Standard Deviation Calculator

Welford’s algorithm accumulates squared deviations.

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How Standard Deviation Calculator works

Welford’s algorithm accumulates squared deviations. Population divides by n; sample divides by n−1. Values are normalized by the largest magnitude first to avoid intermediate overflow.

Try an example

2,4,4,4,5,5,7,9 has population standard deviation 2.

Good to know

Uses double-precision arithmetic; displayed values are rounded to 13 significant digits.

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Processing happens on this device for this tool. We do not upload your input, put it in share links or save it to your favourites. Closing this tab discards the working input; downloaded results remain wherever you save them.

When this tool is useful

Use Standard Deviation Calculator when you need a quick, local result and want the rule or limitation visible alongside it.

How to use it

Enter the input using the labels shown.
Run the operation and review the result.
Download or copy the result only after checking it.

Checks before you rely on the result

Uses double-precision arithmetic; displayed values are rounded to 13 significant digits.
Keep the original input when the operation creates a new copy.
Use the related tools below when the next step needs a different format.

This page is maintained with the tool implementation and its deterministic tests. If the result looks wrong, report the issue with a non-sensitive example.

Read the Standard Deviation Calculator instructions

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