Toolstia / Standard deviation calculator
Standard deviation calculator
Paste or type your numbers and get the standard deviation straight away, both the sample version and the population version. You also get the variance, the mean, the standard error and the coefficient of variation, and for short lists a table that shows every step.
Enter at least one number.
Use the sample version when your numbers are a sample from a larger group, and the population version when they are the whole group.
How it works
- Enter your numbers separated by spaces, commas or new lines.
- Read the sample and population results.
- Open Show the working to see each deviation and its square.
Sample or population
Use the population standard deviation (σ) when your numbers are every value in the group you care about. Use the sample standard deviation (s) when your numbers are only a sample from a bigger group. The sample version divides by n − 1 instead of n to correct for the fact that a sample tends to underestimate the spread.
How it is worked out
Find the mean. Subtract it from each value and square the result. Add up the squares. Divide by n (population) or n − 1 (sample) to get the variance. The standard deviation is the square root of the variance.
Standard error and CV
The standard error of the mean is the sample standard deviation divided by the square root of n. It tells you how precisely the sample mean estimates the true mean. The coefficient of variation is the standard deviation as a percentage of the mean, which lets you compare spread across data with different units.
Reading the result
In data shaped like a bell curve, about 68% of values lie within one standard deviation of the mean and about 95% within two. A larger standard deviation means the values are more spread out.
Questions
Why does the sample version need two numbers?
It divides by n − 1. With one value that would be zero, so the sample standard deviation is not defined.
Can I paste a column from a spreadsheet?
Yes. Line breaks are treated as separators.
Is anything uploaded?
No. Your numbers stays in your browser and is never sent anywhere.