🧮 Pooled Standard Deviation Calculator
Enter the sample size and standard deviation for two or three groups to find their pooled standard deviation.
What this calculator does
Pooled standard deviation combines the variability of two or more independent groups into a single, weighted standard deviation, commonly used before running a t-test or computing an effect size like Cohen’s d.
How the calculation works
Each group’s variance (its standard deviation squared) is weighted by its degrees of freedom (sample size minus 1). The calculator sums these weighted variances and divides by the total degrees of freedom: pooled variance = Σ(nᵢ – 1)sᵢ² / Σ(nᵢ – 1). The pooled standard deviation is the square root of that value.
Groups with larger sample sizes contribute proportionally more to the pooled estimate. Leave Group 3 blank if you only have two groups to combine. This tool is for general and educational statistical use.