Standard Deviation Calculator
Calculate sample and population standard deviation and variance, with the full summary.
Your result will appear here as soon as you add some input.
How to use it
- 1Enter your values in the fields above.
- 2The answer and the working appear immediately below.
- 3Check the working to see the formula with your numbers substituted.
Formulas used
- population: sqrt(sum((x - mean)^2) / n)
- sample: sqrt(sum((x - mean)^2) / (n - 1))
About the Standard Deviation Calculator
Standard deviation is the typical distance of a value from the mean, in the same units as the data. Variance is its square, which is mathematically convenient but has squared units and no intuitive meaning.
The sample version divides by n-1 rather than n. That correction exists because the sample mean is itself estimated from the data, which makes the deviations slightly too small; dividing by one less compensates.
Use the sample figure unless your numbers genuinely are the entire population - every employee, every transaction, not a sample of them.
Questions people ask
Is your figures uploaded to a server?
No. This tool runs entirely in your browser using standard web APIs, so your figures never leaves your device. You can confirm it by opening your browser's network panel while the tool runs, or by disconnecting from the internet after the page has loaded.
Is it free, and do I need an account?
Yes, it is free, and there is no account, no sign-up and no watermark on the result. The project is funded by optional donations.