Population (σ) divides the sum of squared differences by N. Sample (s) divides by N−1 (Bessel's correction), giving an unbiased estimate of population variance when working with a sample.
Standard Deviation Calculator
Calculate standard deviation, variance, mean and dispersion from a list of numbers.
Population and sample standard deviation with all dispersion metrics.
Standard deviation measures the spread of a dataset around its mean. The population version (σ) divides by N and is used when you have all the data for the entire population. The sample version (s) divides by N−1 (Bessel's correction) and is used when the data is a sample of the full population.
Paste your list of numbers and choose the type.
- Type or paste numbers separated by comma, semicolon or newline.
- Select 'Population' if you have all data, or 'Sample' if it's a sample.
- See standard deviation, variance, mean, min, max and range.
Sources and references for this tool
These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
- Standard Deviation — NIST/SEMATECH e-HandbookNIST — Definition, formulas and uses of standard deviation in statistics.
- Bessel's Correction — WikipediaWikipedia — Explanation of the N−1 correction for unbiased sample estimators.
- Standard Deviation — Khan AcademyKhan Academy — Step-by-step standard deviation calculation with examples.