How to calculate std. deviation
σ = √(Σ(x − μ)² ÷ N) s = √(Σ(x − x̄)² ÷ (n − 1))
Worked example. Sample standard deviation: 2.1381.
Example inputs — Numbers (separated by commas or spaces): 2, 4, 4, 4, 5, 5, 7, 9; Data type: Sample (n − 1). Starting values are illustrative.
From George Guju, founder of Calculyn · Educational calculator guidance, not professional advice.
How it works
Standard deviation measures how spread out numbers are from their mean. Use the sample version when your data is a subset of a larger group, and the population version when you have every value.
Assumptions & limitations
- Results are rounded for display.
Formula and assumptions reviewed October 2026 by the Calculyn team. How we build our calculators
Frequently asked questions
Sample or population?
If you measured everyone you care about, use population. If you measured a sample to estimate a bigger group, use sample.