Variance Calculator

Data type

Data set — numbers separated by commas or spaces

Variance —

Standard deviation —

Mean —

Count (n) —

How to Calculate Variance

Enter your numbers and choose whether they are the whole population or a sample drawn from one.

Enter the data set

Type your numbers separated by commas, spaces or new lines, like 600, 470, 170, 430, 300. Whole numbers and decimals are both fine.

Pick population or sample

Choose Population to divide by n, or Sample to divide by n−1 (Bessel’s correction) when your numbers are a subset of a larger group.

Read the result and steps

The variance appears first, with the standard deviation and mean beside it. The steps show the mean, the squared deviations and the final division. Prefer the spread in the original units? The Standard Deviation Calculator takes the square root for you.

Frequently Asked Questions

What is variance?

Variance measures how far a set of numbers is spread out from their mean. It is the average of the squared differences between each value and the mean. Because the differences are squared, variance is expressed in squared units; taking its square root gives the standard deviation, which is in the original units.

What is the difference between population and sample variance?

Population variance divides the sum of squared deviations by n and is used when the data is the entire group. Sample variance divides by n−1 instead, correcting for the fact that a sample tends to underestimate the spread of the population it was drawn from. Use sample variance when your numbers are a subset of a larger group.

How do you calculate variance by hand?

Find the mean of the numbers, then subtract the mean from each value and square each result. Add the squared deviations together, and divide by n for a population or n−1 for a sample. The result is the variance. This calculator shows each step of that process.

Why is variance in squared units?

Variance squares each deviation from the mean before averaging, so its units are the square of the data’s units — for example, dollars squared. That makes variance harder to interpret directly, which is why the standard deviation, the square root of variance, is often reported instead: it returns to the original units.

How to Calculate Variance

Enter the data set

Pick population or sample

Read the result and steps

Frequently Asked Questions

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