Standard Deviation Calculator
Calculate sample or population standard deviation, variance and mean.
Results update as you type.
About this calculator
Standard deviation measures how spread out a data set is around its mean. This calculator computes both the sample standard deviation (dividing the sum of squared deviations by n − 1, Bessel’s correction) and the population standard deviation (dividing by n), and reports the variance and mean it used. Choose sample when your numbers are a subset drawn from a larger group, and population when they are the entire group.
Frequently asked questions
What is the difference between sample and population standard deviation?
The population formula divides the summed squared deviations by n; the sample formula divides by n − 1. The n − 1 (Bessel’s correction) compensates for the fact that a sample tends to underestimate the true spread of the population it came from.
Why square the deviations?
Squaring makes every deviation positive so they do not cancel out, and it weights larger deviations more heavily. Taking the square root at the end returns the measure to the original units of the data.
Results are estimates for general guidance only, not financial, medical or tax advice.