Standard Deviation Calculator
Calculate population and sample standard deviation, variance and standard error.
Last updated · View algorithm, constants and default inputs (JSON)
Numbers (comma separated)
About this calculator
Enter up to 10,000 finite numbers separated by spaces or commas, with no empty comma entries. Both entries share compensated centered sums and scaled squared deviations.
Worked example
calculated with the default values below
Numbers (comma separated) 10, 12, 23, 23, 16, 23, 21, 16 · Primary statistic Population standard deviation Population standard deviation 4.8990 · Sample standard deviation 5.2372 · Population variance 24.0000 · Sample variance 27.4286 · Mean 18.0000 · Standard error of the mean 1.8516 · Count 8 · Sum of squared deviations 192.0000
Method and assumptions
Enter up to 10,000 finite numbers separated by spaces or commas, with no empty comma entries. Both entries share compensated centered sums and scaled squared deviations. Population variance divides by n; sample variance by n−1 and is undefined for one value. The primary statistic can be switched. Unrepresentable numeric results are rejected; an overflowing sum of squares alone is omitted when the variance remains representable.
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
μ = Σx/n; σ² = Σ(x−μ)²/n; s² = Σ(x−μ)²/(n−1); σ = √σ²; s = √s²; SE = s/√n
The primary statistic can be switched. Unrepresentable numeric results are rejected; an overflowing sum of squares alone is omitted when the variance remains representable.
Frequently asked questions
What input format is accepted?
Enter up to 10,000 finite numbers separated by spaces or commas, with no empty comma entries. Both entries share compensated centered sums and scaled squared deviations. Population variance divides by n; sample variance by n−1 and is undefined for one value. The primary statistic can be switched. Unrepresentable numeric results are rejected; an overflowing sum of squares alone is omitted when the variance remains representable.