Calculator inputs
Example data table
| Scenario | Bandwidth | SNR | Modulation | Shannon limit | Nyquist rate |
|---|---|---|---|---|---|
| Small wireless link | 1 MHz | 10 dB | 16 levels | 3.459432 Mbps | 8.000000 Mbps |
| Urban broadband channel | 5 MHz | 20 dB | 64 levels | 33.291057 Mbps | 60.000000 Mbps |
| Wideband backhaul | 20 MHz | 15 dB | 256 levels | 100.556153 Mbps | 320.000000 Mbps |
| Narrowband sensor link | 100 kHz | 5 dB | 4 levels | 205.737321 Kbps | 400.000000 Kbps |
Formula used
1) Shannon-Hartley capacity
C = B × log2(1 + SNR)
Use this when noise matters. Capacity depends on bandwidth in hertz and linear SNR, not directly on dB input.
2) Required bandwidth
B = C ÷ (log2(1 + SNR) × efficiency)
This rearranged Shannon form estimates the minimum bandwidth needed to support a target throughput at the chosen SNR.
3) Required SNR
SNR = 2^(C ÷ (B × efficiency)) - 1
After solving the linear SNR, the calculator converts it to decibels using 10 × log10(SNR).
4) Nyquist rate
R = 2 × B × log2(M)
Nyquist estimates the noiseless upper rate for a bandwidth and modulation order, where M is the number of signal levels.
How to use this calculator
- Choose a calculation mode that matches your goal.
- Enter bandwidth and select the correct unit.
- Enter SNR as either dB or linear ratio.
- Add modulation levels for Nyquist comparison.
- Set implementation efficiency if overhead reduces throughput.
- Press the calculate button to display results above the form.
- Review the graph to see how capacity changes with SNR.
- Use the CSV or PDF buttons to export the current result summary.
FAQs
1) What does channel capacity mean?
Channel capacity is the highest theoretical data rate a link can carry with acceptable reliability under stated bandwidth and noise conditions.
2) Why are Shannon and Nyquist both shown?
Shannon covers noisy channels. Nyquist covers noiseless signaling limits. Comparing both helps you see whether noise or symbol signaling is the tighter constraint.
3) Should I enter SNR in dB or linear form?
Use whichever value you already have. The calculator converts dB to linear SNR before applying Shannon capacity equations.
4) Why is implementation efficiency included?
Real systems lose throughput to coding overhead, framing, pilots, guard intervals, and protocol control traffic. Efficiency adjusts ideal theory toward realistic results.
5) Can this calculator predict actual speed tests?
Not exactly. It estimates theoretical limits. Actual speed depends on interference, fading, hardware, scheduling, retransmissions, and many protocol details.
6) What happens if modulation levels are not powers of two?
The math still works for comparison, but practical digital systems usually use powers of two because they map cleanly to whole bits per symbol.
7) Why can Nyquist be higher than Shannon?
Nyquist ignores noise. Shannon includes noise. In real noisy links, Shannon often becomes the stricter upper bound on usable throughput.
8) What units does the calculator support?
Bandwidth supports Hz through GHz. Capacity supports bps through Gbps. Results are also auto-formatted into readable units.