Calculate Shannon-Hartley channel capacity, bandwidth, or SNR from any two values, with link budget inputs to estimate capacity and spectral efficiency.

Ideal band-limited additive white Gaussian noise channel. Capacity is a theoretical limit, not a prediction of practical throughput.

Shannon Hartley Theorem Formula

The following formula is used to calculate the channel capacity.

C = B × log2(1 + SNR)

Variables:

  • C is the channel capacity (bits per second)
  • B is the bandwidth of the channel (Hz)
  • SNR is the linear signal-to-noise power ratio (dimensionless), not its decibel value

To calculate the channel capacity, multiply the bandwidth of the channel by the logarithm base 2 of one plus the signal-to-noise ratio.

What is the Shannon Hartley Theorem?

The Shannon Hartley theorem is a fundamental theorem in information theory that defines the theoretical capacity of a band-limited additive white Gaussian noise channel under an average signal-power constraint. It is a cornerstone of digital communications and has implications for designing and analyzing communication systems.

How to Calculate Channel Capacity?

The following steps outline how to calculate the channel capacity using the Shannon Hartley theorem.

  1. First, determine the bandwidth of the channel (B) in hertz (Hz).
  2. Next, determine the linear signal-to-noise power ratio. Convert a dB value using SNR = 10^(SNRdB/10).
  3. Next, gather the formula from above: C = B * log2(1 + SNR).
  4. Finally, calculate the channel capacity (C) in bits per second.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

bandwidth of the channel (B) = 2000 Hz

signal-to-noise ratio (SNR) = 100