How to use this variance calculator
Enter your dataset above, choose Sample or Population, and Calculate. Along with the variance you will see the sum of squares it came from and the full deviation table, so the working is never a black box.
What is variance?
Variance is the average of the squared distances between each value and the mean. Where standard deviation asks "how far, typically, is a value from the average?", variance answers the same question before the square root is taken, and that squaring is exactly why statisticians love it. Squared distances are smooth, differentiable and add up neatly: the variance of a sum of independent variables is the sum of their variances. That one property carries variance into ANOVA, regression and most of modern statistics.
The price of that convenience is units. If your data is in centimetres, the variance is in square centimetres, which nobody can picture. That is why reports usually give the standard deviation, while calculations work with the variance.
Seedling heights. A student measures six seedlings (cm): 12.4, 15.1, 13.8, 17.2, 14.5, 16.0. The mean height is 14.83 cm. Squaring each seedling's distance from 14.83 and adding gives a sum of squares of 14.13. These six plants are a sample from the whole tray, so divide by n − 1 = 5: sample variance s² ≈ 2.83 cm². Take the square root and you get the more readable sample standard deviation, ≈ 1.68 cm.
How variance is calculated, step by step
- Calculate the mean of the dataset.
- Subtract the mean from every value (the deviations).
- Square each deviation and add them: this total is the sum of squares.
- Divide by N (population) or n − 1 (sample). The result is the variance.
Variance vs standard deviation: which should I report?
Report the standard deviation when a human has to interpret the number, because it shares your data's units. Use the variance when the number feeds into further maths: comparing group variances (ANOVA, Levene's test), building confidence intervals, or working with distributions, where variances combine cleanly. Both describe the same spread; they are never in competition.
Frequently asked questions
How do I convert variance to standard deviation?
Take the square root. A variance of 2.83 corresponds to a standard deviation of about 1.68, in the original units of the data.
Why is variance measured in squared units?
Because each deviation from the mean is squared during the calculation. Variance of heights in centimetres is in cm². The standard deviation removes the squaring, which is why it is easier to interpret.
Can variance be zero or negative?
Variance can be zero (when every value equals the mean) but never negative, because it averages squared quantities.
What is the difference between sample and population variance?
Population variance divides the sum of squared deviations by N. Sample variance divides by n − 1 (Bessel's correction) to correct the bias in estimating a population's variance from a sample.