Pooled Standard Deviation Calculator

What Is Pooled Standard Deviation?

Pooled standard deviation combines sample standard deviations from two or more groups into one overall measure of spread. It is used in two-sample t-tests, meta-analysis, and effect size calculations such as Cohen's d. Related tools: Standard Deviation Calculator and Cohen's d Calculator.

Pooled Standard Deviation Formula

$$s_{pooled} = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}}$$

Each group contributes its sample variance weighted by its degrees of freedom ($n - 1$). The result estimates the common population standard deviation when group variances are assumed equal.

Example

For datasets [5, 7, 9, 11, 13] and [4, 6, 8, 10, 12], each group has sample variance 10 and size 5. The pooled standard deviation is $\sqrt{10} \approx 3.162$.