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Pooled standard deviation calculator

Combines two sample standard deviations into one pooled estimate for equal-variance tests.

What this calculator does

Pooled standard deviation works out combines two sample standard deviations into one pooled estimate for equal-variance tests. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.

The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.

The formula

Formulasp = √[((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2)]

The inputs explained

FieldWhat to enter
Sample 1 standard deviationA number. Starts at 9.
Sample 1 sizeA number. Starts at 20.
Sample 2 standard deviationA number. Starts at 11.
Sample 2 sizeA number. Starts at 25.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How the answer changes with sample 1 standard deviation

Every other input is held at the calculator’s starting values while sample 1 standard deviation varies. Select any row to load that scenario into the calculator.

How the answer changes with sample 1 standard deviation
Sample 1 standard deviationPooled standard deviationStandard error of the mean differenceDegrees of freedom
4.58.7452.62443
6.759.3632.80943
910.1653.04943
13.512.1683.65043
1814.5154.35543
2719.7405.92243