Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the standard deviation and variance calculator works
Population variance = Σ(x−μ)²/N; sample variance = Σ(x−x̄)²/(n−1).
Standard deviation uses the data’s units; variance uses squared units.
Worked example
Standard Deviation and Variance example
For 2, 4, 6, population variance is 2.667 and sample variance is 4.
Population variance = Σ(x−μ)²/N; sample variance = Σ(x−x̄)²/(n−1).
Supported inputs
Precision and limits
Model and design
Choose the sample result when observations estimate a wider population and the population result when the entered values are the complete population of interest.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Standard deviation uses the data’s units; variance uses squared units.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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