Stichprobengrößenrechner
The detailed guide below is currently available in English.
What the sample size formula balances
The standard formula n = z² × p(1−p) ÷ e² trades three demands against each other. More confidence demands a bigger sample — the z multiplier grows from 1.645 at 90% to 2.576 at 99%. A tighter margin of error is expensive: halving e quadruples n, because e is squared in the denominator. And p(1−p) peaks at p = 50%, which is why surveys that know nothing about the answer use 50% as the safe worst case. When the population itself is small, sampling noticeably depletes it and the finite-population correction n ÷ (1 + (n−1) ÷ N) shrinks the requirement — surveying 278 of 1,000 people already gives ±5% at 95% confidence.
Häufige Fragen
Why does 50% give the largest sample size?
The term p(1−p) measures how divided the population could be, and it peaks when opinions split evenly. Assuming 50% plans for maximum variance, so the sample works no matter how the real answers fall.
What if I do not know my population size?
Leave it blank. The uncorrected formula assumes a very large population, which is the right model once the population reaches several thousand — the correction only matters when your sample is a real fraction of the whole.