Formula
The sample size squares the z multiplier times the deviation, divided by the margin:
Sample size = (z × standard deviation / margin)²
The result is rounded up. It assumes a large population and a deviation you already know.
Assumptions
- The margin of error uses the same unit as the standard deviation.
- The population is large enough that a finite correction is not applied.
Worked example
Z of 1.96, standard deviation 10, and a margin of 2 need a sample of 97.
Input definitions
- Margin of error
- How far from the mean you are willing to be.
- Standard deviation
- The expected spread of one observation.
Limitations
This does not adjust for a small population or for a proportion. It is not a study plan.
Questions
Why round up?
A fraction of an observation is not enough, so the next whole number is used.
What if I want a narrower margin?
A smaller margin raises the sample size.