Find the standard deviation of any data set. This free calculator gives the sample and population standard deviation, variance, mean, count and range — just paste your numbers.
Use sample when your numbers are a subset of a larger group (divides by n-1); use population when they’re the entire group (divides by n).
Standard deviation measures how spread out your numbers are around the mean. A larger value means more spread. The calculator also shows variance (the square of the standard deviation).
How the Standard Deviation Calculator Works
This tool measures how spread out a set of numbers is around its average. Paste or type your numbers in, tell it whether your data is a sample or the whole population, and it works out the standard deviation, variance, mean and a few other summary statistics in one step.
Formula: Mean = (sum of all numbers) ÷ n. For each number, find its deviation from the mean and square it: (x − mean)^2. Population variance = (sum of all squared deviations) ÷ n. Sample variance = (sum of all squared deviations) ÷ (n − 1). Standard deviation = √variance, using whichever variance (sample or population) matches the data set type you selected.
- Numbers — your data set, entered separated by commas, spaces or new lines
- Data set type — “a sample” (divides by n − 1) if your numbers are a subset of a larger group, or “the whole population” (divides by n) if they’re the entire group
Example Scenarios
| Data set | Type | Standard deviation |
|---|---|---|
| 2, 4, 4, 4, 5, 5, 7, 9 | Population | 2 |
| 2, 4, 4, 4, 5, 5, 7, 9 | Sample | 2.14 |
| 1, 2, 3, 4, 5 | Population | 1.41 |
| 1, 2, 3, 4, 5 | Sample | 1.58 |
| 10, 10, 10, 10 | Population | 0 |
| 5, 7, 9 | Sample | 2 |
Standard Deviation Calculator FAQ
Should I choose sample or population standard deviation for my data?
Choose “population” only if your numbers represent every member of the group you care about. Choose “sample” if your numbers are a subset meant to estimate a larger group — this is the more common choice for surveys, experiments and most real-world data sets.Why is sample standard deviation always slightly bigger than population standard deviation?
Sample variance divides the sum of squared deviations by n − 1 instead of n, which produces a slightly larger number. This correction compensates for the fact that a sample tends to underestimate the true spread of the full population.What does a standard deviation of 0 mean?
A standard deviation of 0 means every number in your data set is identical — there is no spread at all around the mean, as shown when all four entries equal 10 in the examples above.How is variance related to standard deviation?
Variance is the standard deviation squared. The calculator computes variance first (the average squared distance from the mean), then takes its square root to get the standard deviation, which is easier to interpret because it’s back in the original units.Can I paste numbers directly from a spreadsheet?
Yes, the Numbers field accepts values separated by commas, spaces or new lines, so you can paste a column or row copied straight from a spreadsheet without reformatting it first.Does the order I enter my numbers in matter?
No. Standard deviation, mean and variance are all based on the full set of values, not their order, so entering the same numbers in any sequence gives identical results.Related Calculators
Standard deviation is easier to interpret alongside the center of your data — try the average calculator for a quick mean, or the weighted average calculator if some values in your set should count more than others. To see how much a value has shifted over time rather than how spread out it is, check the percentage change calculator.