P-Value
Calculator
Exact p-value from a z-score or t-score.
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Statistics — Dispersion
Variance Calculator
Paste any list of numbers to get the sample and population variance — with the mean, squared deviations and standard deviation.
Sample variance (s²)
—
Divides the squared deviations by n−1.
| Count n | — |
|---|---|
| Mean | — |
| Sum of squared deviations | — |
| Population variance σ² | — |
| Sample std. deviation s | — |
| Population std. deviation σ | — |
Show our math
Enter your figures above to see the step-by-step working.
Paste comma, space or line-separated numbers — sample and population both shownEverything computed client-side — nothing leaves this page
How the Variance Calculator Works
Variance measures how far a set of numbers spreads out from their mean. The calculator finds the mean, adds up the squared distance of every value from it, then divides — by n−1 for a sample, or by n for a whole population. Standard deviation is simply the square root of the variance.
Use the sample variance when your numbers are a sample drawn from a larger group; the n−1 divisor (Bessel’s correction) makes it an unbiased estimate. Use the population variance only when your data covers every member of the population.
s² = Σ(x − x̄)² ÷ (n − 1) · σ² = Σ(x − x̄)² ÷ n
Frequently Asked Questions
What is the difference between sample and population variance?
Sample variance divides the summed squared deviations by n−1, giving an unbiased estimate when your data is a sample of a larger group. Population variance divides by n and is used only when you have the entire population. This tool shows both.
Why square the deviations?
Squaring makes every difference positive so they do not cancel out, and it weights larger deviations more heavily. The trade-off is that variance is in squared units, which is why standard deviation — its square root — is often reported instead.
Is variance the same as standard deviation?
No, but they are directly related: standard deviation is the square root of the variance. Variance is in squared units; standard deviation is in the same units as your data, which makes it easier to interpret.
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