Shannon Channel Capacity Calculator
The theoretical maximum error-free data rate of a channel from its bandwidth and signal-to-noise ratio.
Results
What this tool does
Claude Shannon proved in 1948 that every communication channel has an absolute speed limit, set by its bandwidth and by how far the signal stands above the noise — and, remarkably, that error-free transmission is possible right up to that limit and impossible beyond it. Because the noise enters through a logarithm, doubling the bandwidth doubles the capacity while doubling the power adds only about one bit per second per hertz.
Formula
C = B log2(1 + S/N)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
bw | Channel bandwidth | MHz |
sn | Signal to noise ratio | dB |
CM | Channel capacity | Mbit/s |
SR | Signal to noise as a ratio | — |
SE | Spectral efficiency | bit/s/Hz |
CB | Channel capacity | bit/s |
Worked example
- Channel bandwidth20 MHz
- Signal to noise ratio25 dB
- Channel capacity166.1875 Mbit/s
- Signal to noise as a ratio316.2278
- Spectral efficiency8.3094 bit/s/Hz
- Channel capacity166,187,505 bit/s
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
Why does real Wi-Fi never reach this number?
Shannon's limit is what is theoretically possible with perfect coding and unlimited complexity. Real systems give away margin to error-correcting overhead, guard bands, protocol headers, retransmissions and the fact that several devices share the air. Getting within a few decibels of the limit is considered excellent engineering, and modern codes do manage it.