Variance Calculator
Last updated: June 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
Quick reference
Variance formulas:
| Type | Divisor | Formula |
|---|---|---|
| Population | N | sum (x - mean)^2 / N |
| Sample | n - 1 | sum (x - mean)^2 / (n - 1) |
functions Shows the working, not just the answer
For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.
calculate Accurate to the spec
Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.
school Free for classroom use
Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.
tips_and_updates Pair with the spoke articles
Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.
Interpretation guide
Interpreting variance:
| Result | Meaning |
|---|---|
| Low variance | Data clustered near the mean |
| High variance | Data spread widely |
| Variance = 0 | All values identical |
| Std dev | Square root of variance (same units as data) |
Formula & methodology
Formula: Sample variance s^2 = sum (x - mean)^2 / (n - 1); population variance uses N
Variance measures how far data points spread from their mean by averaging the squared deviations. Use the population formula (divide by N) when you have every value, and the sample formula (divide by n-1, Bessel's correction) when estimating from a sample. The standard deviation is the square root of variance and is easier to interpret because it shares the data's units. The calculator shows the mean, squared deviations, and both statistics.
Frequently asked questions
Explore the full statistics toolkit
Every CalcaTools statistics calculator — descriptive measures, probability distributions, hypothesis tests, confidence intervals, and Six Sigma process metrics — with step-by-step workings on each result.