Standard Deviation Calculator

Paste a dataset to calculate sample or population standard deviation, variance, mean, range, and other quick descriptive stats.

Dataset Inputs
Separate values with commas, spaces, semicolons, or line breaks.
Statistics Summary
Using the n - 1 denominator for variance.
Standard deviation
3.991061
Sample estimate
Variance
15.928571
Mean
17.75
Count
8
Sum: 142
Minimum to maximum
12 to 24
Range: 12
Sorted data
12, 15, 15, 16
4 more values
Which denominator should you use?
The choice depends on whether your values represent the whole population or just a sample.

Use population standard deviation when your list contains every value you care about, such as all orders placed yesterday.

Use sample standard deviation when the list is only a subset of a larger group, such as 25 surveyed customers out of thousands.

Formula overview
Standard deviation is the square root of the variance.

Population variance: sum of squared differences from the mean divided by n.

Sample variance: sum of squared differences from the mean divided by n - 1.

A larger standard deviation means values are spread out farther from the mean. A smaller one means the dataset is tighter and more consistent.

Frequently Asked Questions

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