Margin of Error Calculator

The margin of error (MOE) is a measure of the uncertainty in a survey result. It tells you how much the survey result could differ from the true population value. For example, if 60% of respondents favor a policy with a ±3% margin of error, the true population support is likely between 57% and 63%.

The standard formula is MOE = z* × √(p(1−p)/n), where z* is the critical value for your chosen confidence level, p is the proportion (expressed as a decimal), and n is the sample size. When a finite population size N is provided, a correction factor √((N−n)/(N−1)) is applied to reduce the MOE.

The 95% confidence level is by far the most widely used in research and reporting. It means that if the same survey were repeated 100 times, roughly 95 of those results would fall within the calculated margin of error. Use 99% when the stakes are higher and you need greater certainty, accepting a larger MOE.

The formula p(1−p) is maximized when p = 0.5, producing the most conservative (widest) margin of error estimate. When you don't know the expected proportion in advance, using 50% is standard practice because it guarantees your sample size and MOE calculations will be sufficient regardless of the true result.

For large populations (generally over 10,000), the population size has almost no effect on the margin of error, so it's typically ignored. For smaller, finite populations, a finite population correction (FPC) factor is applied, which reduces the MOE — meaning you actually need a smaller sample than you would for an infinite population.

The most effective way to reduce your MOE is to increase your sample size — the MOE shrinks proportionally to the square root of n. You can also lower your confidence level (e.g. from 99% to 95%), though this reduces certainty. Doubling precision requires quadrupling your sample size, so there are real diminishing returns to consider.

A margin of error of ±5% or less is generally considered acceptable for most consumer and business surveys. Academic and political polls often aim for ±3% or better. The 'right' MOE depends on the stakes: a tight product decision might demand ±2%, while an exploratory poll might tolerate ±7%.

The margin of error is the ± value, while the confidence interval is the full range constructed around the survey result using that MOE. If your survey finds 55% support with a ±3% MOE at 95% confidence, then your 95% confidence interval is [52%, 58%]. The two terms are closely related but describe different aspects of the same concept.