Variance Calculator
Drop in a list of numbers and see how far they scatter around the mean, with both the sample and population variance side by side.
How it works
Variance measures spread. First we find the mean, then for every value we take its distance from that mean, square it, and add all those squared distances together. Squaring keeps negatives from cancelling positives and gives bigger gaps extra weight.
The two flavors differ only in what we divide by. Population variance divides the total by n, treating your numbers as the whole group. Sample variance divides by n − 1 instead — that slightly larger answer corrects for the fact that a sample tends to underestimate the true spread.
Take 4, 8, 15, 16, 23, 42. The mean is 18, the squared distances add up to 890, so the population variance is 890 ÷ 6 ≈ 148.3 and the sample variance is 890 ÷ 5 = 178.
Frequently asked questions
Should I use sample or population variance?
It depends on what your numbers represent. If they're the entire group you care about — every employee, every test in the room — use population variance. If they're a sample standing in for something larger, reach for the sample version with its n − 1 divisor.
Why divide by n minus one for a sample?
A sample almost always clusters a little tighter than the full population, which would make the spread look smaller than it truly is. Dividing by n − 1 nudges the estimate upward to compensate. Statisticians call it Bessel's correction.
How is variance related to standard deviation?
They're two views of the same thing. Standard deviation is just the square root of the variance, which brings the answer back into the original units instead of squared units. Variance is easier to work with in formulas; standard deviation is easier to interpret.
Why do I need at least two numbers?
A single value has nothing to spread against, and the sample formula would divide by zero. With two or more the calculation has something to measure, so give it a real list and the answer appears.