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Standard Deviation Calculator

Calculate standard deviation for a set of numbers. Measures how spread out the values are from the mean. Choose population or sample (n−1) depending on whether your data represents the full population or a sample.

Standard deviation calculator

Standard deviation

What is this?

Standard deviation measures how spread out numbers are from their average. A low standard deviation means values cluster near the mean; a high one means they are more spread out. It is the square root of the variance. You can choose population or sample standard deviation: use population when you have data for the entire group, and sample (n−1) when your data is a subset of a larger population. In practice, sample standard deviation is more common because we usually work with samples.

When to use

Use in statistics, quality control, finance (volatility), and research. Example: test scores of 70, 72, 71 have low spread; 50, 90, 70 have high spread. Helps assess consistency. In finance, standard deviation of returns measures volatility or risk. In manufacturing, it measures process consistency. Researchers use it to describe data spread. Students use it in statistics courses. Always pair it with the mean to get a full picture.

How to use

Enter numbers separated by commas, spaces, or new lines. σ = √(Σ(x − μ)² / n). Use sample when data is a sample of a larger population.

Frequently asked questions

What is standard deviation?
Standard deviation measures how spread out numbers are from the mean. A low standard deviation means values are close to the average; a high one means they are spread out.
When to use population vs sample standard deviation?
Use population (n) when you have data for the entire group. Use sample (n−1) when your data is a sample from a larger population.

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