Statistics & probability
Survey sample size estimate
Plan a sample for a proportion using a supplied margin of error.
A clear answer. Here’s how.
Uses the normal planning formula n₀=z²p(1−p)/e², rounded up. If population N is supplied, applies n=n₀/[1+(n₀−1)/N] before rounding, with at least one observation. Assumes simple random sampling, no non-response or design effect. This plans estimation precision, not hypothesis-test power.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Absolute margin of error (percentage points)
- 5
- Two-sided confidence level (%)
- 95
- Planning proportion (0–1)
- 0.5
- Finite population size (0 means large / unknown)
- 0
Example result
- Required completed observations
- 385
- Unrounded large-population size
- 384.145882069
- Critical z value
- 1.95996398454
Simple-random-sample planning estimate. Allow separately for non-response and sampling design.