Margin of Error Calculator
Calculate the normal-approximation margin for a proportion.
How the margin of error calculator works
Margin of error is the half-width added to and subtracted from a sample proportion under a chosen confidence level. The calculation combines expected binomial variability with sample size, then scales the standard error by a z critical value. Using one half as the expected proportion gives the largest variance and therefore the most conservative margin when no prior estimate is available.
The defaults use expected proportion 0.5, sample size 400, and 95 percent confidence. The standard error is 0.025, and 1.96 times that value gives the verified decimal margin 0.049. The result is 4.9 percentage points, so a 50 percent estimate would span approximately 45.1 through 54.9 percent.
Reading margin of error calculator results privately
This is a sampling-error calculation, not a correction for biased questions, nonresponse, bad coverage, or measurement error. It uses a simple-random-sample normal approximation and does not include finite-population correction or survey design effects. Very small samples and extreme expected proportions call for a more specialized interval method. This margin of error calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
Why is 0.5 the conservative expected proportion?
The product p times one minus p is largest at one half, producing the widest margin for a fixed sample size.
Does a small margin prove a survey is accurate?
No. It quantifies random sampling variation only and does not capture bias or measurement problems.
Is the margin of error calculator private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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