Standard Deviation Calculator
Paste a data set and get its spread and summary statistics at once.
| Sample standard deviation (s) | 2.13809 |
|---|---|
| Population standard deviation (σ) | 2 |
| Mean | 5 |
| Sample variance (s²) | 4.571429 |
| Population variance (σ²) | 4 |
| Count | 8 |
| Sum | 40 |
| Median | 4.5 |
| Min / max | 2 / 9 |
How to use it
- Paste or type your numbers. Commas, spaces and line breaks all work, so you can paste a spreadsheet column.
- Use the sample standard deviation when your numbers are a sample from a larger group; use the population value when they are the whole group.
Formula
Mean x̄ = Σx ÷ nSample standard deviation s = √( Σ(x − x̄)² ÷ (n − 1) )Population standard deviation σ = √( Σ(x − x̄)² ÷ n )Variance is the standard deviation squared
Example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 40 ÷ 8 = 5. The squared differences add up to 32, so the population variance is 32 ÷ 8 = 4 and σ = 2. The sample variance is 32 ÷ 7 = 4.571429, so s = 2.13809.
Questions
Why divide by n − 1 for a sample?
Using n − 1 (Bessel's correction) makes the sample variance an unbiased estimate of the population variance.
What does standard deviation tell me?
How spread out values are around the mean. In roughly bell-shaped data, about two-thirds of values fall within one standard deviation of the mean.
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Last reviewed 2026-10-11. Found a mistake? Tell us.