Pooled Standard Deviation Calculator

This calculator finds the pooled standard deviation of two groups, the single combined estimate of variability that underpins the two-sample t-test and effect-size measures like Cohen's d. When you compare two groups that you assume share a common underlying variability, it makes sense to combine their separate variances into one pooled estimate rather than using either alone. The pooled standard deviation does this by taking a weighted average of the two groups' variances, weighting each by its degrees of freedom, the sample size minus one, so the larger group has more influence, then taking the square root. The result is a more stable estimate of the common spread than either group provides on its own, which is why it sits at the heart of the classic pooled-variance t-test and standardised effect sizes. This calculator computes it. You paste the values for each of the two groups, and it returns the pooled standard deviation, each group's individual standard deviation, and the combined degrees of freedom. The results update as you type. Use it for statistics study, as a step in computing a t-test or Cohen's d, or whenever you need a combined measure of variability for two groups. The pooled standard deviation is the square root of the sum of each group's degrees of freedom times its variance, divided by the total degrees of freedom, which is the two sample sizes added together minus two. It assumes the two groups have similar true variances, the assumption of equal variances; when that assumption is doubtful, methods that do not pool, such as Welch's t-test, are preferred. Comparing the two individual standard deviations the calculator reports is a quick way to judge whether pooling is reasonable: if they are close, pooling is sound, while a large difference suggests the equal-variance assumption may not hold.

Pooled SD = sqrt( ((n1-1)s1² + (n2-1)s2²) / (n1+n2-2) ). Assumes the groups share a common variance. If the two SDs differ greatly, prefer methods that do not pool.