Standard Deviation Calculator

Paste a list of numbers to get the sample or population standard deviation, variance, mean, sum and count.

How the standard deviation calculator works

Standard deviation measures how spread out a set of numbers is. Paste your data, choose sample or population, and this calculator returns the standard deviation, variance and the basic statistics.

Use “sample” when your data is a subset of a larger group, and “population” when it’s the whole set.

Worked example

The calculator opens with a numbers of 4, 8, 15, 16, 23, 42. On those figures the standard deviation is 13.4907. Underneath, Mean comes out at 18 and Variance at 182. Change any field and every figure updates as you type.

How to fill it in

  1. Paste or type your numbers.
  2. Choose sample or population.
  3. Read the standard deviation, variance and mean.

The maths behind it

variance = Σ(x − mean)² ÷ N sample uses N−1; standard deviation = √variance

Common questions

What’s the difference between sample and population SD?
Sample SD divides by N−1 (Bessel’s correction) to better estimate a larger group; population SD divides by N when you have all the data.
What does standard deviation tell me?
How tightly values cluster around the mean. A small SD means values are close to the average; a large SD means they’re spread out.
How is variance related?
Variance is the average squared distance from the mean; standard deviation is its square root, back in the original units.