Population standard deviation
sigma = sqrt(sum((x - mean)^2) / n)
Mathematics calculator
Standard Deviation Calculator
Calculate mean, variance, sample standard deviation, and population standard deviation.
Calculator
Enter values
Results update automatically as soon as enough values are available.
Result
About this calculator
How it works
Standard deviation measures how spread out values are around the mean.
Formulas
Formulas used
Sample standard deviation
s = sqrt(sum((x - mean)^2) / (n - 1))
Worked example
Example calculation
Sample standard deviation
For 10, 12, 13, 16, 19, s = 3.49
Guide
How to use this calculator
- Enter the requested values. For datasets, separate numbers with commas, spaces, or line breaks.
- Choose an operation where the calculator provides a menu.
- Read the highlighted answer first, then use the supporting values for checking your work.
Reference
What the results mean
Sample standard deviation
Spread estimate when the values are a sample.
Population standard deviation
Spread when the values represent the full population.
Assumptions and limits
Before using the result
- Results are rounded for readability.
- Use the formula and supporting values to check important calculations.
- For engineering, finance, or coursework decisions, confirm the required method, units, and significant figures.
FAQ
Standard Deviation Calculator questions
Can I enter decimals or negative numbers?
Yes. Calculators that accept numeric datasets or values support decimals and negative values where the math operation allows them.
Are the results rounded?
Displayed values are rounded for readability, while the calculation uses the entered numeric values directly.
Can I use this for engineering checks?
Yes, these tools are useful for quick technical math checks, but final engineering work should still be reviewed against project requirements.
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