Standard Deviation Calculator

Calculate population and sample standard deviation with variance and mean.

Enter Numbers

Population SD (σ)

Sample SD (s)

Mean

Pop Variance

Sample Variance

Step-by-step solution

Formula

σ = √(Σ(xᵢ − μ)² / N)

σ = population standard deviation
s = sample standard deviation (÷ n−1)
μ = mean of the dataset
N = number of values

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Pro Tips

A low SD means data points cluster near the mean; a high SD indicates they are spread out.

Use population SD (σ) when you have data for the entire group; use sample SD (s) for subsets.