Standard Deviation Calculator

What standard deviation tells you

Standard deviation measures how spread out a set of numbers is around their average. A small value means the data clusters tightly near the mean; a large value means it's widely scattered. This calculator also reports the mean, variance, count, and sum.

Sample vs. population

Use population when your numbers are the entire group you care about, and sample when they're a subset you're using to estimate a larger group. The sample version divides by (n − 1) instead of n — Bessel's correction — which slightly increases the result to account for the uncertainty of sampling.

FAQ

How is variance related?

Variance is the average squared distance from the mean, and standard deviation is simply its square root. Standard deviation is usually more useful because it's in the same units as your data.

Should I pick sample or population?

Choose population when your numbers represent the entire group you care about, and sample when they're a subset used to estimate a larger group. When in doubt with real-world data drawn from a bigger population, sample is the safer default.

Why does the sample version divide by n − 1?

Dividing by n − 1 instead of n is Bessel's correction. Because a sample's mean is itself an estimate, it slightly underestimates spread, and using n − 1 nudges the result upward to give an unbiased estimate of the true population standard deviation.

How do I enter my numbers?

Type or paste your values separated by commas, spaces, or line breaks — decimals and negatives are fine. The calculator reports the standard deviation alongside the mean, variance, count, and sum.

Is this calculator free and private?

Yes — it's free with no sign-up, works on mobile, and runs entirely in your browser, so the data you paste is never uploaded or stored anywhere.