Calculate sample or population variance to measure how spread out your data values are from the mean
Use when data is a subset of a larger group (divides by n-1)
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Variance measures how far each data point is from the mean on average, squared. Our calculator shows the complete breakdown of deviations, making it perfect for learning statistics or verifying your calculations. Get both sample and population variance with detailed steps.
Variance (σ² or s²) is the average of squared differences from the mean. It tells you how spread out your data is. A variance of 0 means all values are identical to the mean. Higher variance means data is more spread out. Standard deviation is simply the square root of variance.
Variance Formula
Learn variance calculation with step-by-step breakdown.
Measure consistency in manufacturing processes.
Analyze investment risk and portfolio diversification.
Assess data variability in experiments.
Measures data spread and consistency
Foundation for standard deviation
Used in statistical tests (F-test, ANOVA)
Key metric in portfolio theory
Helps identify outliers
Standard deviation is the square root of variance. While variance is in squared units (which can be hard to interpret), standard deviation is in the original units of your data, making it more intuitive for understanding spread.
Squaring serves two purposes: (1) it makes all deviations positive so they don't cancel out, and (2) it gives more weight to larger deviations, making variance sensitive to outliers. This is why we take the square root to get standard deviation.
No, variance can never be negative because we're squaring the deviations. The minimum variance is 0, which occurs when all data points are identical.
Standard deviation is the square root of variance. Variance is expressed in squared units (e.g. dollars²), which is hard to interpret, so standard deviation — in the original units — is usually reported. Variance is still preferred in the math of ANOVA and regression because squared terms add cleanly.