Standard deviation
calculator
Standard deviation measures how spread out a set of numbers is around their average. Paste your values and get both the sample and population figures, with the mean.
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Sample vs population
If your numbers are the whole group you care about, use the population standard deviation, which divides the squared differences by n. If they are a sample standing in for a bigger group, use the sample version, which divides by n minus 1 (Bessel's correction) and is a little larger.
Reading the number
A small standard deviation means the values cluster tightly around the mean; a large one means they are spread out. It is in the same units as your data, so scores in points give a spread in points. Variance is simply the square of it.
Standard deviation FAQ
Use population when your data is the entire set. Use sample when it is a subset you are generalising from, which is the more common case in statistics.
Variance is the average of the squared differences from the mean. Standard deviation is its square root, which puts the spread back into the original units.
Separate values with commas, spaces or new lines. Decimals and negatives are fine; anything that is not a number is ignored.
Dividing a sample by n minus 1 corrects a bias that would otherwise make the spread look smaller than the true population value.