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Variance Calculator

Sample or population variance from a data set.

Best for: Use it in statistics to quantify variability, or as a step toward standard deviation.

Complete guide

Input

How it's calculated & sources
The Variance Calculator uses the standard, deterministic formula, so the same inputs always produce the same result. It runs entirely in your browser, so your inputs are never uploaded. Last reviewed June 2026.

Free & no sign-up · runs entirely in your browser. Results are estimates for general information, not professional advice — verify important decisions with a qualified expert. Last reviewed June 2026.

How it works

Variance = Σ(xᵢ − x̄)² / (n or n−1)

Example

2,4,4,4,5,5,7,9 → sample variance ≈ 4.571

Frequently asked questions

Why square the differences?+

Squaring removes negatives and weighs larger deviations more heavily.

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Complete guide

Quick answers

Short, sourced answers to the questions people (and AI assistants) ask most.

What is Variance?
A variance calculator measures how spread out a data set is - the average of the squared distances from the mean.
Why does Variance matter?
A larger variance means more spread. It is in squared units; take its square root for the standard deviation, which is in the original units.
How is Variance calculated?
It finds the mean, squares each value's distance from it, and averages those squares. Population variance divides by N; sample variance divides by n - 1. Formula: Population: sigma^2 = sum(x - mu)^2 / N; Sample: s^2 = sum(x - xbar)^2 / (n - 1).
What are common variance mistakes?
Using population variance (N) when you have a sample (should use n - 1).
When should you use the Variance Calculator?
Use it in statistics to quantify variability, or as a step toward standard deviation.

What is the Variance Calculator?

A variance calculator measures how spread out a data set is - the average of the squared distances from the mean.

How the Variance Calculator works

It finds the mean, squares each value's distance from it, and averages those squares. Population variance divides by N; sample variance divides by n - 1.

Population: sigma^2 = sum(x - mu)^2 / N; Sample: s^2 = sum(x - xbar)^2 / (n - 1)

Empirical rule — data within ±k standard deviations (normal)

±1σ68.27%31.73%
±1.5σ86.64%13.36%
±2σ95.45%4.55%
±2.5σ98.76%1.24%
±3σ99.73%0.27%

Common mistakes to avoid

  • Using population variance (N) when you have a sample (should use n - 1).
  • Forgetting the result is in squared units.
  • Letting a single outlier dominate via the squaring.

Keywords: variance.

Sources: NIST/SEMATECH e-Handbook of Statistical Methods

Reviewed by the Free Tools Galaxy editorial team · Updated June 2026 · Calculated privately in your browser.

Frequently asked questions

Is the Variance Calculator free to use?+

Yes. Every tool on Free Tools Galaxy is 100% free, runs in your browser and requires no signup.

How accurate is the Variance Calculator?+

Variance Calculator uses the standard variance formula in double-precision arithmetic, so the same inputs always produce the same result and you can verify any figure by hand. It is an educational estimate — real-world outcomes depend on your actual rates, rules and assumptions.

Do you store my inputs?+

No. The Variance Calculator runs entirely in your browser. Nothing is uploaded or saved to a server.

Can I use the Variance Calculator on mobile?+

Yes — the interface is fully responsive and works on phones, tablets and desktops.

What are common mistakes to avoid?+

The most frequent mistake is mixing units. Double-check your inputs use a single, consistent unit before clicking Calculate.

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Sample or population variance from a data set.

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