What is the difference between population and sample standard deviation?

Population standard deviation divides by N (the count) and is used when your data is the entire population. Sample standard deviation divides by N − 1 (Bessel's correction) and is used when your data is a sample drawn from a larger population, giving a less biased estimate.

How do I enter my numbers?

Type or paste your values separated by commas, spaces, or new lines. The calculator ignores anything that is not a number.

Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of the variance, which returns the measure to the original units.

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Math & Statistics

Standard Deviation Calculator

Paste a list of numbers to get the mean, both population and sample standard deviation, variance, count, and sum, with the calculation explained.

Sample standard deviation (s)

5.24

Population SD (σ)—

Mean—

Variance (sample)—

Count / Sum—

Values vs. the mean

Each data point; the spread around the mean is what standard deviation measures.

How it works

Standard deviation measures how spread out a set of numbers is. A low value means the data clusters near the mean; a high value means it is more dispersed. It is the square root of the variance, the average squared distance from the mean.

Mean: x̄ = Σxᵢ / n
Population variance: σ² = Σ(xᵢ − x̄)² / n
Sample variance: s² = Σ(xᵢ − x̄)² / (n − 1)
Standard deviation = √variance

Which one should I use?

Use population SD when your numbers are the whole group you care about. Use sample SD when they are a sample meant to represent a larger group — dividing by n − 1 corrects for the bias in small samples.

Frequently asked questions

Population vs sample standard deviation?

Population divides by N; sample divides by N − 1 (Bessel's correction) for a less biased estimate from a sample.

How do I enter numbers?

Separate them with commas, spaces, or new lines — anything that isn't a number is ignored.

What is variance?

The average squared distance from the mean; standard deviation is its square root, back in the original units.