How to use the Shannon Channel Capacity Calculator
- 1. Enter bandwidthFor example 3k for a 3 kHz telephone channel.
- 2. Enter SNRIn dB or as a plain ratio S/N.
- 3. See capacityOptionally add signal levels M and a target data rate.
Shannon-Hartley theorem
The highest error-free data rate over a noisy channel is C = B log₂(1 + S/N) bits per second, where B is the bandwidth in hertz and S/N is the plain power ratio (not dB). Convert dB first with S/N = 10SNR_dB/10.
Worked example: a telephone line with B = 3,000 Hz and SNR = 30 dB. S/N = 10³ = 1,000, so C = 3,000 × log₂(1,001) = 3,000 × 9.967 = 29,902 bps, about 30 kbps. If S/N = 3,162 (35 dB), C = 3,000 × log₂(3,163) = 34,881 bps.
The noiseless Nyquist formula, C = 2B log₂M, gives the rate for M signal levels. Shannon tells you the ceiling; Nyquist tells you how many levels you would need to approach it, about M = √(1 + S/N).
Exam questions
- Find the capacity of a channel with B = 1 MHz and SNR = 63 (C = 6 Mbps).
- Find the minimum SNR to send 50 kbps through 3 kHz: S/N = 2R/B − 1.
- How many signal levels are needed to reach the Shannon limit?
- Why can doubling bandwidth help more than doubling power?
Capacity grows linearly with bandwidth but only logarithmically with signal power, which is the key trade-off in communication system design.
Frequently asked questions
Is the Shannon capacity achievable?
It is a theoretical upper limit. Good modern codes such as LDPC and turbo codes get close, but real systems always run somewhat below it.
Why must SNR be a ratio and not dB?
The formula uses the power ratio inside the logarithm. Using 30 instead of 1,000 would give a wrong, much smaller answer.
What is spectral efficiency?
It is C/B in bit/s/Hz, the data rate per hertz of bandwidth. At 30 dB SNR the Shannon limit is about 10 bit/s/Hz.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.