What is the Standard Deviation Calculator?

Calculate standard deviation and variance from any data set with this free online standard deviation calculator. Enter numbers and get sample SD (s), population SD (σ), variance, mean, and each squared deviation with full step-by-step work. Runs entirely in your browser with no signup.

How to use the Standard Deviation Calculator

Enter your data set (comma, space, or newline separated).
Click Calculate.
Review sample and population standard deviation.
Follow the squared-deviation steps.
Copy the sample SD or the full summary.

Common use cases

Finding SD for test scores: 72, 85, 90, 68, 95
Computing σ for a complete data set of measurements
Checking that identical values give SD = 0

Frequently asked questions

What is standard deviation?: Standard deviation measures how spread out values are from the mean. Low SD means values cluster near the average; high SD means they are more dispersed.
What is the difference between sample and population SD?: Sample SD (s) uses n−1 in the variance formula (Bessel's correction) and is for data drawn from a larger population. Population SD (σ) divides by n and treats your data as the full population.
What formulas are used?: σ² = Σ(x−μ)² ÷ n, s² = Σ(x−x̄)² ÷ (n−1), then SD = √variance.
How many numbers do I need?: At least 2 data points. Up to 10,000 per calculation.

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Frequently asked questions

What is standard deviation?

Standard deviation measures how spread out values are from the mean. Low SD means values cluster near the average; high SD means they are more dispersed.

What is the difference between sample and population SD?

Sample SD (s) uses n−1 in the variance formula (Bessel's correction) and is for data drawn from a larger population. Population SD (σ) divides by n and treats your data as the full population.

What formulas are used?

σ² = Σ(x−μ)² ÷ n, s² = Σ(x−x̄)² ÷ (n−1), then SD = √variance.

How many numbers do I need?

At least 2 data points. Up to 10,000 per calculation.