Science & Engineering

Standard Deviation (and Variance) Calculator

Paste a list of numbers and get the standard deviation. It returns both the sample and population versions, plus variance, mean, range, and more.

How to use
  1. Paste comma- or line-separated numbers.
  2. Check variance, mean, range, and the min and max.
Example
Sample standard deviation (s, n−1)

Population SD (σ, n)
Mean (x̄)
Sample variance
Range
Min / Max
For study and estimation. Verify against authoritative data before relying on a result.
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How it's calculated

s = √( Σ(xᵢ − x̄)² ÷ (n − 1) )

xᵢ = each value, x̄ = mean of the list, n = count, Σ = sum over all values. Shown is the sample standard deviation (n − 1); the population version divides by n.

Common questions

Should I use sample or population SD?

Use sample SD (n-1) when your data is a sample of a larger group. Use population SD (n) when you have the entire population.

How does standard deviation relate to variance?

Standard deviation is the square root of the variance, which puts the spread back into the original units.