# Signal-to-Noise Ratio Calculator

Created by Luis Hoyos
Last updated: Aug 06, 2022

Welcome to our signal-to-noise ratio calculator, a tool designed to calculate the signal-to-noise ratio (SNR) in dB (decibels) and other ways.

The noise of a signal is one of the limiting factors in communication systems, keeping us from transmitting infinite amounts of information, and the SNR is one of the ways to express the relevance of that noise. For that reason, we created this calculator.

## What is the signal-to-noise ratio?

In information theory, the signal-to-noise ratio is simply the amount of signal transmission compared to the noise that that signal carries. For example, if we keep the noise constant while simultaneously increasing the signal transmission, the SNR increases.

The information of the signals can be a constant or a random variable. For the latter case, we use the expected values (averages) of the variables to perform the calculations.

## Formulas for signal-to-noise ratio calculation

There are various ways to calculate the signal-to-noise ratio, and the one to choose will depend on the information available.

1. Simple ratio: this is the most "general" mathematical form of the SNR formula, although rarely used:

SNR = signal/noise

We can express the signal and the noise using any units, as long as we clarify it. Even so, the most common way to express SNR is by using signal and noise power.

2. Using signal and noise power: As SNR values are large, we usually express them using the logarithmic decibel scale. In this case, the SNR equation is:

SNRdB = 10log₁₀(Psignal/Pnoise)

Where:

• SNRdB — Signal-to-noise ratio, in decibels (dB);
• Psignal — Signal power, in watts (W); and
• Pnoise — Noise power, in W.
3. Using voltages: To calculate SNR using signals and noises voltages, use the following formula:

SNRdB = 20log₁₀(Vsignal/Vnoise)
Where:

• Vsignal — Signal voltage, in volts (V); and
• Vnoise — Noise voltage, in V.
4. If we already know the signal and powers in decibels, we can calculate the SNR in dB by taking their difference:

SNRdB = signal (dB) − noise (dB)

If we don't know the signal or the power in dB:

• signal (dB) = 10log₁₀(Psignal) = 20log₁₀(Vsignal)
• noise (dB) = 10log₁₀(Pnoise) = 20log₁₀(Vnoise)
5. SNR from the coefficient of variation: As mentioned before, the signal and the noise can be random or time-varying variables. In this case, an alternative way to calculate SNR is using the reciprocal of the coefficient of variation (σ/μ), a statistical measure of the dispersion of a random variable:

SNR = μ/σ

Where:

• μ — Signal expected value; and
• σ — Standard deviation of the noise.

Finally, another common way to calculate SNR is by using the square of the previous definition:

SNR = μ²/σ²

These are the ways to calculate the signal to noise. Feel free to use the calculator and verify the results using the previous SNR formulas.

Luis Hoyos
Type of SNR
Power SNR
Signal
hp(E)
Noise
hp(E)
Signal-to-noise ratio
dB(s)
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