Sampling Error, Quantified

Every survey estimate carries uncertainty: ask 400 people and you will rarely hit the population value exactly. This margin of error calculator turns that uncertainty into a number — the radius around your sample statistic that should contain the true value at your chosen confidence level.

The Mechanics

Start from the standard error σ/√n, which shrinks as the sample grows. Multiply by the critical z-value for your confidence level (1.645, 1.96, or 2.576) to get the margin of error. If you sample from a known finite population and take more than 5% of it, the finite population correction tightens the result.

Reading the Interval

Report the interval alongside the estimate: "150 ± 2.45 at 95% confidence" means that if you repeated the study many times, roughly 95% of such intervals would capture the true mean. Narrower intervals need larger samples — there is no shortcut around n.