Variance Calculator
Compute the variance of a dataset — sample or population — along with the corresponding standard deviation and mean. Variance measures how spread out values are around the mean, expressed in squared units of the original data.
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Enter at least two numbers and press Calculate.
Variance formulas
Sample variance
s² = Σ(xᵢ − x̄)² / (n − 1)
Population variance
σ² = Σ(xᵢ − μ)² / n
Variance is the mean of the squared deviations from the mean. It is expressed in squared units — if your data is in metres, variance is in square metres — which is why standard deviation (the square root of variance) is often easier to interpret.
Worked examples
Example 1 — Small dataset
Values: 2, 4, 4, 4, 5, 5, 7, 9
Mean = 5. Deviations squared sum = 32. Population variance = 32/8 = 4. Sample variance = 32/7 ≈ 4.571.
Population variance = 4 · Sample variance ≈ 4.571
Example 2 — Repeated value
Values: 3, 3, 3, 3
Every deviation is 0. Variance is 0.
Variance = 0
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Frequently asked questions
Standard deviation is the square root of variance. SD is expressed in the same units as the original data, making it easier to interpret; variance is in squared units but is mathematically more convenient for some analyses.
No. Variance is an average of squared deviations, and squares are always non-negative.
Variance appears directly in many statistical formulas, including ANOVA, regression analysis, portfolio risk, quality control and hypothesis testing. It quantifies the "spread" of a distribution.