What is the difference between sample and population standard deviation?

Population standard deviation divides by N and is used when you have the entire group. Sample standard deviation divides by N−1 (Bessel's correction) and is used when your data is a sample from a larger population — the more common case.

Standard Deviation Calculator

Q: What is standard deviation?

Standard deviation measures how spread out numbers are around the mean. A small value means data clusters near the average; a large value means it's widely dispersed. It's the square root of the variance.

Q: What does standard deviation tell you?

For roughly normal data, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three — the empirical rule. It's a standard measure of risk and consistency.

Enter a data set to get its standard deviation and variance — as both a sample and a population — plus the mean, count, and sum.

Sample standard deviation (s)

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Population std dev (σ)

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Sample variance (s²)

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Population variance (σ²)

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Mean

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Count

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Sum

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The formulas

Variance = Σ(x − mean)² ÷ N (population) or ÷ (N − 1) (sample)
Standard deviation = √variance

The steps

1) Find the mean. 2) Subtract it from each value and square the result. 3) Average those squares (dividing by N for population, N−1 for sample). 4) Take the square root. The N−1 for samples corrects for the fact that a sample slightly underestimates the true spread.

Reading the result

Standard deviation is the standard measure of spread — how consistent or variable your data is. For roughly bell-shaped data, the empirical rule says ~68% of values lie within one standard deviation of the mean, ~95% within two, and ~99.7% within three. That makes it central to risk (a volatile investment has a high standard deviation of returns), quality control, and grading on a curve. Use sample (N−1) when your numbers are a sample of something larger — the usual case — and population (N) only when you have every member of the group. Pair with the average calculator for the mean and median.

Frequently asked questions

What is standard deviation?

A measure of how spread out numbers are around the mean — the square root of variance.

Sample vs. population?

Population divides by N (whole group); sample divides by N−1 (a subset) — sample is more common.

What does it tell you?

For normal data, ~68% of values fall within 1 SD, 95% within 2, 99.7% within 3.

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Last reviewed: July 2026.