Poll Margin of Error Calculator
Calculate the margin of error for a poll or survey result from its sample size, confidence level and reported percentage.
How it works
MOE = z · √( p·(1−p) ÷ n ) · reported as ± percentage points
A poll estimates a percentage from a sample, and the margin of error is how far that estimate can plausibly sit from the true value. It shrinks with the square root of the sample size, so quadrupling the respondents only halves the margin. The margin is widest when the result is near 50% and narrows toward the extremes, which is why headline "±3 points" figures are the conservative 50% case.
Worked example
For n = 1,000, p = 50% and 95% confidence: MOE = 1.96 × √(0.25 ÷ 1000) = 1.96 × 0.0158 = 0.031, i.e. ±3.1 percentage points.
Sources: Margin of error — Wikipedia
Frequently asked questions
Why do pollsters usually quote the margin at 50%?
Because p(1−p) peaks at p = 0.5, the 50% margin is the largest any single number in the poll can have. Quoting it means every reported figure is at least that precise.
Does the margin of error cover every kind of polling error?
No. It only reflects random sampling error. Coverage bias, non-response, question wording and turnout modelling add further uncertainty that the formula does not capture.
How do I compare two candidates within one poll?
The margin on the gap between two candidates is larger than on either number alone. Use a poll-lead significance test rather than simply checking whether the lead exceeds the single-number margin.
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This calculator is for educational purposes. Double-check important results before acting on them.