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Variance Calculator
Last updated: June 19, 2026
A variance calculator is a statistical utility that computes the variance of a data set, measuring how far the numbers are spread out from their average value. It calculates both the population variance, which divides the sum of squared deviations by the total count (N), and the sample variance, which uses Bessel's correction by dividing by N-1. The tool also provides auxiliary statistics including the count, sum, mean, and standard deviation. Researchers, financial analysts, and students use this calculator to quantify volatility, evaluate risk, and analyze statistical dispersion.
Paste or type a list of numbers. We compute the mean, count, both sample and population variance, and the corresponding standard deviations — useful for stats homework, quick analysis, and sanity-checking spreadsheets.
Quick Answer
Calculate sample and population variance for any data set. Enter your numbers to see the variance, mean, and standard deviation with work.
Comma-, space-, or line-separated. Decimals and negatives are fine. Anything that isn't a number is silently ignored.
Sample variance (s²)
4.5714
divided by n − 1 (n = 8)
Examples
Wikipedia textbook set: 2, 4, 4, 4, 5, 5, 7, 9
sample var ≈ 4.571 · pop var = 4.000
10, 12, 23, 23, 16, 23, 21, 16
mean 18.0 · sample var ≈ 24.0
−5, 0, 5, 10
mean 2.5 · sample var ≈ 41.67
How it works
We compute the mean, then sum the squared distance of each value from the mean. Dividing by n gives population variance; dividing by n − 1 gives sample variance.
Mean · μ = (Σx) ÷ n
Sample variance · s² = Σ(x − μ)² ÷ (n − 1)
Population variance · σ² = Σ(x − μ)² ÷ n
Related statistics calculators
- Standard deviation calculator for standard deviation and step-by-step variance growth math.
- Standard error calculator for standard error of the mean (SEM).
- Confidence interval calculator for an interval around a sample mean or proportion.
- Expected value calculator
- Correlation coefficient calculator for the Pearson r between two paired variables.
- Linear regression calculator for a best-fit line and slope on paired data.
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Frequently asked questions
Sample variance divides by n − 1 (Bessel's correction) — it's the right choice when your data is a sample from a larger population. Population variance divides by n and is correct only when you have data for the entire population. Most real-world stats use the sample formula.
Comma-separated, space-separated, or one per line — all work. The calculator strips empty entries and ignores anything that isn't a valid number. Negative numbers and decimals are fine.
Standard deviation is the square root of variance. The variance is in the squared units of your data; the standard deviation is in the original units, which is why it's usually easier to interpret.
When every value in your dataset is the same, there's no spread — both variance and standard deviation are exactly zero. With a single value, sample variance is undefined (you'd divide by zero); population variance is zero.
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