Standard Deviation Calculator: instructions, examples and limits
Welford’s algorithm accumulates squared deviations.
Open Standard Deviation CalculatorThis tool is registered for local processing. Its tool input is handled in the current page; LittleKit’s product analytics do not include the input value.
What it does
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.
Worked example
2,4,4,4,5,5,7,9 has population standard deviation 2.
The example demonstrates the operation. For file-based tools, results depend on the selected file and options.How the result is produced
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.
Important limits
Uses double-precision arithmetic; displayed values are rounded to 13 significant digits.
Choosing the next step
Enter values in the units and convention named by the page, then compare the displayed formula with your question. For money, change the assumptions rather than treating an estimate as an offer; for statistics, decide whether the data represents a sample or a full population.
See a mismatch between these instructions and the tool? Report a correction with a non-sensitive example.