Calculate SNR in dB from signal and noise power levels. Includes Shannon capacity, ENOB, Eb/N₀, and application-specific requirement comparisons.
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.
Every engineer working with signals — RF, audio, optical, or digital — needs to compute and interpret SNR. This calculator provides the full picture: not just the dB value, but Shannon capacity, ENOB, Eb/N₀, and application-specific comparisons that put the number in context. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain.
SNR = P_signal / P_noise (linear). SNR_dB = 10·log₁₀(P_signal / P_noise). Shannon Capacity: C = B·log₂(1 + SNR). ENOB = (SINAD_dB − 1.76) / 6.02. Eb/N₀ = SNR_dB − 10·log₁₀(Rb / B).
Result: SNR = 30.00 dB, Shannon Capacity = 9.97 Mbps
SNR = 10·log₁₀(1 / 0.001) = 10·log₁₀(1000) = 30 dB. Shannon capacity = 1 MHz × log₂(1 + 1000) = 1e6 × 9.97 = 9.97 Mbps.
| 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 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.
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.
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.
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.
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.
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.
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.
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.