Standard Deviation Calculator
Paste a list of numbers to get the standard deviation, variance, mean and median.
Median: —
Range: —
About this tool
Shows both the sample standard deviation (dividing by n − 1) and the population standard deviation (dividing by n), with the variance, mean, median and range. Numbers are worked out in your browser.
Standard deviation tells you how spread out a set of numbers is: a small value means the numbers sit close to the average, a large one means they are scattered. Paste test scores, measurements or prices and get the sample and population standard deviation, the variance, mean, median and range in one go. It handles numbers separated by commas, spaces or new lines, so you can paste a column straight from a spreadsheet.
How to use the Standard Deviation Calculator
- Paste or type your numbers, separated by commas, spaces or new lines.
- Read the sample standard deviation if your numbers are a sample from a bigger group, or the population figure if they are the whole group.
- Check the mean, median, variance and range underneath.
The numbers 2, 4, 4, 4, 5, 5, 7, 9
There are 8 numbers adding up to 40, so the mean is 5. The squared distances from the mean are 9, 1, 1, 1, 0, 0, 4 and 16, which add up to 32. The population variance is 32 ÷ 8 = 4, so the population standard deviation is √4 = 2. The sample variance is 32 ÷ 7 = 4.571, giving a sample standard deviation of about 2.138.
Sample or population?
Use the population standard deviation (σ) when your numbers include every member of the group you care about, such as the marks of every pupil in one class. Use the sample standard deviation (s) when your numbers are a sample used to estimate a bigger group, such as 50 customers out of thousands. The sample formula divides by n − 1 instead of n (Bessel’s correction), which makes the estimate slightly larger to allow for the extra uncertainty. Variance is simply the standard deviation squared. In a roughly bell-shaped set of data, about 68% of values fall within one standard deviation of the mean and about 95% within two. In Excel and Google Sheets, STDEV.S gives the sample value and STDEV.P the population value.
Frequently asked questions
What is a good standard deviation?
There is no single good value; it depends on the data. Compare it with the mean: a standard deviation of 2 on an average of 100 is very tight, but on an average of 5 it is a lot of spread.
Why are there two answers?
Sample and population standard deviation use slightly different formulas. Use the sample value unless your list is the whole group.
Can standard deviation be negative?
No. It is the square root of an average of squared distances, so it is zero or positive. It is zero only when all numbers are the same.
How do I calculate it by hand?
Find the mean, subtract it from each number and square the result, add those squares, divide by n (or n − 1 for a sample) and take the square root.