Shannon Capacity Calculator

The Shannon-Hartley theorem gives the theoretical maximum data rate for a channel given its bandwidth and signal-to-noise ratio.

What is Shannon Capacity?

The Shannon-Hartley theorem, published by Claude Shannon in 1948, defines the theoretical maximum information rate (channel capacity) that can be transmitted over a communication channel with a given bandwidth and noise level. It establishes the fundamental limit on data rate regardless of modulation scheme or coding complexity.

Shannon capacity is an upper bound — real-world systems cannot exceed it and typically achieve 50–80% of the theoretical maximum due to protocol overhead, guard intervals, coding redundancy, and implementation imperfections. However, it is invaluable for quickly assessing whether a proposed link design can support a target data rate, and for comparing different frequency bands and antenna configurations.

For MIMO systems with N spatial streams, the Shannon capacity of each stream adds to give N times the single-stream capacity — each independent channel contributes additively to total throughput.

Why Does It Matter?

Quick Shannon Capacity Calculator

Formulas Used by LinkBudgetPro

\[ C = N_s \cdot B \cdot \log_2(1 + \text{SNR}_{\text{lin}}) \quad [\text{b/s}], \qquad \text{SNR}_{\text{lin}} = 10^{\,\text{SNR}_{\text{dB}}/10} \]
\[ \text{SNR}_{\text{req}} = 10\log_{10}\!\left(2^{\,R\,/\,(B \cdot N_s)} - 1\right) \]

Minimum SNR to achieve target rate \(R\) [b/s] in bandwidth \(B\) [Hz] with \(N_s\) spatial streams

\[ N_s = \min(N_{\text{tx}},\, N_{\text{rx}}) \quad \text{[MIMO spatial multiplexing]} \]

Each independent stream contributes additively to total capacity

Parameter Explanation

ParameterSymbolUnitDescription
Channel CapacityCMbpsTheoretical maximum data rate achievable over the channel
BandwidthBHzChannel bandwidth — capacity scales linearly with B
SNRSNRdB / linearSignal-to-noise ratio at the receiver input
Spatial StreamsN_sNumber of independent MIMO channels: min(Tx ant., Rx ant.)
Spectral Efficiencyηb/s/HzC / (B × N_s) — bits per second per Hz per stream
Required SNRSNR_reqdBMinimum SNR to achieve a target data rate; determines receiver sensitivity

Worked Example

Find the Shannon capacity and required SNR for a 20 MHz channel with 15 dB SNR, 2×2 MIMO:

B = 20 MHz = 20×10⁶ Hz; SNR = 15 dB; N_s = 2 streams
SNR_linear = 10^(15/10) = 10^1.5 = 31.62
C = 2 × 20×10⁶ × log₂(1 + 31.62)
C = 2 × 20×10⁶ × log₂(32.62)
C = 2 × 20×10⁶ × 5.027 bits/s/Hz
C = 201 Mbps (theoretical)
For 100 Mbps target with 2×2 MIMO, 20 MHz:
SNR_req = 10·log₁₀(2^(100×10⁶/(20×10⁶×2)) − 1)
SNR_req = 10·log₁₀(2^2.5 − 1) = 10·log₁₀(4.657) = 6.68 dB

When Should You Use It?

Related Calculations

Enable the Capacity tab in the full calculator to compute Shannon capacity and required SNR for your link.

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