The Shannon-Hartley theorem gives the channel capacity 
of a band-limited channel with additive
white Gaussian noise as
![C=Blog_2[1+S/N],](/images/equations/Shannon-HartleyTheorem/NumberedEquation1.svg) |
where 
is the bandwidth in hertz, 
is the average power of the
signal, and 
is the average power of the noise in that bandwidth.
The capacity is measured in bits per second.
The theorem states an upper bound on reliable communication rather than a rate attained by every coding scheme. Rates below 
can be approached with arbitrarily small error by sufficiently
long codes, whereas rates above 
cannot. Writing 
as the signal-to-noise
ratio shows the tradeoff between bandwidth and signal quality.
