# Voltage Ratio to dB

This tool converts from Voltage Ratio to dB or deciBel.

Enter the Voltage Ratio (a positive real number) to get the equivalent dB value.

## Formula

PdB = 20*Log10(Vratio)

Vratio = 10(PdB/20)

## Example Calculations

A voltage ratio of 10 is equivalent to 20 dB. A voltage ratio of 0.1 is equivalent to -20 dB.

## Background

A Ratio is a measure of how many times one number contains another. In this case, if the output voltage is 25 times the input power, then Vout:Vin = 25:1. Alternatively Vin:Vout is 1:25 and it can also be expressed as a fraction 1/25 or as a number 0.04.

A ratio has no units as the input and the output are expressed in the same units. For instance, in this case it’s Volt.

The dB scale is a convenient way to represent both large and small numbers. For instance, the voltage ratio 10000000000:1 = 200 dB while 0.0000000001:1 = -200 dB.

The dB value does not 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 20*Log10(100) = 40 dB greater than B.

## Example calculation

Let’s say an operational amplifier increases the input signal voltage by a factor of 100. The ratio of output to input is 100:1. Using the calculator, we can say that it is a 40 dB amplifier.

## Why Convert to dB?

There are a few reasons for this. Here are a couple of main ones:

• the dB scale makes it easy to represent large and small ratios in fewer digits. For example a voltage ratio of 10000000 = 140 dB
• When making calculations in Radio Frequency systems such as calculating the gain in a transmitter chain, it’s easy to add and subtract gain and attenuation expressed in dB. For example, consider a signal chain consisting of two amplifiers with gain levels 10 and 15 dB and a 3 dB insertion loss equates to a total gain of 22 dB. RF component vendors specify gain and attenuation in dB so it’s easy to get these numbers from a data sheet and even do the arithmetic mentally (if there are a small number of components). Operating in the linear regime means you have to multiply and divide. It’s much more difficult to do this in your head, unless you’re a super math nerd 🤓.