Math calculator

Standard Deviation Calculator

Calculate population and sample variance and standard deviation from a numeric dataset.

Dataset

Sample variance and deviation require at least two values.

Population standard deviation

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How it works

Standard deviation measures typical distance from the mean. Use the population result when the values are the entire group of interest; use the sample result when the values estimate a larger population. Sample calculations require at least two observations.

Population variance = Σ(x − μ)² ÷ N; Sample variance = Σ(x − x̄)² ÷ (n − 1)

Worked example

For 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5, population variance is 4, and population standard deviation is 2.

How to use this tool

Enter the known values and choose units where available.
Check the primary result and supporting details.
Clear or replace an input to calculate another case.

Frequently asked questions

What happens with invalid or incomplete inputs?

The result remains blank until the required inputs form a finite, meaningful calculation. Zero denominators and physically impossible negative quantities are not calculated.

Can I use decimal values?

Yes. The tool accepts decimals and keeps full precision for the calculation while rounding the displayed result for readability.