Work out sample size for proportion instantly with clear inputs, formula shown and shareable results.
Rearranging the margin of error formula gives n = z²p(1 − p)/E². Since p(1 − p) peaks at 0.25 when p = 0.5, using that value gives the largest sample any proportion could need.
Sample size
n = z²·p(1 − p) / E², rounded up
z = 1.96 and p(1−p) = 0.25 give n = 1068 — which is why national polls typically survey about a thousand people.
Because n depends on 1/E², so precision improves only as the square root of effort.