About the Variance Calculator
Variance measures how spread out a set of numbers is around its mean. A small variance means the values cluster tightly, while a large one means they are scattered. This calculator takes any list of numbers and gives both the sample variance, which divides by n minus one and is used when your data is a sample from a bigger group, and the population variance, which divides by n and is used when you have every value. You also get the mean, the sum, the sum of squared differences, both standard deviations and the coefficient of variation, so you can see the whole calculation at once.
Updated October 2026
How to use the Variance Calculator
- 1Type or paste your numbers into the box, separated by commas, spaces or new lines.
- 2Decide whether the numbers are a sample or the whole population.
- 3Read the sample variance in the big result box, or the population variance in the list.
- 4Check the mean and sum of squares to follow the working by hand.
- 5Copy the summary line into your report.
Choosing sample or population
Ask whether your list is everything you care about. Test scores for all students in one class, if the class is your whole interest, form a population. Test scores for 30 students used to describe all students in a country form a sample. Most real data in surveys and experiments is a sample, so the n minus 1 version is the usual choice.
Reading the result
- A variance near zero says the values are almost identical.
- Compare variances only for data on the same scale.
- Take the square root to turn the spread back into the original units.
- A very large variance often points to an outlier, so look at the highest and lowest values.
Where variance shows up
Variance is behind the standard deviation, z-scores and confidence intervals, and it plays a central role in finance, where it measures the risk of an investment, and in quality control, where it checks how consistent a machine is. For the next steps try the Standard Deviation Calculator, the Z-Score Calculator and the Confidence Interval Calculator.
Features
- Sample variance and population variance together
- Both standard deviations
- Mean, sum, count and sum of squared differences
- Coefficient of variation as a percentage
- Accepts commas, spaces, semicolons and new lines
- Points out any entry that is not a number
Frequently asked questions
What is the difference between sample and population variance?
Population variance divides the sum of squared differences by n and is for data that includes every member of the group. Sample variance divides by n minus 1, which corrects for the fact that a sample tends to underestimate the spread of the whole group.
How do I calculate variance by hand?
Find the mean, subtract it from each value, square each difference, add the squares and divide by n for a population or n minus 1 for a sample. For 2, 4, 6 the mean is 4, the squares are 4, 0 and 4, the sum is 8 and the sample variance is 4.
What is the relationship between variance and standard deviation?
Standard deviation is the square root of variance. It is easier to interpret because it uses the same units as the data, whereas variance uses squared units. If the variance is 4 square metres, the standard deviation is 2 metres.
Can variance be negative?
No. It is built from squared differences, which are never negative, so variance is zero or positive. It is zero only when every value is exactly the same.
Why does the sample variance need two numbers?
With a single value there is nothing to compare it with, so the spread cannot be estimated. Dividing by n minus 1 would also mean dividing by zero. The calculator shows the population figures for one number and asks for at least two for the sample.
What is the coefficient of variation?
It is the standard deviation divided by the mean, shown as a percentage. It lets you compare the spread of data measured on different scales, such as prices in dollars and weights in kilograms. It is not meaningful when the mean is near zero.