Initial power". - Choose the value of
`400 W`

and put it in the field "Final power". - 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**.

- Enter the initial voltage of
`2 V`

and the final voltage of`400 V`

into the appropriate fields of the db gain calculator. - 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:

- Put
`P₂ = 150 W`

and`dB = 20`

in the equation:

**10log₁₀(150 W/P₁) = 20**. - Use the antilog to find the P₂:

**150 W/P₁ = 10**.^{20/10}= 10^{2}= 100 - Find that:

**150 W/P₁ = 100**, and

**P₁ = 150 W/100 = 1.5 W**. - 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**:

- Use the formula for voltage gain in dB:
`dB = 20log₁₀(V₂/V₁)`

. - Insert
`V₁ = 12 V`

and`dB = -10`

:

**-10 = 20log₁₀(V₂/12 V)**

**-0.5 = log₁₀(V₂/12 V)** - Use the antilog of the base 10:

**10**^{0.5}= V₂/12 V

**0.3162 = V₂/12 V**

**V₂ = 0.3162×12 V = 3.79 V**.