A received signal usually contains both a desired component and unwanted noise.

If the desired signal has average power $P_s$ and the noise has average power $P_n$, the signal-to-noise ratio is

$$\mathrm{SNR}=\frac{P_s}{P_n}.$$

In decibels,

$$\mathrm{SNR}{\mathrm{dB}}=10\log{10}\frac{P_s}{P_n}.$$

A larger SNR means the desired component dominates the noise more strongly. It does not by itself determine whether communication is reliable: performance also depends on how the signal is represented and how the receiver makes decisions.

SNR must refer to a specified observation point and bandwidth. Filtering can remove out-of-band noise and therefore change the measured SNR even when the desired signal amplitude is unchanged.