Standard Deviation Calculator

Calculate standard deviation for a list of numbers.

How to Do It Manually

Standard deviation measures how spread out values are from the mean. A low value means data is clustered; a high value means it is spread out.

σ = √( Σ(xᵢ − μ)² / N ) [Population] | s = √( Σ(xᵢ − x̄)² / (N−1) ) [Sample]
  1. Calculate the mean (average) of the dataset.
  2. Subtract the mean from each data point and square each result.
  3. Sum all the squared differences.
  4. Divide by N (population) or N−1 (sample).
  5. Take the square root of the result.

Frequently Asked Questions

When do I use population vs. sample standard deviation?

Use population (σ) when you have data for the entire group. Use sample (s) when your data is a sample from a larger population.

What does a standard deviation of 0 mean?

All values in the dataset are identical — there is no variation.