Statistics

Pooled Standard Deviation Calculator

Calculate the pooled standard deviation for two independent samples under the equal-variance model.

Statistics

Move between weighted summaries, t statistics, chi-square goodness-of-fit and one-way ANOVA calculations.

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Calculate the pooled standard deviation for two independent samples under the equal-variance model.

How it works

Enter compatible statistical values. The calculator validates the inputs and applies sₚ = √(((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2)).

The formula

sₚ = √(((n₁−1)s₁² + (n₂−1)s₂²) / (n₁+n₂−2))

Variables: n₁ = Sample size 1; s₁ = Standard deviation 1; n₂ = Sample size 2; s₂ = Standard deviation 2.

Worked example

Example: n₁=20, s₁=4, n₂=30 and s₂=5 give a pooled standard deviation of approximately 4.6301.

Frequently asked questions

What is this Statistics calculator intended for?

It is an educational tool for descriptive and inferential statistical calculations from supplied values or summary statistics.

Does this calculator make a complete statistical decision?

No. Where a test statistic is calculated, the tool does not automatically replace study design, assumption checks, p-value interpretation, confidence intervals or subject-matter judgment.

Last content reviewSeptember 26, 2026
Editorial reviewHe-Sab Editorial Review

Sources and references

These sources are used to verify terminology, formulas, and information related to this calculator.