Margin of Error Calculator

It is the half-width of the confidence interval around a survey result. A result of 50% with a 3% margin means the true value likely lies between 47% and 53%.

It uses the two-sided critical values of the standard normal distribution: 1.644854 for 90% confidence, 1.959964 for 95% and 2.575829 for 99%. The chosen z is shown on its own result card, rounded to four places for display.

The product p times (1 minus p) is largest at 0.5, so using 0.5 gives the widest, most conservative margin when the true proportion is unknown. Any proportion nearer 0 or 1 produces a smaller margin.

Higher confidence needs a larger z-value, so the margin grows. 99% confidence gives a wider margin than 95%, and 95% is wider than 90%, for the same sample and proportion.

Use it when your sample is a large share of a small, finite population. The finite-population correction multiplies the margin by the square root of (N - n) / (N - 1), which shrinks it, and it has almost no effect once the population is much larger than the sample.

Yes, but with diminishing returns. The margin falls with the square root of the sample size, so halving it needs about four times the respondents. Going from 1,000 to 4,000 respondents only cuts a 95% margin from roughly 3.1% to about 1.5%.

It is the large-sample normal (Wald) formula for a single proportion. That approximation is dependable when the sample is reasonably large and the proportion is not close to 0 or 1. For very small samples or extreme proportions, an exact or Wilson interval is more trustworthy than this method.

No. It assumes simple random sampling. Real polls often weight responses and use clustered or stratified designs, which change the true margin by a design effect this tool does not model, so treat the result as a floor rather than the whole story.

Yes. The calculation runs in your browser and none of your inputs are sent to a server.