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Pooled Standard Deviation Calculator — result sheet
Combine two sample standard deviations using their degrees of freedom to estimate a common pooled spread.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: sₚ = √[((n₁-1)s₁²+(n₂-1)s₂²)/(n₁+n₂-2)].
The pooled estimate weights each group variance by its degrees of freedom. It is appropriate only when treating the two population variances as common is justified.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Group 1 sample standard deviation — minimum 1.0E-6; maximum 1000000000
- Group 1 sample size — minimum 2; maximum 1000000000
- Group 2 sample standard deviation — minimum 1.0E-6; maximum 1000000000
- Group 2 sample size — minimum 2; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Group 1 sample standard deviation | 8 |
| Group 1 sample size | 20 |
| Group 2 sample standard deviation | 12 |
| Group 2 sample size | 30 |
Pooled standard deviation: about 10.65; pooled degrees of freedom: 48.
Assumptions and limits
- Both groups have at least two observations and their sample standard deviations use n-1 in the denominator.
- A common-variance model is assumed for the pooled estimate; unequal-variance analyses should use another method.
- The result is an estimate for a statistical model, not a weighted average of the two standard deviations.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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