Result
Enter values and select Calculate.
Formula and method
Welford’s online algorithm updates the mean and sum of squared deviations without relying on the fragile mean(x²) − mean(x)² identity. Population variance divides by N. Sample variance divides by n − 1 and requires at least two values.
Worked example
For 1, 2, 3, 4, 5, population variance is 2 and sample variance is 2.5. The corresponding standard deviations are shown only as supporting context.
Assumptions and boundaries
- Choose population when the entered values are the complete population; choose sample for a sample-based estimate.
- Sample variance requires at least two values.
- Malformed or nonfinite tokens are rejected rather than discarded.
- Standard Deviation Calculator retains dataset-to-standard-deviation ownership.
Inputs and results stay in this browser and are not sent to analytics, storage, URLs, or network services.