Guide

The two standard deviation formulas

σ divides by N. s divides by n − 1. That one-term difference is Bessel’s correction. Both formulas start with the mean, then squared deviations, then a square root.

Population

N is the count of every value in the population. μ is the population mean. You take the square root of the average squared distance from that mean.

σ = √( Σ(xᵢ − μ)² / N )

Sample

n − 1 keeps a sample from underestimating the population spread.

s = √( Σ(xᵢ − x̄)² / (n − 1) )

Variance

Variance is SD². SD is √variance. Taking the square root returns to the original scale.

Computational form

On a handheld, an algebraically equivalent shortcut avoids storing every deviation: sum the values, sum the squares, then divide. This app uses the two-pass method instead — mean first, then squared deviations — which stays accurate when values are large.

How Standard Deviation Calculator helps

Show solution substitutes your numbers into the matching formula and prints the table. You can check the divisor line to confirm sample vs population.

See the formula with your numbers

In-app solution showing the standard deviation formula filled with dataset values