Standard Deviation Calculator

Enter your numbers and choose population or sample.

At least two values, separated by commas or spaces

Result

Enter values and press Calculate to see the result.

Formula

σ=∑(xi−μ)2n\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n}}

Population standard deviation.

s=∑(xi−xˉ)2n−1s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}

Sample standard deviation uses n − 1 (Bessel’s correction).

How to use this calculator

  1. Enter the data and choose population if it is the whole group, or sample if it is part of a larger group.
  2. Press Calculate.

Worked example

Population: 2, 4, 4, 4, 5, 5, 7, 9

The mean is 5 and the squared deviations add up to 32.

Variance = 32 / 8 = 4, so the standard deviation is √4 = 2.

Frequently asked questions

Population or sample?

Use population when you have every member of the group; use sample when your data is a subset used to estimate the whole.

What does standard deviation tell me?

How far values typically are from the mean. Larger means more spread out.

Learn more