Signal-to-Noise Ratio
Ratio of signal power to noise power, in decibels.
Formula
Variables
Example
P_s/P_n = 1000: SNR = 30 dB
How it works
Signal-to-noise ratio compares how much useful signal power you have relative to unwanted noise power. The log base 10 and the factor of 10 are used because power ratios can span huge ranges, and decibels compress them into a more manageable scale while preserving multiplicative differences as additive changes. A larger SNR means the signal stands out more clearly above the noise, which usually makes detection, measurement, or communication more reliable.
When to use it
Use this when analyzing audio, radio, image, or communication systems and you need to quantify how clean a signal is. It is also useful in electronics and data acquisition whenever you want to compare a desired signal against background noise.
Worked example, step by step
Given: signal power P_s = 50 mW, noise power P_n = 2 mW Step 1: Form the power ratio P_s / P_n = 50 / 2 = 25 Step 2: Take the base-10 logarithm log10(25) ≈ 1.3979 Step 3: Multiply by 10 to convert to decibels SNR = 10 × 1.3979 ≈ 13.98 dB Final answer: SNR ≈ 14.0 dB
Common mistakes to avoid
- Using signal amplitude instead of signal power in the formula
- Forgetting the factor of 10 before the logarithm
- Reversing the ratio and computing noise power divided by signal power
Did You Know?
Every extra bit of audio resolution adds roughly 6 dB of SNR — the '6 dB per bit' rule.
Share this formula
More in Signal Processing & DSP
View allNyquist Rate
IntermediateSample at least twice the highest frequency to avoid aliasing.
FFT Bin Frequency
AdvancedFrequency represented by the k-th bin of an N-point FFT.
Frequency Resolution
IntermediateSpacing between adjacent FFT bins.
Quantisation SNR
AdvancedBest possible SNR (dB) of an ideal b-bit converter.
Decibel (Power Ratio)
BasicExpress a power ratio in decibels.
Decibel (Amplitude Ratio)
BasicExpress a voltage/amplitude ratio in decibels.