Standard Deviation Calculator
Paste or type a list of numbers to get the count, sum and mean, plus variance and standard deviation calculated both ways — for a whole population and for a sample.
Separate values with commas, spaces or new lines — you can paste a column from a spreadsheet.
Use the population figures when your data includes every member of the group you care about (divide by N). Use the sample figures when the data is a sample used to estimate a larger population (divide by N − 1, Bessel's correction) — this is the usual choice for survey or experiment data.
8
Count (N)
40
Sum
5
Mean (average)
Population (σ, divide by N)
2
Population standard deviation σ
4
Population variance σ²
Sample (s, divide by N − 1)
2.138089935
Sample standard deviation s
4.571428571
Sample variance s²
Everything you enter is processed in your browser and isn't sent to our servers.
How to use standard deviation calculator
- 1Type or paste your numbers, separated by commas, spaces or new lines.
- 2Check that any non-numeric values flagged were meant to be ignored.
- 3Use the population figures if your data covers the entire group, or the sample figures if it's a sample.
About this tool
Standard deviation measures how spread out numbers are from their mean. The calculation finds the mean, squares each value's distance from it, adds those squares up, divides to get the variance, and takes the square root to get the standard deviation. The textbook dataset 2, 4, 4, 4, 5, 5, 7, 9 has a mean of 5 and a population standard deviation of exactly 2.
The only difference between the two versions is the divisor. Population variance (σ²) divides by N, the number of values, and is correct when your data is every member of the group. Sample variance (s²) divides by N − 1 (Bessel's correction), which corrects the tendency of a sample to underestimate the spread of the larger population it came from — the usual choice for survey, experiment and measurement data.
Numbers are summed using a two-pass method that stays accurate even for large values with a small spread. A single value has a population standard deviation of 0 but no sample standard deviation, because you can't estimate spread from one observation.
Frequently asked questions
Use population if your list includes every item you care about (all 30 students in one class). Use sample if the list is a subset used to draw conclusions about something bigger (30 students surveyed out of a whole school). When in doubt, sample is the more common choice.