Standard Deviation Calculator

Your Data

Separate values with commas, spaces, or new lines.

Is this a sample or the whole population?

Sample Population

Most real-world data (a survey, a study, a class) is a sample. Choose Population only if your data covers every member of the group you care about.

About This Tool

What Is Standard Deviation?

Standard deviation measures how spread out your data is around the average. A small standard deviation means most values sit close to the mean; a large one means the values are scattered widely.

Sample vs. Population

Use Sample when your data is a subset of a larger group you're trying to draw conclusions about — this is the far more common case.
Use Population only when your data covers every single member of the group you care about, with nothing left out.

The Formula

\[ s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} \quad \text{(sample)} \qquad \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n}} \quad \text{(population)} \]

Worked Example

10 exam scores: 72, 85, 90, 65, 78, 88, 95, 70, 82, 91.

Mean = 81.6
Sample standard deviation ≈ 10.04
This means a typical score is about 10 points away from the class average of 81.6.

Your Results

Count (n)

Sum

Mean

Variance

Std. Deviation

Std. Error (SEM)

Min

Max

Range

Coeff. of Variation

What This Means

Your Data, Visualized

Each dot is one of your data points. The solid line marks the mean; the shaded bands mark 1 and 2 standard deviations from it.

If Your Data Is Roughly Bell-Shaped (Empirical Rule)

This only applies if your data follows a roughly normal distribution — treat it as a rough guide, not a guarantee.

About 68% of values fall within
About 95% of values fall within
About 99.7% of values fall within

Perfect for students, researchers, and professionals looking to build real statistical skills.

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