Variance calculator

How it works

Population variance = Σ(x − mean)² ÷ n · Sample variance = Σ(x − mean)² ÷ (n − 1)

Both conventions are always shown, because picking one blind is the mistake this calculator exists to prevent. Divide by n when your list is the entire population you care about; divide by n−1 when it is a sample and you are estimating a wider population's variance. The n−1 version is always slightly larger, and with small lists the gap is substantial — on eight values it is about 14%.

This tool runs entirely in your browser. Nothing you type is sent to a server, stored or logged.

Frequently asked questions

Sample or population?

Population when the numbers are everything you care about — the twelve months of last year, say. Sample when they stand in for something larger, like fifty customers out of five thousand.

Why divide by n − 1?

Because a sample's spread around its own mean systematically understates the population's spread. Dividing by n−1 corrects that bias, and the correction matters most when the sample is small.

What about standard deviation?

It is the square root of the variance, shown here for the sample convention. It is in the same units as your data, which usually makes it the easier of the two to interpret.

How should I format the input?

Commas, spaces or new lines all work — paste a spreadsheet column straight in. Use a point for decimals, since the comma is doing separator duty.