Signal-to-Noise Ratio Calculator Formula

Understand the math behind the signal-to-noise ratio calculator. Each variable explained with a worked example.

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Formulas Used

Signal-to-Noise Ratio (S/N)

snr = signal_height / noise_level

S/N in dB

snr_db = 20 * log10(signal_height / noise_level)

Variables

VariableDescriptionDefault
signal_heightSignal Height (S)100
noise_levelNoise Level (N)5

How It Works

Signal-to-Noise Ratio in Analytical Chemistry

The signal-to-noise ratio quantifies the quality of an analytical measurement. Higher S/N means the signal is more reliably distinguishable from background noise.

Formula

S/N = Signal Height / Noise Level

Noise is typically measured as peak-to-peak variation in a blank region. S/N of 3 is the detection limit criterion; S/N of 10 is the quantitation limit criterion.

Worked Example

A chromatographic peak has a height of 100 units and baseline noise of 5 units peak-to-peak.

signal_height = 100noise_level = 5
  1. 01S/N = 100 / 5 = 20
  2. 02S/N (dB) = 20 × log10(20) = 20 × 1.301 = 26.0 dB
  3. 03Well above quantitation limit (S/N = 10)

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