# Power Ratio to dB

This tool converts from Power Ratio to dB or deciBel.

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

???? dB to Power Ratio

## Formula

PdB = 10*Log10(Pratio)

Pratio = 10(PdB/10)

## Background

A Ratio is a measure of how many times one number contains another. In this case, if the output power is 5 times the input power, then Pout:Pin = 5:1. Alternatively Pin:Pout is 1:5 and it can also be expressed as a fraction 1/5 or 0.2.

A ratio has no units. The input and the output are expressed in the same units to compute the ratio correctly. For instance, in the case of power this could be Watt. For the ratio to make sense, both Pin and Pout should be expressed in Watt.

The deciBel or dB scale is a convenient way to represent the ratio of both large and small amplitude levels. For instance, the ratio 10000000000:1 = 100 dB while 0.0000000001:1 = -100 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 10*Log10(100) = 20 dB greater than B.

## Notes

• Power is always a number greater than or equal to zero. It is a positive number
• Within the context of this conversion, ratio is referred to as linear value. Sometimes it is also referred to as a normal value as in what most people are familiar with on a non-logarithmic scale.

## Example Calculation

Let’s say an amplifier module increases the input signal power by a factor of 1000. The ratio of output to input is 1000:1. Using the calculator, we can say that it is a 30 dB amplifier. The gain of an RF amplifier is almost always specified in terms of dB.

## 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 ratio of 1000000000000000 = 150 dB
• When performing computations in communication systems such as calculating the gain in a receive 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 – much more difficult to do this in your head ????.