Standard Deviation Calculator

Enter numbers separated by commas (e.g., 5, 10, 15, 20):

What standard deviation measures

Standard deviation tells you how spread out your numbers are. A small value means most numbers sit close to the average. A large value means they are spread widely.

How this calculator works

Find the mean (average) of your numbers.
Subtract the mean from each number and square the result.
Find the average of those squares. This is the variance.
Take the square root of the variance. This is the standard deviation.

σ = √[ Σ(x − mean)² ÷ n ]

This calculator divides by n, the number of values, which gives the population standard deviation. If your numbers are a sample from a bigger group, statisticians usually divide by n − 1 instead (the sample standard deviation). The z-score calculator lets you choose either.

Worked example

Numbers: 2, 4, 4, 4, 5, 5, 7, 9.

Mean = 40 ÷ 8 = 5
Squared differences: 9, 1, 1, 1, 0, 0, 4, 16, which add up to 32
Variance = 32 ÷ 8 = 4
Standard deviation = √4 = 2

Frequently asked questions

Why square the differences?

Some differences are negative and some positive, so they would cancel out if you just added them. Squaring makes them all positive and gives more weight to values far from the mean.

What is a 'good' standard deviation?

There is no single good value. Compare it with the mean: a standard deviation of 5 is large if the mean is 10, but small if the mean is 1,000.