Standard Deviation Calculator

Measure the spread of a population or sample with variance and mean.

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Behind the answer

σ = √(Σ(x − mean)² / N); sample s uses N − 1

How to use this calculator

Population deviation describes every member of a group. Sample deviation uses Bessel’s correction when the values represent a sample. The standard error is standard deviation divided by √n. Margin of error and intervals use a normal approximation, not an exact small-sample t interval.

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Formula and method

σ = √(Σ(x − mean)² / N); sample s uses N − 1

A sample requires at least two observations.

Worked example

The default population has mean 5 and standard deviation 2.

Questions about standard deviation calculator

When should I choose sample standard deviation?

Choose sample when the list represents observations sampled from a larger population. It divides squared deviations by n − 1 and requires at least two observations. Population mode divides by n when describing the entire group.

What assumptions should I check?

A sample requires at least two observations.

Are my inputs saved?

Calculations run in your browser. We store only tool IDs for favorites and recent tools. A calculation link contains your inputs only when you explicitly choose to copy one.