--- title: "Standard Deviation Calculator - Sample & Population | CanDoYa" description: "Standard deviation calculator for sample or population data. Paste numbers to get standard deviation, variance, mean, and calculation steps instantly." url: https://candoya.com/tools/standard-deviation-calculator/ locale: en type: browser-tool --- # Free Standard Deviation Calculator Category: Calculators ## What does a standard deviation calculator do? A standard deviation calculator measures how far values typically spread from their mean. Enter a data set, choose sample or population, and the calculator finds the standard deviation, variance, mean, and sum of squared deviations. Results update instantly in your browser, with no data uploaded. This calculator accepts decimals, negative values, and scientific notation. Separate values with commas, spaces, semicolons, or new lines. It uses the sample formula by default because most real data sets represent part of a larger population. Switch to population only when your list contains every member of the group you want to describe. The result panel shows each quantity used in the calculation. Standard deviation keeps the original unit of your data, while variance uses that unit squared. ## How to use it 1. **Enter the data** - Paste or type at least two numbers, separated by commas, spaces, semicolons, or new lines. 2. **Choose sample or population** - Keep Sample when the values represent part of a larger group. Choose Population when the list covers the entire group. 3. **Read the result** - Review the standard deviation, formula, mean, variance, count, standard error, and sum of squared deviations. 4. **Copy the statistics** - Select Copy results to put the complete summary on your clipboard. ## Who it's for - **Students** checking statistics homework and comparing the sample and population formulas. - **Researchers** summarizing the spread of measurements before further analysis. - **Teachers** demonstrating how an outlier changes variance and standard deviation. - **Analysts** verifying a small data set before entering it in a spreadsheet or report. - **Quality teams** comparing variation in repeated process or product measurements. ## Expert note The only arithmetic difference between the two modes is the divisor: population variance uses n, while sample variance uses n - 1. That adjustment, called Bessel's correction, reduces the tendency of a sample to underestimate population variance. Also check the data shape before interpreting the number: a single extreme value can inflate standard deviation because every deviation is squared. ## Frequently asked questions ### Is my data uploaded when I calculate standard deviation? No. The numbers are parsed and calculated locally in your browser. They are not sent to a server or stored by this tool, so you can check private class, research, or business data without uploading the values. ### Is this standard deviation calculator free? Yes. The calculator is free to use, requires no account, and has no paywall. Enter your values, choose the data set type, and copy the result without signing up or installing software. ### How many numbers can I enter? The tool does not impose a fixed count limit. Practical limits depend on your browser and device memory, but lists with thousands of ordinary numeric values calculate quickly because all work happens with lightweight JavaScript arithmetic. ### Should I use sample or population standard deviation? Use sample standard deviation when your observations are a subset used to estimate a larger population. Use population standard deviation only when the values include the complete group of interest. The sample formula divides by n - 1; the population formula divides by n. ### How is standard deviation calculated? First find the mean. Subtract the mean from each value, square those deviations, and add them. Divide that sum by n for a population or n - 1 for a sample to get variance. The positive square root of variance is the standard deviation. ### What is the standard deviation of 2, 4, 5, 6, 6, 9, and 10? For this seven-value data set, the mean is 6 and the sum of squared deviations is 46. The sample standard deviation is about 2.7689 because sqrt(46 / 6) is used. The population standard deviation is about 2.5635 because sqrt(46 / 7) is used. ### Why is standard deviation different from variance? Variance is the average squared distance from the mean, so its unit is squared. Standard deviation is the square root of variance and returns to the original data unit. That makes standard deviation easier to compare directly with measurements such as points, seconds, or centimeters. ## Related tools - [Mean, Median & Mode Calculator](https://candoya.com/tools/mean-average-calculator/) - [Z-Score Calculator](https://candoya.com/tools/z-score-calculator/) - [Correlation Coefficient Calculator](https://candoya.com/tools/correlation-coefficient/) - [Percentage Calculator](https://candoya.com/tools/percentage-calculator/) - [Integral Calculator](https://candoya.com/tools/integral-calculator/) --- *Markdown edition of , published for AI agents and other automated readers. 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