What does standard deviation measure?

Standard deviation measures how spread out values are around the mean. A larger standard deviation means the values are more spread out.

What is the difference between sample and population standard deviation?

Population standard deviation uses all values in the full population. Sample standard deviation uses a smaller sample and divides by n minus 1.

What separators can I use?

You can separate numbers with commas, spaces, or new lines.

Quick Tool Labs

Standard Deviation Calculator

Use this standard deviation calculator to measure how spread out a list of numbers is. It shows the population standard deviation, sample standard deviation, mean, and count.

Calculator

Numbers

Population SD0

Sample SD0

Mean0

Count0

Enter a list of numbers to calculate standard deviation.

How this standard deviation calculator works

This calculator finds the mean, measures how far each value is from that mean, squares those differences, and then takes the square root of the variance.

Population SD = sqrt(sum of squared differences / n), Sample SD = sqrt(sum of squared differences / (n - 1))

Use it when you want a quick view of consistency, spread, or variability in a set of values.

Examples

Example 1

The population standard deviation of 2, 4, 4, 4, 5, 5, 7, and 9 is 2.

Example 2

A smaller standard deviation means the values are closer together around the mean.

Example 3

A larger standard deviation means the values are more spread out.

Frequently asked questions

Which result should I use, sample or population?

Use population standard deviation when your list contains the full set of values. Use sample standard deviation when your list is a sample from a larger group.

Can I use decimals?

Yes. Decimals and negative numbers are accepted and included normally.

What if I enter only one value?

The population standard deviation is 0, while the sample standard deviation is undefined because a sample needs at least two values.