Standard Deviation and Variance Calculator
Works out both versions of the standard deviation and variance, since they differ and software varies in which it gives by default.
Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
The formula
sample variance s² = Σ(x − x̄)² ÷ (n − 1) population variance σ² = Σ(x − μ)² ÷ n standard deviation = √variance
Dividing by n − 1 (Bessel’s correction) corrects for the sample mean sitting closer to its own data than the true mean does.
What to watch out for
In a spreadsheet, STDEV.S and VAR.S are the sample versions, and STDEV.P and VAR.P are the population versions. Most reports of survey or experimental data want the sample version.
Frequently Asked Questions
What is the difference between sample and population standard deviation?
The divisor. For 2, 4, 4, 4, 5, 5, 7, 9 the population figure is 2 and the sample figure is 2.13809. The gap shrinks as n grows.
How do variance and standard deviation relate?
The standard deviation is the square root of the variance. It is in the same units as the data, which makes it easier to read.