Interactive Standard deviation calculator
Calculated result
Enter the known values and select Calculate.
How to use this calculator
- Enter numbers separated by commas, spaces, or line breaks.
- Choose population when the entries are the full group of interest.
- Choose sample when the entries are used to estimate a larger population.
- Review the count, mean, sum of squared deviations, variance, and standard deviation together.
Formula and method
Population variance divides the sum of squared deviations by N. Sample variance divides by N − 1. Standard deviation is the square root of the selected variance.
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; the sample results are larger because they divide by 7 instead of 8.
Assumptions and result interpretation
- Every parsed number receives equal weight.
- A sample calculation requires at least two values.
- The tool performs descriptive arithmetic and does not judge whether the dataset is representative or normally distributed.
- Entered data remains in the browser and is excluded from analytics.
Understanding the result
Variance is expressed in squared data units, while standard deviation returns to the original unit. The choice between N and N − 1 is therefore visible in both variance and standard deviation.
Common mistakes
- Choosing population merely because the dataset is large
- Leaving units inside the numeric list
- Treating variance and standard deviation as the same unit
- Ignoring outliers or data-entry errors before calculation
Methodology sources
Use this result as a calculation aid. Confirm input definitions, required precision, and any governing policy or professional standard separately.