This tool converts from **Power Ratio** to **dB** or deciBel.

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

**Formula**

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

**P _{ratio}** =

**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.

A ratio has no units as the input and the output are expressed in the same units. For instance, in the case of power this could be Watt.

The dB scale is a convenient way to represent both large and small numbers. 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*Log_{10}(100) = 20 dB greater than B.

**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.