📊 Standard Deviation Calculator
Paste a list of numbers to see how spread out they are. Standard deviation is used in grades, science and finance.
How the Standard Deviation Calculator works
The mean is subtracted from each value, the differences are squared and averaged. Population variance divides by n; sample variance divides by n − 1. Standard deviation is the square root of the variance.
Step-by-step calculation
- 1Enter the numbers.
- 2Find the mean.
- 3Average the squared differences (÷ n or n − 1).
- 4Take the square root.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9: mean = 5, population standard deviation = 2, sample standard deviation ≈ 2.138.
Standard Deviation Calculator examples
| Numbers (commas, spaces or new lines) | Standard deviation |
|---|---|
| 1, 2, 3, 4, 5 | σ = 1.414214 · s = 1.581139 |
| 2, 4, 4, 4, 5, 5, 7, 9 | σ = 2 · s = 2.13809 |
| 10, 20, 30 | σ = 8.164966 · s = 10 |
| 5, 5, 5, 5 | σ = 0 · s = 0 |
| 3, 7, 7, 19 | σ = 6 · s = 6.928203 |
Other inputs kept at the calculator's default values. Results calculated by this calculator.
Why use a Standard Deviation Calculator?
Measure spread in statistics, science and finance.
Important factors that can affect your results
- Sample vs population formula.
- Outliers.
- Small data sets.
Frequently asked questions
Sample or population?
Use population if you have every value in the group, and sample if your data is a selection from a larger group.
What does a small standard deviation mean?
The values are close to the mean.
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Last reviewed November 2026 · How we build and check our tools · Report a problem