Variance Calculator – Population and Sample
Free variance calculator: enter numbers to get variance, standard deviation, and mean. Choose population or sample. No sign-up.
Variance Calculator
Compute variance, standard deviation, and mean for a set of numbers. Choose population or sample.
How variance is calculated
Population variance: σ² = Σ(x − μ)² / n. Sample variance: s² = Σ(x − x̄)² / (n−1). Standard deviation = √variance. The calculator requires at least one value; sample variance requires at least two.
Understanding variance
Variance quantifies the spread or dispersion of a dataset. If all values are the same, variance is zero. As values spread out from the mean, variance increases. Variance is the average of squared deviations, which gives more weight to larger deviations. The square root of variance (standard deviation) returns to the original units and is often easier to interpret.
Use population variance when you have complete data (e.g. all students in a class). Use sample variance when you have a sample and want to estimate the population variance (e.g. a survey of 100 people). The standard deviation calculator provides the same statistics; both tools are useful for data analysis and statistics homework.