What do the variables in the Signal-to-Noise Ratio (dB) mean?

In the Signal-to-Noise Ratio (dB): SNR_{dB} = SNR in dB; S = Signal power; N = Noise power.

Basic

Signal-to-Noise Ratio (dB)

Ratio of signal power to noise power in decibels.

Formula

SNR_{dB} = 10\log_{10}\frac{S}{N}

Variables

SNR_{dB}SNR in dB

SSignal power

NNoise power

Example

S/N=1000: SNR = 30 dB

How it works

This formula compares the power of a desired signal to the power of unwanted noise, then expresses that comparison on a decibel scale. The logarithm is used because signal and noise levels can vary over huge ranges, and the 10 in front appears because decibels for power are defined using a base-10 log. A larger SNR means the signal stands out more clearly above the noise, while a smaller SNR means the noise is closer in strength to the signal.

When to use it

Use this when analyzing communication systems such as radio links, Wi‑Fi, mobile networks, audio equipment, or sensor readings to judge how clean or reliable the signal is. It is also useful whenever you know the signal and noise powers and need to compare them in decibels.

Worked example, step by step

Given: Signal power S = 50 mW, Noise power N = 2 mW Step 1: Form the power ratio S/N = 50/2 = 25 Step 2: Take the base-10 logarithm log10(25) ≈ 1.398 Step 3: Multiply by 10 to convert to dB SNR_dB = 10 × 1.398 ≈ 13.98 dB Final answer: SNR ≈ 14.0 dB

Common mistakes to avoid

Using amplitudes or voltages directly instead of power values
Forgetting that the logarithm is base 10, not natural log
Swapping signal and noise, which gives the negative of the correct dB value

Did You Know?

A clean digital link usually needs an SNR above about 20 dB to stay error-free.

telecom snr noise

Signal-to-Noise Ratio (dB)

Formula

Variables

Example

How it works

When to use it

Worked example, step by step

Common mistakes to avoid

Did You Know?

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