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Variance Calculator

Sample and population variance, plus standard deviation, from any list of numbers.

Sample & Population

Both the n − 1 and n versions in one go

Std Dev Too

The square root, in the same units as your data

Step by Step

Mean and sum of squared deviations shown

Variance of a Data Set
Paste your numbers to get both the sample and population variance, along with the matching standard deviations.

Comma- or space-separated numbers (at least two).

How Variance Works

The Formula

s² = Σ(xᵢ − x̄)² / (n − 1)  (sample)
σ² = Σ(xᵢ − x̄)² / n  (population)

Square every deviation from the mean, add them up, then divide by n − 1 for a sample or n for a population. The square root of the result is the standard deviation.

Why It Matters

Variance is the foundation of dispersion statistics. In finance the standard deviation of returns is the volatility, and portfolio variance — built from variances and covariances — is the engine of diversification.

Full Portfolio Analytics

Beyond a single data set

ARIA builds the full variance-covariance matrix across your holdings to measure true portfolio risk — the step beyond a one-series variance.

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Frequently Asked Questions