Signal-to-Noise Ratio (SNR) Calculator
Enter your signal and noise values to get the signal-to-noise ratio in decibels (dB) and as a plain ratio. Choose from five calculation methods: power-based SNR, voltage (amplitude) SNR, simple ratio, dB subtraction, or the statistical coefficient-of-variation form used in imaging and spectroscopy. Results appear instantly with a full worked-step breakdown.
Formula
Worked example
A Wi-Fi receiver picks up a signal at 1 mW and a noise floor of 0.01 mW. Power SNR = 10 log10(1/0.01) = 10 log10(100) = 20 dB, which is a good connection. In amplitude terms, the voltage ratio is sqrt(100) = 10, confirmed by 20 log10(10) = 20 dB.
What is signal-to-noise ratio?
Signal-to-noise ratio (SNR) measures how much desired signal is present relative to background noise. A high SNR means the signal dominates; a low SNR means noise is close to, or louder than, the signal itself. Engineers and scientists express SNR in decibels (dB) because the logarithmic scale compresses the enormous range of real-world ratios into manageable numbers: a power ratio of 1000:1 becomes 30 dB, and 1,000,000:1 becomes 60 dB. SNR is fundamental in electronics, audio engineering, radio communications, medical imaging, spectroscopy, and data science.
Power SNR vs. voltage (amplitude) SNR
Two decibel formulas appear in the literature and their difference trips up many engineers. When signal and noise are measured as power (watts, milliwatts, or any squared quantity), use SNR(dB) = 10 log10(P_signal / P_noise). When measured as amplitude, voltage, current, or field strength, use SNR(dB) = 20 log10(A_signal / A_noise), because power is proportional to the square of amplitude and log10(x^2) = 2 log10(x). Mixing up the factor of 10 vs. 20 produces a 2x error in dB, which translates to an order-of-magnitude error in the power ratio. Always check whether your measurement is a power quantity or an amplitude quantity before choosing the formula.
dB subtraction and the coefficient of variation
If your signal and noise readings are already expressed in dBm or dBV from a spectrum analyzer, SNR is simply the difference: SNR(dB) = signal(dB) - noise(dB). No logarithms needed. The fifth method - coefficient of variation - is widely used in image processing, MRI, and spectroscopy: SNR = mean / standard deviation (mu / sigma), where mu is the mean pixel (or sample) value and sigma is the standard deviation of a homogeneous background region. This captures both the strength of the signal and the variability of the noise in a single dimensionless figure, with higher values indicating cleaner data.
How to improve SNR in practice
Practical SNR improvement strategies depend on the domain. In electronics, use a lower-noise amplifier, shield cables, filter at the source, and keep signal paths short. In audio, choose higher-quality converters, reduce room noise, and position microphones closer to the source. In wireless, move the receiver closer to the transmitter, switch to a less congested channel, use a directional antenna, or increase transmit power where regulations allow. In imaging and spectroscopy, average multiple frames or scans (SNR improves with the square root of the number of averages), cool the detector to reduce thermal noise, and use a narrower bandwidth filter. The key insight is that doubling the averaging count improves SNR by only about 3 dB, so large SNR gains require addressing the root noise source rather than relying on averaging alone.
SNR ranges and their practical meaning
| SNR range (dB) | Quality | Typical applications / effect |
|---|---|---|
| Below 5 | Very poor | Signal indistinguishable from noise; unusable connection or image |
| 5-10 | Poor | Very noisy audio/image; Wi-Fi barely connects; data errors likely |
| 10-20 | Marginal | Acceptable telephone quality; weak Wi-Fi; visible image noise |
| 20-25 | Good | CD-quality audio threshold; reliable Wi-Fi; usable camera sensor |
| 25-40 | Very good | Hi-fi audio; strong Wi-Fi; high-quality imaging sensors |
| Above 40 | Excellent | Studio audio; 5G NR; scientific instrumentation; near-perfect fidelity |
These thresholds apply across Wi-Fi, audio, imaging, and RF engineering. Higher dB always means less noise relative to the signal.
Frequently asked questions
What is a good SNR in decibels?
It depends on the application, but a common rule of thumb: above 20 dB is considered good for most uses, above 30 dB is very good, and above 40 dB is excellent. For Wi-Fi, 25 dB and above gives a strong, stable connection. For audio recording, consumer gear typically achieves 60-80 dB, while professional equipment exceeds 100 dB. For medical imaging and scientific instruments, 20-30 dB is often acceptable, though higher is always better.
Why do some formulas use 10 log10 and others use 20 log10?
The factor depends on whether the quantity being measured is a power or an amplitude. Use 10 log10 for power, energy, or intensity ratios (watts, milliwatts, etc.). Use 20 log10 for amplitude, voltage, current, or pressure ratios. The reason is that power is proportional to the square of amplitude, so log(A^2/B^2) = 2 log(A/B), which introduces the factor of 2 in front of the 10.
What SNR is needed to distinguish image features reliably?
The Rose criterion, established in the 1940s for human visual detection of features in images, states that an SNR of at least 5 (about 14 dB on an amplitude basis) is required to detect a feature with near certainty. Below this threshold, the probability of false detection or missed features rises sharply. Modern imaging algorithms can often push below this limit using statistical methods, but 5:1 (or 14 dB) remains a practical benchmark.
What is the SNR of a 16-bit audio system?
For a uniformly quantized n-bit digital system with a full-scale sine wave, the theoretical SNR is approximately 6.02 x n + 1.76 dB. For 16-bit audio, that works out to roughly 98 dB. For 24-bit audio, the theoretical maximum is about 146 dB. Real-world ADC and DAC hardware falls somewhat short of these limits due to jitter, thermal noise, and non-linearity, but 96-100 dB is typical for a quality 16-bit converter.
How does averaging improve SNR?
Incoherent noise averages toward zero while a coherent signal does not, so averaging N repeated measurements improves SNR by a factor of sqrt(N), or about 3 dB per doubling of measurements. For example, averaging 4 scans improves SNR by 6 dB, and averaging 100 scans improves it by 20 dB. This is a standard technique in NMR, seismology, and lock-in amplifier measurements, but the time cost grows quickly, making hardware noise reduction preferable when large SNR gains are needed.
What is the difference between SNR and PSNR?
Peak signal-to-noise ratio (PSNR) uses the peak (maximum possible) signal value in the numerator rather than the actual signal power. It is almost exclusively used in image and video compression quality assessment, where the maximum pixel value (255 for 8-bit images) is fixed and PSNR provides a standard benchmark across different images. Plain SNR uses the actual measured signal power and is more appropriate for physical measurements in audio, RF, and instrumentation.