Shannon Channel Capacity Calculator
Work out the maximum theoretical data rate of a communications channel from its bandwidth and signal-to-noise ratio using the Shannon–Hartley theorem. Enter the bandwidth in hertz and the SNR in decibels to get the capacity in bits per second, kbps and Mbps.
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How to use this calculator
- Enter the channel bandwidth B in hertz (e.g. a 20 MHz Wi-Fi channel = 20000000 Hz).
- Enter the signal-to-noise ratio in decibels — the value quoted on a link budget or measured at the receiver.
- Read the channel capacity in bits/s, kbit/s and Mbit/s, along with the linear SNR the tool used internally.
How it works
Capacity is C = B · log₂(1 + SNR_linear). The decibel SNR is first turned into a linear power ratio with SNR_linear = 10^(SNR_dB / 10), so 20 dB becomes 100. Then the bandwidth is multiplied by log₂(1 + SNR_linear). Bandwidth scales capacity linearly, while SNR only helps logarithmically, so a wider channel is a far more powerful lever than extra transmit power once the SNR is already reasonable.
Worked example
Worked example. A 20 MHz channel with a 20 dB SNR: SNR_linear = 10^(20/10) = 100, so C = 20,000,000 × log₂(101) = 20,000,000 × 6.658211 ≈ 133,164,230 bits/s ≈ 133.16 Mbps. A real device on that channel would deliver well under this figure.
Common mistakes
- Entering the SNR as a linear ratio instead of decibels — this field expects dB, and it is converted internally.
- Entering bandwidth in MHz or kHz instead of hertz; a 20 MHz channel must be typed as 20000000.
- Treating the result as an achievable throughput — it is an unreachable upper bound, so real rates are a fraction of it.
Frequently asked questions
Why is my real Wi-Fi or LTE speed much lower than this number?
Shannon capacity assumes an ideal error-correcting code with unlimited complexity and delay. Practical modulation and coding schemes leave a large gap, and protocol overhead, interference and retransmissions reduce it further, so measured throughput is typically well below the Shannon limit.
Can the SNR be zero or negative?
Yes. At 0 dB the signal and noise powers are equal (SNR_linear = 1), giving C = B bits/s. Negative dB values (signal weaker than noise) still yield a positive but small capacity, which is why spread-spectrum systems can work below the noise floor.
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- Link Margin Calculator
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Tip: Enter any known values to calculate the remaining results.
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