CalcOS calculator
Standard Deviation Calculator
Calculate sample or population standard deviation with strict data validation, variance, mean, range, and dataset summary.
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7 values
Paste a column from Excel or Google Sheets into any row.
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How this calculator works
Calculate the standard deviation of any data set with our free statistics calculator. Enter your numbers as a comma-separated list to instantly compute the mean, variance, and both population and sample standard deviations. View step-by-step working to understand exactly how the result is derived.
- Method
- Strict finite-number parsing followed by compensated two-pass mean and squared-deviation summation
- Source
- NIST/SEMATECH e-Handbook of Statistical Methods; NIST Statistical Reference Datasets
- Last reviewed
- 2026-08-26
Method limitations
- Sample mode requires at least two values; population mode accepts one or more values.
- Every entered token must be a finite decimal or scientific-notation number; malformed values are rejected rather than ignored.
- The calculator accepts at most 10,000 values per calculation.
- Standard deviation is sensitive to outliers and does not establish that a dataset is normally distributed.
- The calculation describes the supplied values and does not by itself establish statistical significance or causation.
Engine-backed example
Population standard deviation: worked example
What is the population standard deviation of 2, 4, 4, 4, 5, 5, 7, and 9?
- Data values
- 2, 4, 4, 4, 5, 5, 7, 9
- Data type
- Complete population
Population Standard Deviation2.0000
- Mean (Average)
- 5.0000
- Variance
- 4.0000
- Data Points (N)
- 8
The eight values have a mean of 5 and population variance of 4. The square root of 4 gives a population standard deviation of 2.
Trust and review
Who created and reviewed this calculator?
- Author
- CalcOS Editorial TeamResponsible for statistical terminology, examples, assumptions, and clear sample-versus-population guidance.
- Reviewed by
- CalcOS Scientific ReviewTechnical review of sample and population variance, strict finite-number parsing, two-pass numerical stability, boundaries, rounding, engine parity, and narrative examples.
- Substantive review date
- 2026-08-26Sample and population modes, n versus n − 1 denominators, one-value population behavior, invalid-token rejection, 10,000-value limit, compensated two-pass summation, summary metrics, and worked-example parity.
Sources
- NIST/SEMATECH e-Handbook — Measures of Scale
- NIST Statistical Reference Datasets — Certification Method and Definitions
- NIST — Validation of Software in Measurement Systems
Assumptions used by this calculator
- Sample mode treats the supplied values as a sample from a larger population and divides squared deviations by n − 1.
- Population mode treats the supplied values as the complete population and divides squared deviations by N.
- All tokens must be finite decimal or scientific-notation numbers; malformed tokens are rejected rather than silently omitted.
- Results are descriptive statistics for the supplied values and do not imply normality, statistical significance, or causation.
- Standard deviation has the same unit as the input values; variance has squared units and is sensitive to outliers.