Standard deviation calculator
Paste a list of numbers and get the standard deviation straight away, for a sample or a whole population, together with the variance, the mean and the steps.
Separate the numbers with a semicolon, space or new line. Commas work as long as you don't use decimal commas.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
-
Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
-
Instant answer
The answer appears as you type, with the most important intermediate values.
-
See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
Sample or population?
- Sample (s): your numbers are a selection from a larger group, such as 50 people from a survey. You divide by n − 1. This is the usual choice, and what
STDEV.Sin a spreadsheet does. - Population (σ): your numbers are the entire group, such as all pupils in one class. You divide by n, like
STDEV.P.
The difference is small for large lists, but noticeable for a handful of numbers.
How it works
- Work out the mean.
- Subtract the mean from every number and square the result.
- Add those squares up and divide by n − 1 (sample) or n (population). That is the variance.
- Take the square root: that is the standard deviation.
For 2, 4, 4, 4, 5, 5, 7 and 9 the mean is 5 and the population standard deviation is exactly 2. A small standard deviation means the numbers are close to the mean; a large one means they are spread out.
Frequently asked questions
Is the standard deviation free?
Yes. The standard deviation is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.