Sample size for a proportion
This calculator estimates the minimum sample size needed to estimate a population proportion at a selected confidence level and margin of error. It uses the common large-sample proportion formula and applies finite population correction when a population size is supplied.
Formula
For a large population: n₀ = Z²p(1−p) ÷ e², where Z is the confidence-level critical value, p is the expected proportion and e is the desired margin of error.
For a finite population N: n = n₀ ÷ [1 + (n₀−1)/N].
Choosing the expected proportion
When no prior estimate is available, p = 0.50 is commonly used because it produces the largest sample size for a given confidence level and margin of error.
Interpretation
The result is a statistical minimum under the stated assumptions. Real studies may need larger samples for non-response, design effects, subgroup analyses, clustering or expected attrition.
Method reference: Cochran’s standard sampling formula for proportions.
Frequently asked questions
Why is 50% often used for expected proportion?
At a fixed confidence level and margin of error, 50% gives the maximum variance and therefore a conservative sample-size estimate.
Should I add non-response?
Usually yes when non-response or dropout is expected. Adjust the minimum sample upward according to the study plan.