Standard Deviation Calculator
Calculate sample or population standard deviation with the mean, coefficient of variation and standard error, using a numerically stable method.
Your inputs
Results
Population standard deviation (σ)
2
- Mean
- 5
- Sample SD (for comparison)
- 2.1380899353
- Coefficient of variation
- 40%
- Standard error of the mean
- 0.755928946
✓Exact calculation — rounded only for display
What this calculator does
Standard deviation measures how spread out values are around the mean. Use the sample version when your data is a sample from a larger population.
Formula and method
Worked example
Calculated by this tool with its default inputs:
Inputs
- Numbers (separated by commas, spaces or new lines): 2, 4, 4, 4, 5, 5, 7, 9
- Data is a: Population (divide by n)
Results
- Population standard deviation (σ): 2
- Mean: 5
- Sample SD (for comparison): 2.1380899353
- Coefficient of variation: 40%
- Standard error of the mean: 0.755928946
How to read the results
About 68 % of normally distributed data lies within one standard deviation of the mean.
Assumptions and limitations
- Welford’s method avoids precision loss when values are large and close together.
Questions
Why n − 1 for samples?
Bessel’s correction makes the sample variance an unbiased estimate of the population variance.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy