What is the Shannon-Hartley theorem?

The Shannon-Hartley theorem states that the maximum error-free information rate C (in bits per second) of a channel with bandwidth B (Hz) and signal-to-noise ratio S/N is: C = B × log₂(1 + S/N). It was published by Claude Shannon in 1948 and is a cornerstone of information theory.

What is the difference between SNR as a ratio and SNR in dB?

SNR as a linear ratio is the direct power ratio S/N (e.g., 100 means signal is 100× stronger than noise). SNR in dB is 10 × log₁₀(S/N). A 20 dB SNR equals a linear ratio of 100. The calculator handles both — select the appropriate unit before entering your value.

Does this give the actual throughput of a real system?

No — this is the theoretical maximum (Shannon limit). Real systems are always below this bound due to modulation overhead, coding redundancy, protocol headers, and hardware imperfections. The Shannon limit is an absolute ceiling that cannot be exceeded.

Why does doubling bandwidth not double capacity when SNR is high?

It does double capacity when SNR is fixed and high. However, in practice, doubling bandwidth often also doubles the noise power (since thermal noise is proportional to bandwidth), which can reduce or eliminate the gain. This tool assumes a fixed S/N ratio regardless of bandwidth.

What happens with a very high SNR?

As SNR grows large, capacity grows roughly logarithmically. Doubling a very high SNR adds only about 1 bit/s per Hz of capacity. This is why increasing transmitted power has diminishing returns — increasing bandwidth is generally more efficient.

Can SNR be 0 or negative?

A linear SNR of 0 (or negative dB values leading to S/N 0 (linear) or dB values that result in a positive ratio.

Shannon Channel Capacity Calculator

Name: Shannon Channel Capacity Calculator
Availability: InStock
Author: Nham Vu

Enter bandwidth and signal-to-noise ratio to calculate the theoretical maximum data rate of a communication channel using the Shannon-Hartley theorem.

Channel Parameters

Bandwidth (B)

Signal-to-Noise Ratio (S/N)

Enter SNR in decibels (dB). Example: 30 dB = linear ratio of 1000.

Quick Presets

Enter bandwidth and SNR, then click
Calculate Capacity

Summary

Enter bandwidth and signal-to-noise ratio to calculate the theoretical maximum data rate of a communication channel using the Shannon-Hartley theorem.

How it works

Enter the channel bandwidth in Hz, kHz, MHz, or GHz.
Enter the signal-to-noise ratio (SNR) as a linear ratio or in dB.
The calculator converts dB to linear ratio when needed: S/N = 10^(SNR_dB / 10).
Channel capacity is computed as C = B × log₂(1 + S/N).
Results are displayed in bits per second, automatically scaled to kbps, Mbps, or Gbps.

Use cases

Evaluate the theoretical maximum throughput of a Wi-Fi or LTE channel.
Compare channel efficiency of different bandwidth and SNR configurations.
Verify link budget calculations in RF and microwave system design.
Study information theory concepts and validate textbook examples.
Estimate the capacity ceiling of a DSL or cable modem connection.
Analyze the impact of noise on communication system performance.
Determine how much additional bandwidth is needed to double throughput.
Cross-check Nyquist and Shannon limits for baseband channel design.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu