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Welch's Two-Sample t-Test Calculator

Heteroscedastic t-statistic and degrees of freedom.

Compute the Welch (unequal-variances) two-sample t statistic and its Welch-Satterthwaite degrees of freedom from the two sample means, sample SDs, and sample sizes.

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

t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂); df = (s₁²/n₁ + s₂²/n₂)² / ((s₁²/n₁)²/(n₁−1) + (s₂²/n₂)²/(n₂−1)).

In depth

Compute the Welch (unequal-variances) two-sample t statistic and its Welch-Satterthwaite degrees of freedom from the two sample means, sample SDs, and sample sizes.