Compute Your Survey & Conversion Margin of Error
Estimate how far your observed proportion may stray from the true value. Built for A/B testers and analysts who need fast, defensible confidence intervals around a conversion rate.
How the margin of error is calculated
The margin of error (MOE) tells you the half-width of the band around a measured proportion that, on repeated sampling, would contain the true population value at your chosen confidence level. For a single proportion p drawn from a sample of size n, the calculator uses the normal (Wald) approximation:
Here z is the critical value of the standard normal distribution: 1.6449 for 90%, 1.96 for 95%, and 2.5758 for 99% confidence. The quantity under the root is the standard error of the proportion. Because p(1−p) is maximised at p = 0.5, a 50% conversion rate produces the widest possible interval for any given sample size — which is why pollsters quote MOE at p = 0.5 when they want a worst-case figure.
When you supply a finite population, the tool applies the finite population correction (FPC), multiplying the standard error by √((N − n) / (N − 1)). This shrinks the margin when your sample is a meaningful fraction of the whole population, since you have already measured a large share of it. With an infinite or blank population the FPC equals one and has no effect.
The reported confidence interval is simply p ± MOE, clamped to the 0–100% range. The relative margin divides MOE by p, which is often more useful in A/B testing: a ±1.2% absolute margin on a 2% conversion rate is a huge ±60% relative swing, signalling you need far more traffic before the result is trustworthy. Note that the Wald formula loses accuracy for very small samples or proportions near 0% or 100%; in those cases a Wilson or exact interval is preferable.