# Linear to dB Calculator

This tool converts from Linear value to Log or dB (deciBel).

ðŸ”„ dB to Linear

## Formula

In the case of a linear power ratio:

PdB = 10*Log10(Plinear)

Plinear = 10(PdB/10)

In the case of a linear voltage ratio:

PdB = 20*Log10(Vlinear)

Vlinear = 10(PdB/20)

## Example application

### How to use the linear to dB calculator

• Enter the linear value
• Use the radio button to indicate if it’s a power or voltage ratio
• The tool will calculate the power ratio in dB

### Example calculation

Let’s say an amplifier module amplifies the input signal power by a factor of 10,000. Using the calculator, we can say that it is a 40 dB amplifier. The gain of an amplifier is almost always specified in terms of dB.

ðŸ’¡It is important to understand if the specification is for voltage gain or power gain. In the case of an RF amplifier, it’s power gain. For an operational amplifier, it’s often voltage gain. Check the data sheet to be absolutely sure or the calculation could be off by a significant amount!

If the amplifier in this example is an op amp with an output voltage swing that is 10,000 times the input voltage, the gain is 80 dB. In this calculation we assume that the input and output impedance is the same.

## Background

The deciBel or dB scale is a convenient way to represent both large and small numbers. For instance, the following linear ratios of power 10000000000 = 100 dB while 0.0000000001 = -100 dB.

dB is used to represent the ratio of two power or voltage levels.

### Linear ratio of power

In the case or power or energy, the following formula applies PdB = 10*Log10(Plinear). Where Plinear is the ratio of two power levels.

For example the ratio of output power (5 Watt) to input power (2 Watt) of an amplifier can be represented as

Plinear = POUT/PIN

Plinear = 5W/2W = 2.5

In this case

PdB = 10*Log10(2.5) = 3.98 dB

### Linear ratio of Voltage

In the case or voltage or field, the following formula applies VdB = 20*Log10(Vlinear). Where Vlinear is the ratio of two power levels.

For example the ratio of output voltage (5 Volt) to input voltage (2 Volt) of an amplifier can be represented as

Vlinear = VOUT/VIN

Vlinear = 5V/2V = 2.5

In this case

PdB = 20*Log10(2.5) = 7.96 dB

### Units

Neither the linear value representing the ratio nor the equivalent dB value have units. If a number A is 100 times greater than another number B, then on the log scale we can say that A is 10*Log10(100) = 20 dB greater than B.

It is important to note that the dB scale is logarithmic, meaning that small changes in dB correspond to large changes in the actual power level. This conversion ratio is widely used in various fields, such as telecommunications, radio frequency engineering, and audio engineering.