The signal-to-noise ratio is the ratio of the average power 
of a signal to the average power 
of its noise,
 |
When signal and noise are measured by root-mean-square amplitudes 
and 
across the same impedance, this is 
. Signal-to-noise ratios are therefore dimensionless.
The ratio is often expressed in decibels using a base-10 logarithm as 
. In the Shannon-Hartley theorem, the dimensionless
ratio 
determines the channel capacity available in
a fixed bandwidth.
