Standard Deviation Calculator

Enter a list of numbers to calculate the mean, variance, and standard deviation.

How this calculator works

Standard deviation measures how spread out a data set is from its mean. Sample standard deviation divides by n−1 (Bessel's correction), while population standard deviation divides by n.

σ = √( Σ(x − mean)² / (n or n−1) )
Use 'sample' when your data is a subset of a larger population; use 'population' when it's the entire population.

Frequently asked questions

Should I use sample or population standard deviation?

Use sample if your numbers are a subset drawn from a larger group (most common case). Use population only if your data represents the entire group you care about.

Why does sample standard deviation divide by n−1?

Dividing by n−1 (Bessel's correction) corrects for the bias that occurs when estimating a population's variability from a smaller sample.