How to use this calculator
- Enter your own values in the labeled fields. Check the units and assumptions before comparing results. Only the fields needed for your selected calculation mode are shown.
- Your answer updates automatically. Review the calculation steps to see exactly how it was calculated.
- Copy, share, save, or download your result. Saved inputs stay on this device.
How the calculation works
Standard deviation measures spread in the same units as the input data. Population deviation divides by N; sample deviation uses n − 1 when estimating population variance from a sample. Outliers can strongly affect the result. The implementation uses an incremental mean and squared-deviation algorithm to reduce numerical cancellation.
A worked example
For 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5, population variance is 4, and population standard deviation is 2.
Reading your result
Use the main result together with its units and supporting figures. Display values are rounded; calculations keep their underlying precision. A change in inputs or assumptions can change the answer. Compare the step-by-step working with your intended use before relying on an estimate.
Frequently asked questions
Which mode should I choose?
Use population when the list is the complete group you want to describe; use sample when it estimates a wider population.
How many values are needed?
At least one for population mode and at least two for sample mode.
Sources & methodology
Formula review: October 24, 2026. Read our methodology.