📏 Margin of Error Calculator

The margin of error quantifies the maximum expected difference between the true population proportion and a sample estimate. A ±3% MOE with 95% confidence means: if you ran the survey 100 times, 95 of those would produce results within 3% of the true value.

When the true proportion is unknown, p = 0.5 maximises p(1−p) = 0.25, giving the largest (most conservative) MOE. Any other value of p will produce a smaller MOE, so p = 0.5 guarantees your sample is large enough regardless of the outcome.

The standard MOE formula assumes an infinite population. When sampling from a finite population of size N, the FPC factor √((N−n)/(N−1)) reduces the MOE, reflecting the fact that you are sampling a large fraction of the population.

The 95% confidence level is the most common in research and polling. A higher confidence level (99%) gives a wider interval (larger MOE) but more certainty. A lower level (90%) gives a narrower interval but less certainty.

MOE decreases as sample size increases (roughly proportional to 1/√n). Increasing your sample from 400 to 1600 halves your MOE. Using a lower confidence level or a proportion estimate different from 0.5 also reduces MOE.