Standard Deviation Calculator
Measure how spread out your numbers are, for a sample or a whole population.
What standard deviation measures
Standard deviation shows how far values typically sit from the mean. A small number means the values cluster tightly; a large number means they are spread out.
Sample or population?
Choose population when your list contains every value you care about, and divide by n. Choose sample when the list is only a sample of a bigger group, and divide by n − 1, which corrects for the fact that a sample tends to understate the spread.
Formula and example
σ = √(Σ(x − mean)² ÷ N) for a population and s = √(Σ(x − mean)² ÷ (n − 1)) for a sample. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the squared differences add up to 32. The population standard deviation is √(32 ÷ 8) = 2, and the sample standard deviation is √(32 ÷ 7) ≈ 2.14.
Frequently asked questions
When should I use n − 1?
Use it when your data is a sample from a larger group, which is the usual case in surveys and experiments.
What is variance?
Variance is the standard deviation squared. It is the average squared distance from the mean.
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