Standard Deviation Calculator
Both flavors (n and n−1), variance, mean, and standard error in one pass.
Results appear here as soon as you enter data.
How the Standard Deviation Calculator works
The calculation follows the standard method used across the US — no shortcuts, no hidden assumptions. Here is exactly what happens behind the scenes:
Formula
σ = √(Σ(x−μ)²/N); s uses N−1 (Bessel)
Frequently Asked Questions
Sample or population?
Use sample (N−1) when your data is a subset of a bigger group — nearly always true. Population fits censuses and complete sets.
Why n−1?
Bessel's correction removes the downward bias that using the sample mean instead of μ introduces.
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