σ Standard Deviation Calculator
Enter a list of numbers to calculate the mean, variance, and standard deviation for a population or sample.
Data Set
Result
How Standard Deviation Is Calculated
Standard deviation measures how spread out a set of numbers is from the mean. A low standard deviation means values cluster close to the mean; a high one means they're spread over a wider range.
Formulas
Population Variance: σ² = Σ(x − x̄)² / n
Sample Variance: s² = Σ(x − x̄)² / (n − 1)
Standard Deviation: σ (or s) = √variance
Frequently Asked Questions
What's the difference between population and sample standard deviation?
Population standard deviation divides by n (the full data set), while sample standard deviation divides by n−1, which corrects for bias when your data is only a sample of a larger population.
Which one should I use?
Use population standard deviation when your data represents the entire group you're interested in. Use sample standard deviation when your data is a subset used to estimate a larger population.
What input formats are supported?
You can separate numbers with commas, spaces, or new lines — the calculator parses all of these automatically and ignores invalid entries.