Variance Calculator

Variance measures how far a set of numbers spreads out from their mean. It is the average of the squared differences from the mean, so a larger variance means the values are more scattered. Its square root is the standard deviation.

Population variance divides the sum of squared differences by N, the count of values, and is used when your data covers the entire group. Sample variance divides by N minus 1, which corrects for the bias you get when estimating a larger population from a smaller sample.

Use the population formula only when your data includes every member of the group you care about. In most real analysis you have a sample drawn from a bigger population, so the sample variance, dividing by N minus 1, is the right choice.

Standard deviation is the square root of the variance. Variance is in squared units, while the standard deviation is back in the original units of your data, which makes it easier to interpret. This calculator shows both.

Sample variance divides by N minus 1. With a single value that divisor is zero, so the result is undefined. Enter two or more numbers to compute the sample variance and its standard deviation.