About Variance
Variance quantifies spread by averaging the squared distance of every value from the dataset mean. Squaring is what makes it a usable measure: without it, positive and negative deviations would cancel and the average would always be zero regardless of how spread out the numbers were.
The trade-off is interpretability. Variance is expressed in squared units — the variance of a set of metres is in square metres — so it is a figure to be carried through further statistics rather than quoted as a description of the data. Taking its square root gives the standard deviation, which returns to the original units and is what most reporting uses.
This calculator applies the population convention and divides by N, the number of values. A sample-based variance would divide by N-1 and read slightly larger, since it corrects for estimating the mean from the same data. Results are rounded to four decimal places, and pasting the same list into the standard deviation calculator gives the square root of this figure.
How to use Variance
- 1 Drop the dataset into the Numbers box — it is read as a single list of values.
- 2 Click to calculate.
- 3 Read the variance, rounded to four decimal places.
Frequently asked questions
Should I report variance or standard deviation?
Almost always the standard deviation, because its units match the data and readers can compare it directly with the mean. Variance is the intermediate quantity you keep when combining datasets or running an analysis of variance.
What does a variance of zero tell me?
That all values are identical. Any spread at all produces a positive variance, since the squared deviations cannot cancel. A surprising zero usually points to a parsing problem rather than genuinely uniform data.
Is this the population or sample variance?
Population — the sum of squared deviations divided by N. The sample version divides by N-1, which yields a larger result, and is the one most statistical software defaults to when the data is a sample.
Why can variance be much larger than the values themselves?
Because the deviations are squared before averaging, so a spread of ten units contributes a hundred to the sum. That is normal and is exactly why the square root is taken to produce the standard deviation.
Free, online, and private
Free to use
Variance is completely free. There is no account to create, no login, and no hidden charge or usage limit.
Runs online in your browser
It is a free online tool that runs entirely in your browser. Nothing to download or install — open the page and start using it right away.
Your data stays private
All processing happens locally on your device. Your input is never uploaded, stored, or tracked, so it never leaves your browser.
How Variance behaves in detail
These are the specifics of this implementation — the exact ranges, defaults and fixed settings you are working with.
| Parameter | Value |
|---|---|
| Divisor | n — the mean of the squared deviations from the mean, i.e. the population variance |
| Difference from the SD tool | identical arithmetic without the square root, on the same default dataset |
| Precision | 4 decimal places |
| Separators recognised | commas, spaces, tabs and newlines, split on /[, s]+/ |
| Empty result | the words "No numbers" when nothing parses |
| Defaults | 10, 12, 23, 23, 16, 23, 21, 16, which returns 24.0000 |
Compiled from the implementation of this tool and checked against it by itoolnet.
What Variance does not do
Knowing the edges of a tool saves more time than another list of its features. These are the cases where it will not do what you might expect.
- The result is expressed in squared units — pounds squared, or metres squared — because each deviation is squared before the average is taken. It cannot be compared against the original values until the square root is taken, which has to be done somewhere else.
- Only the population form is available. The n − 1 divisor that applies when the list is a sample of a larger group cannot be selected, and since the divisor is hard-coded the output is not labelled with the convention it used the way the standard deviation line is.
- How many values were actually used is never reported. Non-numeric tokens are dropped and a leading or trailing comma turns into a 0 because Number("") is 0, so the variance can be computed over a different list than the one you pasted with nothing to show the substitution.
Tested and documented by itoolnet, the team that builds and maintains this site.