Standard Deviation Calculator
Paste your numbers to get the standard deviation, variance, mean, median, mode and range, for a sample or a whole population.
Your result appears here.
By Shah Rukh, software developer · Last updated:
Standard deviation formulas
Population σ = √( Σ(x − μ)² ÷ N )
Sample s = √( Σ(x − x̄)² ÷ (n − 1) )
Use sample when your numbers are a subset of a larger group (most homework and research). Use population when you have every value in the group.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9: the mean is 5, the squared differences add up to 32, so the population variance is 32 ÷ 8 = 4 and σ = 2. The sample standard deviation is √(32 ÷ 7) ≈ 2.138.
Frequently asked questions
What does standard deviation tell you?
How spread out the numbers are. A small value means they’re close to the mean; a large value means they vary a lot.
Why divide by n − 1 for a sample?
It corrects the tendency of a sample to underestimate the true spread (Bessel’s correction).
How should I enter numbers?
Separate them with commas, spaces or new lines. You can paste straight from a spreadsheet column.
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