What is the difference between population and sample variance?

Population variance (σ²) divides the sum of squared deviations by N (the total count). Sample variance (s²) divides by N-1, applying Bessel's correction to give an unbiased estimate when your data is a sample drawn from a larger population.

How many numbers do I need?

You need at least 2 numbers to compute sample variance (N-1 would be zero otherwise). Population variance can be computed for a single number, but it is always zero in that case.

Does the order of numbers matter?

No. Variance is based on the squared deviations from the mean, so the order of your input values does not affect the result.

What separators can I use?

You can separate numbers with commas, spaces, tabs, or new lines. The calculator strips all whitespace and splits on commas automatically.

What is standard deviation?

Standard deviation is the square root of variance. It expresses spread in the same units as your original data, making it easier to interpret than variance.

Variance Calculator

Enter a list of numbers to instantly calculate population variance, sample variance, mean, and standard deviation.

Enter Numbers

Numbers (comma, space, or new line separated)

Quick examples

Enter numbers on the left to see results

Population Variance (σ²)

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Divides by N

Sample Variance (s²)

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Divides by N-1

Population Std Dev (σ)

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Sample Std Dev (s)

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Count (N)

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Sum

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Mean (x̄)

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Deviation Table

#	Value (xᵢ)	xᵢ - x̄	(xᵢ - x̄)²
Σ	—	0	—

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Summary

Enter a list of numbers to instantly calculate population variance, sample variance, mean, and standard deviation.

How it works

Enter your numbers separated by commas, spaces, or new lines.
The calculator parses and validates each value in real time.
It computes the mean (average) of all values.
Each deviation from the mean is squared and summed.
Population variance divides by N; sample variance divides by N-1.
Standard deviation is the square root of the respective variance.

Use cases

Check homework answers for statistics assignments.
Verify spreadsheet variance formulas (VAR.P vs VAR.S in Excel).
Analyze variability in scientific measurements or survey data.
Compare spread between two datasets using variance.
Understand the difference between population and sample variance.
Quickly compute descriptive statistics for small datasets.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu