Pooled Standard Deviation Calculator

About this calculator

The pooled standard deviation combines the variability of two separate samples into a single, shared estimate of spread, weighting each sample's variance by its degrees of freedom (sample size minus one) rather than simply averaging the two standard deviations together. This weighting means a larger sample has proportionally more influence on the pooled figure than a smaller one.

Statisticians rely on the pooled standard deviation specifically for the independent-samples t-test when the two groups are assumed to have equal population variances (the “Student's t-test” as opposed to Welch's t-test), and it's also the denominator used when computing standardised effect sizes like Cohen's d, which measures how far apart two group means are in units of shared standard deviation.

Enter the sample sizes and standard deviations of two groups, and this calculator returns the pooled variance and pooled standard deviation.