Margin of Error Calculator
Find the margin of error for a survey proportion from your sample size, confidence level and result — the ± figure quoted with poll numbers.
How it works
MOE = z · √[ p·(1 − p) ÷ n ] · optionally × √[(N − n) ÷ (N − 1)] for a finite population
The margin of error is the ± figure reported alongside a poll: half the width of the confidence interval for the proportion. It combines the confidence multiplier z with the standard error of the sample percentage. Because p(1 − p) peaks at 50%, quoting the margin at p = 0.5 gives the largest, most cautious value — which is why headline poll margins usually assume it.
Worked example
A poll of 1,000 people at 50% and 95% confidence has standard error √[0.25 ÷ 1000] ≈ 0.01581, so the margin is 1.96 · 0.01581 ≈ 0.031 — the familiar "±3 percentage points".
Sources: Margin of error — Wikipedia
Frequently asked questions
Is the margin of error the same as the confidence interval?
The margin of error is half the width of the interval. Add and subtract it from the sample result to get the interval: 52% with a ±3% margin means a range of 49% to 55%.
Why do most polls quote about ±3%?
Because a sample of roughly 1,000 at the worst-case 50% split yields a 95% margin near 3 percentage points. It is a sweet spot between cost and precision, not a magic number.
Does the margin of error cover every kind of error?
No. It only captures random sampling variation. Bias from non-response, poor question wording, or an unrepresentative sample is not included and can dwarf the stated margin.
Related calculators
For education — check the assumptions (sample size, independence, distribution) before using these results in real decisions.