# Signal-to-Noise Ratio Calculator

> Calculate signal-to-noise ratio in decibels from signal and noise powers, RMS voltages or dBm levels, with the equivalent power and amplitude ratios.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/signal-to-noise-ratio-calculator

SNR compares the wanted signal with the background noise. In decibels it is 10 log₁₀ of the power ratio, or 20 log₁₀ of the RMS voltage ratio.

Also called: SNR calculator.

## Inputs
- Values are (options: Powers, RMS voltages, Levels in dBm; default power)
- Signal (default 10)
- Noise (default 0.01)

## Results
- SNR
- Power ratio
- Amplitude (voltage) ratio

## Formula

```
SNR(dB) = 10 log₁₀(P_s ÷ P_n) = 20 log₁₀(V_s ÷ V_n);  from dBm: SNR = L_s − L_n
```

Where:
- P_s, P_n: signal and noise power
- V_s, V_n: signal and noise RMS voltage across the same impedance
- L_s, L_n: signal and noise levels in dBm

## Worked example
1. Power ratio = 10 ÷ 0.01 = 1,000.
2. SNR = 10 × log₁₀(1,000) = 10 × 3 = 30 dB.

**Result:** A 10 mW signal over 0.01 mW of noise has an SNR of 30 dB, a power ratio of 1,000.

## What the result means

Every 10 dB is a further factor of 10 in power. As a rough guide, voice links need 10–20 dB, CD audio has a theoretical 96 dB, and a positive SNR at least means the signal is stronger than the noise.

## Assumptions and limits
- Signal and noise are measured over the same bandwidth; voltages are RMS across the same impedance.
- If the measured “signal” includes noise (signal + noise), the true SNR is slightly lower, noticeably so below about 10 dB.

## Questions

### Why 20 log for voltage?

Power is proportional to voltage squared, and log(V²) = 2 log V, so 10 log of the power ratio equals 20 log of the voltage ratio.

### Can SNR be negative?

Yes. Negative SNR means the noise is stronger than the signal; spread-spectrum systems such as GPS still work below 0 dB.

## Related calculators
- [Decibel to Power Ratio Converter](https://calculators.geekmidst.com/calculators/decibels-power-ratio-calculator)
- [Nyquist Rate Calculator](https://calculators.geekmidst.com/calculators/sampling-nyquist-rate-calculator)
- [FFT Frequency Bin Calculator](https://calculators.geekmidst.com/calculators/fourier-frequency-bin-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/signal-to-noise-ratio-calculator