Standard Deviation Calculator

Mean, variance and standard deviation (population or sample) for a list of numbers.

Equations used
Mean barx = (Σ x)/(n)
Population sigma = sqrtdfracΣ (x-barx)^2n
Sample s = sqrtdfracΣ (x-barx)^2n-1

Frequently Asked Questions

Should I use Population or Sample standard deviation?

Use Population when your numbers are the entire group you care about (e.g. every student in a class). Use Sample when your numbers are a subset used to estimate a larger group — the Sample toggle divides by (n−1) instead of n, which gives a slightly larger, less biased estimate.

Why does the Sample result need at least 2 numbers?

The sample formula divides by (n−1). With only 1 number, n−1 = 0 and the division is undefined, so the calculator requires at least 2 entries before it can compute either version.

What's the difference between variance and standard deviation?

Variance is the average of the squared differences from the mean; standard deviation is its square root, which brings the units back in line with your original numbers. This calculator shows both the population and sample versions of each side by side.