Margin of Error Calculator

About this calculator

The margin of error (MOE) measures how much a survey's reported percentage could differ from the true value in the full population, given the size of the sample and how confident you want to be in the estimate. For a proportion, it's calculated as MOE = z × √(p(1−p)/n), where z is the critical value from the standard normal distribution for the chosen confidence level (1.96 for 95%, 2.576 for 99%), p is the sample proportion, and n is the sample size.

Pollsters, market researchers, and social scientists report the margin of error alongside every survey result — "62% support the policy, ±3 percentage points" — so readers know the range the true population value likely falls in. Larger samples shrink the margin of error, which is why national polls often use n≈1,000 to get a MOE near 3%, while smaller focus-group surveys carry much wider uncertainty.