A worked example
A 95% confidence level with a 5% margin of error and a 50% expected proportion requires a sample size of 385 — a number that shows up constantly in survey methodology for exactly these defaults.
Frequently asked questions
Why does 385 show up so often as a recommended sample size?
At the common defaults of 95% confidence, 5% margin of error, and 50% expected proportion, the formula consistently lands very close to 385 for any sufficiently large population — it's become a familiar reference number for that reason.
Why use 50% as the expected proportion if I don't know the real one?
50% produces the largest possible required sample size for given confidence and margin of error settings — using it as a default guarantees your sample is big enough regardless of what the true proportion turns out to be.
When does population size actually matter?
Mainly for smaller populations — once a population is much larger than the calculated sample size (roughly 20x or more), the finite population correction barely changes the result, which is why it's often skipped for large populations.