basic

Pooled Standard Deviation from Two Samples Calculator

s_p = √(((n₁ − 1)·s₁² + (n₂ − 1)·s₂²) / (n₁ + n₂ − 2)).

Compute the pooled (combined) sample standard deviation of two independent samples that are assumed to share a common population variance. Required input for two-sample t-tests, Cohen's d, Hedges' g, and many effect-size formulas. Equal-variance assumption — use Welch's variant otherwise.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

s_p = √(((n₁ − 1)·s₁² + (n₂ − 1)·s₂²) / (n₁ + n₂ − 2)).

In depth

Compute the pooled (combined) sample standard deviation of two independent samples that are assumed to share a common population variance. Required input for two-sample t-tests, Cohen's d, Hedges' g, and many effect-size formulas. Equal-variance assumption — use Welch's variant otherwise.