--- title: "Variance Calculator with Steps | CanDoYa" description: "Variance calculator for sample or population data with formulas, mean, standard deviation, and every squared deviation shown. Free and private." url: https://candoya.com/tools/variance-calculator/ locale: en type: browser-tool --- # Free Variance Calculator Category: Calculators ## What does a variance calculator do? A variance calculator measures how widely numbers spread around their mean. Enter a data set to calculate both sample variance and population variance, compare their different divisors, and inspect every deviation and squared deviation used in the answer. The calculation updates instantly and stays in your browser. **Variance is the average squared distance from the mean.** This calculator accepts decimals, negative values, and scientific notation. It reports both common definitions at once: population variance for a complete group and sample variance for observations used to estimate a larger population. The worked table makes the arithmetic visible. Each row subtracts the mean from one value, squares that deviation, and contributes it to the sum of squares. The selected formula then divides that sum by n or n - 1. ## How to use it 1. **Enter your numbers** - Paste or type up to 2,000 values separated by commas, spaces, semicolons, or new lines. Decimals, negatives, and scientific notation are accepted. 2. **Choose the data set type** - Select sample when the values represent part of a larger group. Select population when the list contains every member you want to describe. 3. **Check the calculation** - Read the selected variance, formula, mean, standard deviation, sum of squares, and the table of individual squared deviations. 4. **Copy the result** - Copy the selected result and its supporting statistics into your worksheet, report, or notes. ## Who it's for - **Students** can check statistics homework against a complete row-by-row variance calculation. - **Teachers** can show how one outlier contributes a large squared deviation and changes the final result. - **Analysts** can compare the sample and population definitions before moving a small data set into a spreadsheet. - **Researchers** can summarize the spread of measurements, trial results, ratings, or response times. ## Expert note Squaring deviations changes both the scale and the influence of extreme values: a value twice as far from the mean contributes four times as much to variance. That is why variance is sensitive to outliers and why its unit is squared. Use the reported standard deviation when you need spread in the original measurement unit. ## Frequently asked questions ### Is my data uploaded to calculate variance? No. The number parsing, mean, squared deviations, and both variance formulas run in your browser. The values are not sent to a calculation server or saved by this tool. After the page loads, you can continue calculating without a network connection. ### Is this variance calculator free? Yes. It is free to use, requires no account, and does not hide the calculation behind a paywall. You can enter up to 2,000 values per calculation and switch between sample and population modes as often as needed. ### What is the difference between sample and population variance? Population variance divides the sum of squared deviations by n because the data contains the complete population. Sample variance divides by n - 1 because the same sample is being used to estimate its unknown population mean. That adjustment is called Bessel's correction. ### How do you calculate variance step by step? Find the arithmetic mean, subtract it from every value, square each deviation, and add the squares. Divide that sum by n for population variance or n - 1 for sample variance. For 4, 7, 13, 16, the mean is 10 and the sum of squares is 90. ### Why does sample variance need at least two values? The sample formula divides by n - 1. With one value, that divisor is zero, and one observation provides no information about variation in a larger population. Population variance can be zero for a one-value population because its only value equals its mean. ### Can variance be negative? No. Each deviation is squared before the values are added, so every contribution is zero or positive. Variance is zero only when all values are identical. A negative result from manual arithmetic usually points to rounding or an unstable shortcut formula. ### What is the relationship between variance and standard deviation? Standard deviation is the non-negative square root of variance. Variance uses squared units, such as square seconds, while standard deviation returns to the original unit. The calculator reports the standard deviation for the selected sample or population mode beside the variance. ## Related tools - [Standard Deviation Calculator](https://candoya.com/tools/standard-deviation-calculator/) - [Mean, Median & Mode Calculator](https://candoya.com/tools/mean-average-calculator/) - [Correlation Coefficient Calculator](https://candoya.com/tools/correlation-coefficient/) - [Z-Score Calculator](https://candoya.com/tools/z-score-calculator/) - [Median & Mode Calculator](https://candoya.com/tools/median-mode-calculator/) --- *Markdown edition of , published for AI agents and other automated readers. Index of key pages: .*