Standard Deviation Calculator
Calculate the standard deviation of a list of numbers.
Population standard deviation
12.3153
- Mean
- 18
- Count
- 6
v1.0 · Reviewed September 2026
How this is worked out
The mean is found first, then each value's difference from the mean is squared. The population standard deviation is the square root of the average of those squares, dividing by n.
Worked example
- 4, 8, 15, 16, 23, 42
mean 18, squared differences totalling 910, 910 ÷ 6 = 151.667, then the square root
12.3153
Assumptions and limits
- Divides by n, giving the population standard deviation. This assumes your numbers are the whole group of interest.
- For a sample drawn from a larger population, statistics coursework normally uses the sample standard deviation, which divides by n − 1 and gives a slightly larger figure. This calculator does not produce that value.
- Non-numeric entries are ignored. A single value gives a standard deviation of zero.