Shannon Capacity

$C = B \log_2\left(1 + \frac{S}{N}\right)$

• $C$ — capacity in bit/s,
• $B$ — bandwidth in Hz,
• $S/N$ — signal-to-noise ratio as a power ratio (not dB).

Example: a 3 kHz telephone line with 30 dB SNR ($S/N$ = 1000) has $C$ ≈ 3000 × log₂(1001) ≈ 30 kbit/s. More bandwidth or a cleaner signal raise the limit; clever coding gets close to it but can never exceed it.