Shannon Capacity Calculator (Shannon–Hartley Theorem)

How it works

C = B × log₂(1 + S/N) · S/N (linear) = 10^(SNR_dB ÷ 10) · spectral efficiency = C ÷ B · Eb/N0 = (S/N) ÷ (C/B) · at high SNR each extra 3 dB adds about 1 bit/s/Hz

The Shannon–Hartley theorem (Claude Shannon, 1948, building on Ralph Hartley) gives the highest data rate that can be sent through a channel of bandwidth B with additive white Gaussian noise with an arbitrarily small error rate. No modulation or coding can beat it; modern LDPC and turbo codes come within about 1 dB. Capacity grows linearly with bandwidth but only logarithmically with signal power, which is why systems chase wider channels and MIMO (several spatial streams) rather than more power.

Worked example

A 20 MHz channel at 25 dB SNR (316.2 linear): C = 20,000,000 × log₂(317.2) = 20,000,000 × 8.309 = 166.2 Mbit/s, about 20.77 MB/s. At that rate Eb/N0 = 316.2 ÷ 8.309 = 15.80 dB.

Sources: Shannon, C. E. (1948) — A Mathematical Theory of Communication, Bell System Technical Journal · Wikipedia — Shannon–Hartley theorem

Frequently asked questions