Standard Deviation Calculator
Measure the spread of a list using either the sample or population convention.
Your result
MATHEnter your values and select calculate.
On this page How it works & practical examples
How to use the Standard Deviation Calculator
Choose population mode when the list contains the entire group you intend to describe. Choose sample mode when the observations are used as a sample of a wider population. Standard deviation is expressed in the original unit, whereas variance is in squared units. The implementation uses an online variance method to avoid subtracting two large, nearly equal sums.
The calculation
Worked example
The list 2, 4, 4, 4, 5, 5, 7 and 9 has a mean of 5. Population variance is 4 and population standard deviation is 2. The sample standard deviation is approximately 2.13809.
Assumptions and limits
Sample standard deviation requires at least two observations; one population observation has zero spread. A large standard deviation does not itself explain why the values vary, and it does not imply a normal distribution. The tool accepts up to 1,000 finite values within one trillion in magnitude. It does not remove outliers or missing values automatically.
Common questions
Why are the sample and population answers different?
The sample formula uses n − 1 in the denominator, so it produces a larger estimate of spread for the same non-constant list.
Can I mix measurements in different units?
Convert them to one unit first. Combining centimeters and inches in a single list would make the result meaningless.