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

**Formula**

In the case of a linear power ratio:

**P _{dB} = 10*Log_{10}(P_{linear})**

**P _{linear}** =

**10**

^{(PdB/10)}In the case of a linear voltage ratio:

**P _{dB} = 20*Log_{10}(V_{linear})**

**V _{linear}** =

**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 **P _{dB} = 10*Log_{10}(P_{linear})**. Where P

_{linear}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

**P _{linear} = P_{OUT}/P_{IN}**

**P _{linear} = 5W/2W = 2.5**

In this case

**P _{dB} = 10*Log_{10}(2.5) = 3.98 dB**

**Linear ratio of Voltage **

In the case or voltage or field, the following formula applies **V _{dB} = 20*Log_{10}(V_{linear})**. Where V

_{linear}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

**V _{linear} = V_{OUT}/V_{IN}**

**V _{linear} = 5V/2V = 2.5**

In this case

**P _{dB} = 20*Log_{10}(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*Log_{10}(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.

## Further Reading

- dBm vs dB – what’s the difference?
- dB difference – how to calculate and what doe it mean?