Standard Deviation Calculator

Sample SD, population SD, and variance for any dataset.

Result

Standard deviation (sample)

Variance

Mean

Count

Sum of squared deviations

The formula

Sample SD (you have a sample from a larger population):

s = √( Σ(xᵢ − x̄)² / (n − 1) )

Population SD (your data is the entire population):

σ = √( Σ(xᵢ − μ)² / n )

Why "n − 1" for samples

When you use the sample mean instead of the true population mean, you underestimate the squared deviations slightly. Bessel's correction (dividing by n−1) compensates and makes the sample SD an unbiased estimator of the population SD.