About the Standard Deviation Calculator
Measure how spread out your data is. Choose sample (n − 1) or population (N) standard deviation and get the variance, mean, sum of squares and coefficient of variation.
Key features
- Sample (n − 1) or population (N) standard deviation
- Variance, mean, count and sum
- Sum of squared deviations
- Coefficient of variation
- Paste data from spreadsheets
- Accurate for decimals and negatives
Measure how spread out your data is
Two data sets can have the same average but very different consistency. Standard deviation measures that spread. It's used in quality control, finance (volatility), science, grading and A/B testing.
Formulas
Population standard deviation:
σ = √( Σ(xᵢ − μ)² ÷ N )
Sample standard deviation:
s = √( Σ(xᵢ − x̄)² ÷ (n − 1) )
Worked example
Data: 2, 4, 4, 4, 5, 5, 7, 9 (mean = 5)
| Step | Result |
|---|---|
| Squared deviations | 9, 1, 1, 1, 0, 0, 4, 16 |
| Sum of squares | 32 |
| Population variance | 32 ÷ 8 = 4 → σ = 2 |
| Sample variance | 32 ÷ 7 ≈ 4.571 → s ≈ 2.138 |
The 68–95–99.7 rule
For normally distributed data:
| Range | Share of values |
|---|---|
| Mean ± 1 SD | ≈ 68% |
| Mean ± 2 SD | ≈ 95% |
| Mean ± 3 SD | ≈ 99.7% |
Related calculators
Get the mean, median and mode with the Average Calculator, or round results with the Rounding Calculator.
How to use the Standard Deviation Calculator
- Enter your numbers in the fields above. Units and options can be changed at any time.
- The result updates instantly as you type; there's no calculate button to press.
- Check the breakdown under the main result for the details behind the number.
- Adjust the inputs to compare scenarios, for example a different rate or term.