When to use this calculator
This pools within-group variation and is not the standard deviation of all observations after combining different group means.
Explore the descriptive statistics calculators for other questions in this topic. For a related calculation, use the Population Standard Deviation Calculator: Find population standard deviation from a list of numeric observations.
PUTTING IT INTO PRACTICE
Pooled Standard Deviation: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| First sample size (integer) | 10 |
| First sample standard deviation | 2 |
| Second sample size (integer) | 10 |
| Second sample standard deviation | 2 |
| Result | 2 |
- Check the input labels and enter the example values above.
- Apply the relationship: Pooled SD = √(((n₁−1)s₁² + (n₂−1)s₂²)/(n₁+n₂−2)).
- The result is 2 , rounded for display.
How to interpret your result
Assumes the samples estimate a common within-group population variance.
The mean, median, range and standard-deviation tools accept variable-length lists with their limits stated. Choose a sample or population denominator appropriately. A summary statistic does not validate the sampling process or explain causation.
Frequently asked questions
Should I use sample or population standard deviation?
Use population deviation for the complete population being described. Use the sample form when estimating variability from a sample under suitable assumptions.
When is the pooled standard deviation calculator useful?
This pools within-group variation and is not the standard deviation of all observations after combining different group means.
How do I use the pooled standard deviation calculator?
Enter first sample size (integer), first sample standard deviation, second sample size (integer), second sample standard deviation. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Pooled SD = √(((n₁−1)s₁² + (n₂−1)s₂²)/(n₁+n₂−2)).
What should I check before using the result?
Assumes the samples estimate a common within-group population variance.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST: exploratory data analysis ↗. This is a topic reference, not an external review or endorsement of this tool.
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