Standard Deviation Calculator

What This Calculator Does

Enter a list of numbers and the tool gives the standard deviation (and the mean and variance), for either a whole population or a sample.

The Formulas

mean (μ)            = sum of values / count
population variance = Σ(x - μ)² / N
sample variance     = Σ(x - x̄)² / (n - 1)
standard deviation  = √variance

Use population when the data is the entire group; use sample when it is a sample drawn from a larger group (it divides by n − 1).

How to Use It

1. Choose population or sample.
2. Enter the numbers, separated by commas.
3. Read the standard deviation, with the mean and variance in the steps.

Worked Examples

Data (population)	Mean	Standard deviation
2, 4, 4, 4, 5, 5, 7, 9	5	2
10, 12, 14, 16, 18	14	2.8284
5, 5, 5, 5	5	0

For the first set as a sample, dividing by 7 instead of 8 gives a standard deviation of about 2.1381.

FAQ

What is the difference between population and sample standard deviation?

Population divides by the count (N); sample divides by one less (n − 1). Use sample when your data is only a portion of a larger group.

How do you calculate standard deviation?

Find the mean, subtract it from each value and square the result, average those squares (the variance), then take the square root.

What does a standard deviation of 0 mean?

Every value is identical, so there is no spread — as with 5, 5, 5, 5.

What is variance?

Variance is the average of the squared differences from the mean; the standard deviation is its square root, in the same units as the data.