Sample Size Margin of Error Calculator

Sample size from margin of error

When you're estimating a proportion in an infinite population, the sample size you need comes from n = z² · p · (1−p) / E². Here z is the critical value of the confidence interval (1.96 for 95%, 2.576 for 99%), p is the expected proportion, and E is the margin of error you're willing to accept. When you have no idea what the proportion is, set p to 0.5, which gives the most conservative number. Say you want 95% confidence with E = 3% and p = 0.5; that works out to n ≈ 1,067. The 2,000-respondent polls Datafolha usually runs land at a margin of around ±2.2 percentage points.

Applications

Electoral polls (Datafolha, IBOPE/Ipec, Quaest). Household and labor surveys such as the IBGE PNAD. Market research, customer satisfaction tracking with NPS, public health surveillance, and figuring out how many users an A/B test really needs.

FAQ

Why use p = 0.5? The product p · (1−p) peaks at 0.5, so that value gives the largest n. When you don't know the real proportion, that's the safe upper bound to plan around.

Does the population size matter? Only when the population is finite. Once n climbs above roughly 5% of N, apply the finite population correction (FPC).

95% or 99% confidence? More confidence costs you a bigger sample. Move from 95% to 99% and n grows by roughly 70%.