How to use the pooled standard deviation calculator
Combine the spread of two samples into one pooled standard deviation. Enter sample 1 size, sample 1 standard deviation, sample 2 size, sample 2 standard deviation in the fields above; the pooled standard deviation is computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “pooled standard deviation”, “combined sd of two samples”, “pooled sd t test”, “calculate pooled standard deviation”, “find pooled standard deviation”.
Formula
Variables
- n1 — Sample 1 size
- s1 — Sample 1 standard deviation
- n2 — Sample 2 size
- s2 — Sample 2 standard deviation
Worked example
With sample 1 size = 20, sample 1 standard deviation = 4, sample 2 size = 25, sample 2 standard deviation = 5, the calculator gives pooled standard deviation ≈ 4.585112.
Frequently asked questions
What is the pooled standard deviation calculator used for?
Combine the spread of two samples into one pooled standard deviation. It helps with questions such as “pooled standard deviation”, “combined sd of two samples”, “pooled sd t test”.
What is the formula for the pooled standard deviation calculation?
Pooled standard deviation = √(((n1-1) × s1 × s1+(n2-1) × s2 × s2) / (n1+n2-2)). Here n1 is sample 1 size, s1 is sample 1 standard deviation, n2 is sample 2 size, s2 is sample 2 standard deviation.
What inputs do I need for the pooled standard deviation calculator?
You need sample 1 size, sample 1 standard deviation, sample 2 size, sample 2 standard deviation. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the pooled standard deviation calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the pooled standard deviation result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.