How to calculate standard deviation
- Paste or type your Numbers, separated by commas, spaces or new lines. A column copied from a spreadsheet works.
- Choose Sample if the numbers are part of a larger group, or Whole population if they're every value there is.
- Read the standard deviation, then the variance, the other kind of standard deviation, the mean, the standard error and the coefficient of variation. The working below shows each step, with every value’s deviation from the mean.
Step by step for 4, 8, 6, 5, 3, 7, 9, 6
There are 8 values adding up to 48, so the mean is 48 ÷ 8 = 6. Next, take each value’s distance from the mean and square it:
| Value | Value − mean | Squared |
|---|---|---|
| 4 | −2 | 4 |
| 8 | 2 | 4 |
| 6 | 0 | 0 |
| 5 | −1 | 1 |
| 3 | −3 | 9 |
| 7 | 1 | 1 |
| 9 | 3 | 9 |
| 6 | 0 | 0 |
The squares add up to 28.
- Sample: variance = 28 ÷ (8 − 1) = 4, standard deviation = √4 = 2
- Population: variance = 28 ÷ 8 = 3.5, standard deviation = √3.5 ≈ 1.870829
The standard error is 2 ÷ √8 ≈ 0.707107, and the coefficient of variation is 2 ÷ 6 = 33.33% for the sample.
Entering your numbers
Separate values with commas, spaces, tabs or new lines. Negative numbers and decimals work. When commas are the only separators, as in 10,20,30, every comma splits two values. When values are separated by spaces or new lines, a comma inside a value belongs to it: 1,234 is one number with a thousands separator, and 3,5 is a decimal comma (3.5). The line under the result lists the numbers as they were read, so you can spot a misreading.
The coefficient of variation is the standard deviation as a percentage of the mean. It’s useful for comparing spread between data sets on different scales, but it means little when the mean is close to 0 or the data can be negative.