Statistics
Standard Deviation Calculator
Paste or type a list of numbers to summarise the mean, variance, standard deviation, and range.
Inputs
Results
Useful next checks
- Check the inputs before relying on the result.
- Try a second scenario to compare outcomes.
- Read the guide below for context.
# Standard Deviation Calculator
Use this standard deviation calculator to summarise a list of numbers with mean, variance, sample standard deviation, population standard deviation, count, and range.
What this calculator does
Paste numbers separated by commas, spaces, or line breaks. Choose sample or population standard deviation as the primary result, then review the supporting summary statistics.
How it works
The calculator finds the mean, measures each number's squared distance from the mean, and averages those squared distances. Population variance divides by `n`; sample variance divides by `n - 1`. Standard deviation is the square root of variance.
Example calculation
For `4, 8, 6, 5, 3, 9`, the mean is 5.8333. The sample variance is 5.3667, so the sample standard deviation is 2.3166.
How to use the result
Use standard deviation to understand how spread out values are around the mean. A larger standard deviation means the values vary more.
Assumptions and limitations
This calculator reads numeric values only and ignores text. It does not produce confidence intervals, hypothesis tests, or charts.
FAQs
Should I choose sample or population?
Choose sample when your values represent part of a larger group. Choose population when your values are the full group.
Can I paste a column from a spreadsheet?
Yes. Line breaks, spaces, and commas are accepted separators.
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Frequently asked questions
When should I use sample standard deviation?
Use sample standard deviation when your numbers are a sample from a larger group.
When should I use population standard deviation?
Use population standard deviation when your list contains every value in the full group.