Variance Calculator
Enter your data and get sample variance, population variance, their standard deviations, and descriptive statistics. This tool is meant to outperform one-purpose variance tools by giving you everything in one place.
Separate numbers with comma, space, semicolon or new line.
Variance formulas
Population variance: \(\sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2\)
Sample variance: \(s^2 = \frac{1}{n - 1} \sum_{i=1}^{n} (x_i - \bar{x})^2\)
Standard deviation: \(\sigma = \sqrt{\sigma^2}, \; s = \sqrt{s^2}\)
FAQs
Why (n − 1) for sample variance?
Because we are estimating the population variance from a sample. Using n − 1 instead of n makes the estimator unbiased.
What if I only have one value?
Population variance will be 0 (no spread). Sample variance is undefined (division by 0) — we report “—”.
Why square the differences?
Squaring keeps all deviations positive and penalizes larger deviations more strongly.
Formula (LaTeX) + variables + units
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Population variance: \(\sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2\) Sample variance: \(s^2 = \frac{1}{n - 1} \sum_{i=1}^{n} (x_i - \bar{x})^2\) Standard deviation: \(\sigma = \sqrt{\sigma^2}, \; s = \sqrt{s^2}\)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.