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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.
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.
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.
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.
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.
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.
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.
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.