Pooled standard deviation calculator
Combine the variability of two independent groups by weighting their variances by degrees of freedom.
How to use this page
- Paste at least two observations in each group.
- Compare the two group standard deviations.
- Read sₚ and the degrees of freedom.
What this page does not do: The calculation assumes independent samples and a defensible common variance. Paired data or clearly unequal variances require a method suited to that design.
Further reading
Pooled standard deviation estimates a shared population spread from two independent samples. Each variance is weighted by n−1, so the larger group contributes more to the result.
The measure is used in the classical equal-variance t test and in Cohen's d for two independent groups.
Frequently asked questions
Can I average the two standard deviations?
No. Variances must be weighted by degrees of freedom before taking the square root.
Must the groups have equal size?
No. The formula handles unequal sizes through weights n₁−1 and n₂−1.
See also
Beta distribution calculator
Calculate beta density, CDF, upper tail and quantile together with its mean and variance.
Chi-square test calculator
Calculate chi-square goodness of fit, independence, or a chi-square critical value.
Continuous uniform distribution calculator
Calculate density, CDF, upper tail, quantile, mean and variance for U(a,b).