Statistics Calculator

Variance Calculator

Calculate sample variance or population variance from a numeric data set and review the mean, standard deviation, sample size, and denominator used.

Free to useRuns in your browserClear formula & method

Enter your data

Variance inputs

Use the fields below. Results update only when you select the calculate button.

Separate values with commas, spaces, semicolons, or new lines.
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What is a variance calculator?

Variance measures spread by averaging squared distances from the mean. Because the deviations are squared, variance is expressed in squared units and gives greater weight to observations farther from the center.

Use this page for a transparent calculation, then compare the result with the Standard Deviation Calculator when a different view of the same data would be useful.

How does this variance calculator work?

The calculator uses a numerically stable one-pass method to find the mean and sum of squared deviations. It divides by n − 1 for a sample or by N for a complete population.

Before interpreting spread or position, it can help to check the center with the Average Calculator. Every tool states its assumptions so results can be reproduced.

Sample: s² = Σ(xᵢ − x̄)² / (n − 1)   |   Population: σ² = Σ(xᵢ − μ)² / N

How to use this calculator

  1. Enter the requested numbers in the labeled fields.
  2. Review unit, sample, confidence, or test choices when shown.
  3. Select Calculate Variance.
  4. Read the main result, supporting facts, and method note.
  5. Use Copy, Download, or Print when you need to keep the result; select Reset to start over.

If you edit any input after calculating, the old result is marked stale and hidden until you calculate again.

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How should you interpret the result?

A variance of zero means every value is identical. Larger variance indicates greater spread, but comparison is clearest when data sets use the same measurement units and similar scales.

For another useful perspective, open the Coefficient of Variation Calculator; it answers a related question without changing the values you entered here.

Assumptions and limitations

Variance is sensitive to outliers, and its squared units may be less intuitive than standard deviation. The sample formula also assumes the observations reasonably represent the target population.

Consider the Interquartile Range Calculator for a complementary summary and the Mode Calculator when your question involves another statistical property. No single statistic describes every important feature of a data set.

Scope: Results are educational calculations, not a substitute for an appropriate study design, subject-matter expertise, or professional statistical review.

Frequently asked questions

Variance measures spread by averaging squared distances from the mean. Because the deviations are squared, variance is expressed in squared units and gives greater weight to observations farther from the center.
Use the labeled fields in the calculator and enter finite numeric values. The page validates missing, impossible, and mismatched inputs before showing a result.
Sample: s² = Σ(xᵢ − x̄)² / (n − 1)   |   Population: σ² = Σ(xᵢ − μ)² / N
A variance of zero means every value is identical. Larger variance indicates greater spread, but comparison is clearest when data sets use the same measurement units and similar scales.
Variance is sensitive to outliers, and its squared units may be less intuitive than standard deviation. The sample formula also assumes the observations reasonably represent the target population.
Yes. The calculator and BMI-style result panel are responsive for phones, tablets, laptops, and desktop screens.
No. Calculations run in your browser. This page does not require an account, and the entered values are not sent to a calculation server.
No. It is an educational tool for transparent calculations and quick checks. Important research, clinical, legal, financial, or policy decisions should use an appropriate study design and qualified review.

Sources and methodology

The formulas and cautions on this page are documented so the calculation can be checked against authoritative statistical guidance.

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