Calculator

Numbers (comma or space separated)

Mean

Sample Std Dev

Population Std Dev

Sample Variance

Population Variance

Count

Use sample standard deviation when your numbers are a sample from a larger population (the common case); use population standard deviation only when your numbers are the entire population.

Enter a list of numbers to calculate the sample and population standard deviation.

How to Use the Standard Deviation Calculator

Same list-of-numbers input as the Average calculator; sample and population standard deviation both show at once, since which one applies depends on whether the list is the whole dataset or a sample of it.

Two data sets can share an identical mean and still look completely different once you plot them — one tight and clustered, the other scattered wide. Standard deviation is what captures that difference, which the mean alone can't.

variance = Σ(x − mean)² ÷ n
standard deviation = √variance

This Standard Deviation Calculator reports both sample and population versions, and picking the right one actually matters. Population divides by n and applies only when your numbers are the whole population you care about. Sample divides by n − 1 instead, correcting for the fact that a sample systematically underestimates the true spread — this is the version almost everyone actually wants, since most data is a sample, not a census.