Standard Deviation Calculator

Enter a data set to get the sample standard deviation, plus population SD, mean, and variance.

What standard deviation tells you

Standard deviation measures how spread out a data set is around its average. A small standard deviation means the values huddle close to the mean, while a large one means they scatter widely. It is the most widely used measure of variability in statistics.

There are two versions. Population standard deviation applies when your data covers the entire group, while sample standard deviation applies when your data is a sample meant to represent a larger group, and it divides by one less than the count to correct for bias. This calculator reports both so you can use the one your situation calls for.

The formula

sample SD = sqrt( sum of (x - mean)^2 / (n - 1) )

Worked example

For 10, 12, 23, 23, 16, 23, 21, 16, the sample standard deviation is about 5.24.

How to read your result

Standard deviation measures how spread out a data set is around its mean. A small value means the data clusters tightly; a large value means it is widely scattered.

Frequently asked questions

Sample or population SD?: Use sample when your data is a sample of a larger group; use population when you have the entire group.
Why divide by n minus 1 for a sample?: It corrects for the bias of estimating the mean from the same data.
What is variance?: It is the square of the standard deviation.

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