When is pooled standard deviation appropriate?

Use pooled SD when you have two independent groups and can reasonably assume they come from populations with the same variance. It is the standard approach for the independent two-sample t-test with equal variances assumed.

How do I know if pooling is appropriate?

Check the ratio of the larger SD to the smaller SD. If the ratio exceeds about 2, the equal-variance assumption is questionable. Use Levene's test formally; if significant, switch to Welch's t-test.

What does pooled SD tell me in meta-analysis?

In meta-analysis, pooled SD is used to compute Cohen's d effect size: d = (mean1 - mean2) / Sp. This standardises the mean difference so it can be compared across studies using different measurement scales.

Pooled Standard Deviation Calculator

Calculate the pooled standard deviation for two groups from their individual standard deviations and sample sizes. Used in independent two-sample t-tests and meta-analysis when assuming equal population variances.

By AbraCalc Editorial Team · Reviewed by AbraCalc Methodology Review · Last reviewed: 2026-06-25

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How to use this tool

Enter standard deviation (group 1), sample size (group 1), standard deviation (group 2) and sample size (group 2) in the fields above.
Results update instantly as you type — or click Calculate.
Read your pooled standard deviation and the full breakdown beneath it.

Formula

Sp^2 = [(n1-1)*SD1^2 + (n2-1)*SD2^2] / (n1+n2-2); Sp = sqrt(Sp^2)

How it works

Weight each group's variance by its degrees of freedom (n-1), sum them, and divide by total degrees of freedom (n1+n2-2). Take the square root for the pooled SD.

Worked example

Clinical trial two groups

Group 1: SD=10, n=20; Group 2: SD=12, n=25
Numerator = 19*100 + 24*144 = 1900 + 3456 = 5356
df = 20+25-2 = 43
Pooled Var = 5356/43 = 124.5581
Pooled SD = sqrt(124.5581) = 11.1604

Common mistakes to avoid

Pooling standard deviations by averaging them directly (SD1 + SD2) / 2 — the correct pooled formula weights by degrees of freedom (n-1), not a simple average.
Using pooled SD when the two group variances are very different — pooled SD assumes equal population variances; if Levene's or Bartlett's test shows unequal variances, use Welch's t-test with separate SDs instead.
Forgetting to take the square root of the pooled variance Sp^2 to get the pooled standard deviation Sp.

Key terms

Frequently asked questions

When is pooled standard deviation appropriate?: Use pooled SD when you have two independent groups and can reasonably assume they come from populations with the same variance. It is the standard approach for the independent two-sample t-test with equal variances assumed.
How do I know if pooling is appropriate?: Check the ratio of the larger SD to the smaller SD. If the ratio exceeds about 2, the equal-variance assumption is questionable. Use Levene's test formally; if significant, switch to Welch's t-test.
What does pooled SD tell me in meta-analysis?: In meta-analysis, pooled SD is used to compute Cohen's d effect size: d = (mean1 - mean2) / Sp. This standardises the mean difference so it can be compared across studies using different measurement scales.