Variance Calculator
Enter your numbers below to instantly get population and sample variance.
What Is Variance?
Variance measures the average squared distance between each value in a data set and the mean. It's the foundation standard deviation is built on. For step-by-step work and the square-rooted result in the data's original units, see the standard deviation calculator.
Worked example
Data set: 4, 8, 6, 5, 3 (n = 5)
Mean = 26 / 5 = 5.2
Sum of squared differences from the mean = 14.8
Population variance = 14.8 / 5 = 2.96
Sample variance = 14.8 / 4 = 3.7
Frequently Asked Questions
What is variance?
Variance measures how spread out a data set is by averaging the squared distance of every value from the mean. It's the step right before standard deviation, which is just the square root of variance.
Why square the differences instead of just averaging them?
If you average the raw differences from the mean, the positive and negative differences cancel out and always sum to zero, which tells you nothing. Squaring makes every difference positive before averaging, so the spread actually shows up in the result.
Should I use population or sample variance?
Use population variance when your data is the entire group you care about. Use sample variance when your data is a sample used to estimate a larger population — it divides by n − 1 instead of n, which corrects for a sample's tendency to slightly underestimate the true spread.
Why is variance harder to interpret than standard deviation?
Variance is in squared units, since the differences were squared during the calculation. If your data is in dollars, variance is in dollars². Standard deviation undoes that by taking the square root, putting the result back in the original units.
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