Standard Deviation Calculator
Sample and population standard deviation, variance, and mean from your data
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Quick summary
Paste a list of numbers (separated by commas, spaces, or new lines) and choose sample or population to get the standard deviation, variance, and mean, along with count, sum, min, max, and range. Both sample (n − 1) and population (n) standard deviations are always shown. For the classic set 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5 and the population standard deviation is 2.
Reviewed by Simple Calculators TeamLast reviewed
How to use this calculator
- Enter the inputs requested by the calculator.
- Choose the units or options that match your situation and review the assumptions.
- Run or update the calculation to see the result.
- Review the result, breakdown, and formulas shown on the page.
- Check the inputs, units, dates, and limitations before saving or sharing the result.
Frequently asked questions
What is standard deviation?
Standard deviation measures how spread out a set of numbers is around their mean. A low value means the data cluster tightly near the average; a high value means they're more dispersed. It's the square root of the variance, and shares the same units as your data, which makes it easier to interpret than variance.
What's the difference between sample and population standard deviation?
Use population standard deviation (dividing by n) when your data is the entire group you care about. Use sample standard deviation (dividing by n − 1, 'Bessel's correction') when your data is a sample meant to estimate a larger population — the n − 1 correction reduces bias. This calculator shows both.
How do I calculate standard deviation?
Find the mean, subtract it from each value and square the result, average those squared differences (dividing by n for population or n − 1 for sample) to get the variance, then take the square root. This tool does every step from your pasted numbers and also reports variance, mean, and range.
What number format can I paste?
Any mix of commas, spaces, tabs, and new lines works — paste a column from a spreadsheet or a comma-separated list. Non-numeric entries are ignored. You need at least one value (two for sample standard deviation).
Key terms
- Standard Deviation
- How far values typically fall from the mean; √variance.
- Variance
- The average squared distance from the mean.
- Sample (n − 1)
- Bessel's correction, used when data is a sample of a larger group.
- Mean
- The arithmetic average of the values.
Methodology, sources & limitations
This page shows the formula, assumptions, and limitations used for this estimate. Rates, thresholds, and other time-sensitive inputs can change, so verify them against the relevant official source before relying on a result.
For our review approach and the primary sources we consult, see the methodology and source policy. If you spot an outdated figure or formula, please contact us with a correction.