Standard Deviation Calculator

Calculate population and sample standard deviation. Enter your data set for instant results with mean and variance.

Standard Deviation Formulas

Population Standard Deviation (σ)

σ = √( Σ(xᵢ − μ)² / N )

Sample Standard Deviation (s)

s = √( Σ(xᵢ − x̄)² / (n−1) )
Data: 2, 4, 4, 4, 5, 5, 7, 9   (n=8, mean=5)
Population σ = 2

Population vs Sample

Use population when you have data for the entire group. Use sample when your data is a subset (the denominator changes to n−1, known as Bessel's correction).

Last updated: 2026-08-08