Signal to Noise Ratio Formula
The signal to noise ratio formula is used to calculate the value of the signal to noise ratio which tells us about the quality of the signal. The signal to noise ratio formula is expressed as S/N formula or SNR formula. This signal to noise ratio is a qualitative measure. The signal to noise ratio formula gives us the ratio of the power of the signal received to the power of the noise in the signal transmission. Let us study the signal to noise ratio formula using solved examples.
What is Signal to Noise Ratio Formula?
The signal to noise ratio formula is the ratio of the power of the signal to the power of the noise in the surrounding of the signal that is causing disturbance to the signal transmission. The signal to noise ratio formula is given as:
SNR = (P_{signal})/(P_{noise}) = μ / σ
where,
 P_{signal} is the power of the signal.
 P_{noise }is the power of the noise.
 μ is the signal mean
 σ is the standard deviation of the noise
Let's take a quick look at a couple of examples to understand the signal to noise ratio, better.
Solved Examples Using Signal to Noise Ratio Formula

Example 1: What will be the signal to noise ratio of the given data: 10, 8, 5, 1, 6, if the standard deviation of the given data is 3.39.
Solution:
To find: SNR
Given, σ = 3.39
Finding mean of the given data,
μ = (1 + 5 + 6 + 8 + 10)/5 = 6Using the signal to noise ratio formula,
Answer: The signal to noise ratio of the given data is 1.77.
SNR = μ / σ
SNR = 6/3.39
SNR = 1.77 
Example 2: What will be the signal to noise ratio, if the mean of the data is 45 and the standard deviation of the given data is 39.5.
Solution:
To find: SNR
Given, σ = 39.5
μ =45Using the signal to noise ratio formula,
Answer: The signal to noise ratio of the given data is 1.1309.
SNR = μ / σ
SNR = 45/39.5
SNR = 1.139
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