Signal-to-Noise Ratio (SNR) Calculator

About the Signal-to-Noise Ratio (SNR) Calculator

Signal-to-noise ratio (SNR) is the fundamental measure of signal quality in any communication, measurement, or sensing system. Defined as the ratio of signal power to noise power, SNR determines whether a signal can be reliably detected, decoded, or measured. In decibels, SNR = 10·log₁₀(P_signal / P_noise). A higher SNR means a cleaner signal — 40 dB SNR is excellent for voice, 96 dB is CD-quality audio, and radio astronomers routinely work with negative SNR by using integration time to dig signals out of the noise.

Claude Shannon's channel capacity theorem C = B·log₂(1 + SNR) established the theoretical maximum data rate for a noisy channel, connecting SNR directly to information throughput. This foundational result from 1948 underpins all modern digital communications, from 5G networks to deep-space probes. The related quantity Eb/N₀ (energy per bit to noise spectral density) is the standard metric for comparing digital modulation and coding schemes independent of bandwidth.

This SNR calculator works bidirectionally — enter signal and noise powers to find SNR, or enter a target SNR and noise level to find the required signal power. It computes Shannon capacity, effective number of bits (ENOB), and Eb/N₀, and compares your result against requirements for voice, radio, Wi-Fi, cellular, radar, and medical imaging applications.

When This Page Helps

SNR is the standard way to judge whether a signal is strong enough to measure, decode, or store without distortion from noise. This calculator turns raw power levels into dB, capacity, ENOB, and Eb/N₀ so you can compare a link, sensor, or ADC against the margin it actually needs.

How to Use the Inputs

1. Select a preset or choose a calculation mode.
2. For power-to-SNR mode, enter signal power and noise power.
3. For SNR-to-signal mode, enter the desired SNR in dB and noise power.
4. Select the power unit (mW, W, or µW).
5. Enter bandwidth (Hz) and bit rate (bps) for Shannon capacity and Eb/N₀.
6. Review SNR, ENOB, Shannon capacity, and application comparisons.
7. Use the quality scale to assess your signal quality at a glance.

Example Calculation

Tips & Best Practices

• Shannon capacity assumes Gaussian noise — real channels with interference may perform worse.
• To improve SNR: increase signal power, reduce noise (filtering, shielding), or narrow bandwidth.
• SNR_dB improves by 3 dB for every doubling of signal power.
• Halving the bandwidth improves SNR by 3 dB but also halves maximum data rate.
• For ADC selection, look at ENOB rather than stated resolution — a "16-bit" ADC may have only 12 ENOB.
• In digital communications, Eb/N₀ is more useful than SNR because it normalizes for bandwidth and data rate.

SNR in Different Domains

| Domain | Typical SNR | Key Metric | |---|---|---| | Thermal noise (290 K) | −174 dBm/Hz | Noise floor | | AM radio | 30–40 dB | Intelligibility | | FM radio | 50–65 dB | Audio fidelity | | CD audio | 96 dB | Dynamic range | | 24-bit audio | 144 dB | Theoretical max | | Wi-Fi (MCS9) | 35+ dB | Throughput |

Shannon Capacity and Modern Codes

Shannon proved in 1948 that reliable communication is possible at any rate below C = B·log₂(1 + SNR) and impossible above it. For decades, practical codes fell far short of this limit. Modern iterative codes — Turbo codes (1993) and LDPC codes (1960s, rediscovered 1996) — approach within 0.05 dB of Shannon's limit, revolutionizing digital communications.

Processing Gain and Spread Spectrum

Spread-spectrum systems (like GPS and CDMA) intentionally spread the signal across a wide bandwidth, making the raw SNR appear negative. The receiver "despreads" the signal, achieving processing gain = 10·log₁₀(BW_spread / BW_data). GPS uses 1.023 MHz spreading on 50 bps data for about 43 dB processing gain, allowing reception at −25 dB pre-despread SNR.

Frequently Asked Questions

• What is a good SNR?

  It depends on the application. For voice telephony, 30 dB is adequate. For HD video streaming, 25+ dB is needed. For studio audio recording, 60+ dB is expected. For scientific instruments, 80–120 dB may be required.

• Can SNR be negative?

  Yes. Negative SNR (in dB) means the noise power exceeds the signal power. GPS signals arrive at Earth at about −25 dB SNR. Radio astronomy signals can be −40 dB or lower. These are recovered using long integration times and correlation techniques.

• What is Shannon capacity?

  Shannon's theorem (1948) gives the maximum error-free data rate: C = B·log₂(1 + SNR). No coding scheme can exceed this limit. Modern codes like LDPC and Turbo codes approach within 0.1 dB of the Shannon limit.

• What is ENOB?

  Effective Number of Bits measures ADC quality. An ideal N-bit ADC has SNR = 6.02N + 1.76 dB. ENOB = (measured SINAD − 1.76) / 6.02 tells you how many bits of real resolution the ADC achieves, accounting for noise and distortion.

• What is the difference between SNR and SINR?

  SNR compares signal to noise. SINR (Signal-to-Interference-plus-Noise Ratio) also includes interference from other signals. In cellular networks, SINR is more relevant because neighboring cell interference often exceeds thermal noise.

• How does averaging improve SNR?

  Averaging N measurements improves SNR by √N (or 10·log₁₀(N) dB). This is why oscilloscopes offer averaging modes and radio telescopes integrate for hours — 100 averages give +20 dB improvement.