Standard Deviation Calculator

Find the mean of your data set, then find how far each value is from that mean, square each of those differences, average the squared differences (that average is the variance), and take the square root of the variance to get the standard deviation. For the default data set, 10, 20, 30, 40, 50: the mean is 30, the squared differences from the mean are 400, 100, 0, 100, and 400, their average (the population variance) is 200, and the square root of 200 is about 14.142.

Population standard deviation divides the sum of squared differences by the total count of values, n. Sample standard deviation instead divides by n minus 1, which produces a slightly larger result. This correction exists because a sample tends to underestimate the true spread of the full population it was drawn from, and dividing by a smaller number compensates for that. Use Sample whenever your data is a subset, such as a survey of 50 people out of a much larger group, use Population only when your data genuinely covers every member of the group you're measuring.

For the same default data set, switching from Population to Sample changes the variance from 200 to 250, and the standard deviation from about 14.142 to about 15.811.

Mean is the plain average of your data set. Count (n) is how many values were found in what you entered, useful for confirming nothing was accidentally left out or double counted when pasting a long list. For a related measure comparing a single value against a data set's mean and spread, see the Z-Score Calculator.