Standard Deviation Calculator
Measure the spread of a dataset using population or sample standard deviation. See variance and the mean alongside the result.
Standard deviation
Accepts comma or whitespace separated finite numbers. Sample deviation requires at least two values.
Formula checked · NumberSwift · Review process
How this calculator works
Standard deviation measures spread around the mean in the same units as your input. Choose population when the data include the complete group of interest. Choose sample when the data are used to estimate a larger population; dividing by n−1 adjusts the variance estimate. At least two values are required for a sample.
Formula
mean = Σx / n; variance = Σ(x − mean)² / n (population) or / (n − 1) (sample)
Assumptions & limitations
Accepts comma or whitespace separated finite numbers. Sample deviation requires at least two values.
Sources & reference material
- OpenStax: descriptive statistics ↗
Reference for the centre and spread of data.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5 and the sum of squared deviations is 32. Population variance is 32 ÷ 8 = 4, so standard deviation is 2. For a sample, divide by 7 instead: the standard deviation is about 2.1381.
For median, mode and range alongside the mean, use the Average Calculator on the same observations.
Our approach to calculations ↗Common questions
Should I choose population or sample?
Choose population for the complete group you are describing. Choose sample when estimating spread in a larger population from sampled observations.
Why divide sample variance by n−1?
Using the sample mean leaves one fewer degree of freedom; n−1 is the standard correction for sample variance.
What units does standard deviation use?
The same units as the inputs. Variance uses squared units.