Combine two samples’ standard deviations into one pooled standard deviation for a two-sample comparison.
Pooled standard deviation (sp)
How to use this tool
Enter the first sample’s size and standard deviation.
Enter the second sample’s size and standard deviation.
Read the pooled standard deviation and variance.
Use it with the degrees of freedom in an equal-variance t-test.
Formula & worked example
Two samples of 10 with standard deviations of 2 each pool to a standard deviation of 2 with 18 degrees of freedom.
Limitations — read this before you rely on it
Assumes equal population variances and independent samples; it is not a substitute for Welch’s test when variances differ.
Frequently asked questions
In the equal-variance (Student) two-sample t-test, where one common variance is assumed for both groups.
Each sample contributes its degrees of freedom, so the larger sample influences the pooled value more.
Pooling may mislead; Welch’s t-test, which does not assume equal variances, is then the safer choice.
No. It combines within-group variation only and ignores any difference between the group means.
A sample of one has no measurable variation, so its variance is undefined.