Pooled Standard Deviation
Pooled Standard Deviation with explicit assumptions and reproducible inputs.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Weights sample variances by degrees of freedom. Appropriate as a common-SD estimate only when equal population variances are defensible.
Example Calculation
- Group 1 sample SD: 2
- Group 1 n: 10
- Group 2 sample SD: 4
- Group 2 n: 10
SDs2 and4 with n10 in each group give pooled SD√10≈3.1623.
Frequently asked questions
How do I use this calculator?
Enter group 1 sample sd, group 1 n, group 2 sample sd, group 2 n. The result updates automatically. Use Reset to restore the example values.
What method does it use?
sₚ=√[((n₁−1)s₁²+(n₂−1)s₂²)/(n₁+n₂−2)]. Weights sample variances by degrees of freedom. Appropriate as a common-SD estimate only when equal population variances are defensible.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.