Standard Deviation Calculator - Mean, Variance & SD

Enter a list of numbers and this calculator will compute the mean, variance, population standard deviation and sample standard deviation. Separate values with commas, spaces or line breaks.

Count (n)
Mean
Population variance
Population standard deviation (σ)
Sample variance
Sample standard deviation (s)

Population formulas use n in the denominator. Sample formulas use (n − 1) and are typically used when your data are a sample from a larger population.

Standard Deviation, Variance and Mean Explained

Standard deviation measures how spread out a set of numbers is around the mean. A small standard deviation means the values are close to the average, while a large standard deviation means the values are more spread out.

This calculator computes:

Mean – the average of all values
Population variance – average squared distance from the mean, dividing by n
Population standard deviation (σ) – square root of the population variance
Sample variance – squared distance from the mean, dividing by (n − 1)
Sample standard deviation (s) – square root of the sample variance

In statistics, the sample formulas (using n − 1) are usually used when the data represent a sample from a larger population. The population formulas (using n) are used when your data set includes the entire population you care about.

This tool is intended for educational and general-purpose data analysis and does not replace professional statistical software.