Standard Deviation Calculator
Paste a list of numbers to get the standard deviation and variance, for a sample or a whole population, with the mean and every step of the working.
Population standard deviation
2
- Variance
- 4
- Mean
- 5
- Count
- 8
The population standard deviation is 2: values typically sit about 2 from the mean of 5.
How it's worked out
- Mean
sum ÷ 85 - Sum of squared differences
Σ(x − mean)²32 - Variance
32 ÷ 84 - Standard deviation
√42
Working
| x | x − mean | (x − mean)² |
|---|---|---|
| 2 | -3 | 9 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 4 | -1 | 1 |
| 5 | 0 | 0 |
| 5 | 0 | 0 |
| 7 | 2 | 4 |
| 9 | 4 | 16 |
- Use the sample version (dividing by n − 1) when your numbers are a sample used to estimate a bigger group.
The formulas
Population σ = √( Σ(x − μ)² ÷ n ) · Sample s = √( Σ(x − x̄)² ÷ (n − 1) )
Example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the squared distances add up to 32. As a population, the variance is 32 ÷ 8 = 4 and the standard deviation is 2. As a sample, the variance is 32 ÷ 7 ≈ 4.571 and the standard deviation is about 2.138.
Questions people ask
What does standard deviation tell you?
How spread out the numbers are around their mean. A small value means they sit close to the average; a large value means they are widely scattered.
Sample or population?
Use population when you have every value in the group. Use sample when your numbers are a sample from a bigger group; it divides by n − 1 instead of n, which gives a slightly larger answer.
What is variance?
The average of the squared distances from the mean. The standard deviation is its square root, which puts it back in the same units as the data.
How should I enter the numbers?
Separate them with commas, spaces or new lines. You can paste a column straight from a spreadsheet.
About this calculator
Formula and rules last checked 25 October 2026Written and tested by the CalculatorDex teamReport a problem