Margin of Error Calculator
Why polls stop at a thousand people.
Work out Margin of Error. Why polls stop at a thousand people. Shows the working, not just the answer.
As a decimal — 0.5 for 50%.
Margin of error at 95% confidence
± 3.10%
46.9% to 53.1%
Margin of error shrinks with the square root of sample size, so quadrupling the sample only halves it. That square root is why national polls stop at about 1,000 people: going to 4,000 costs four times as much to move the margin from roughly 3 points to 1.5. It is widest at 50% and narrows towards either extreme, and it accounts only for sampling error — not for a biased sample, a leading question or people who decline to answer, which are usually the larger problems.
How the Margin of Error Calculator works
Enter an observed proportion, a sample size and a confidence level for the margin of error and the resulting interval. It shrinks with the square root of sample size, which is why quadrupling a survey only halves its margin.
Also known as: poll margin of error calculator · confidence interval for a proportion · survey accuracy calculator · sample size margin of error
Frequently asked questions
How is margin of error calculated?
z × √(p(1−p)/n), with z set by the confidence level — 1.96 for 95%. It is widest at p = 0.5 and narrows towards either extreme.
Why do most polls sample about 1,000 people?
Because the margin falls with the square root of the sample. A thousand gives roughly ±3 points; getting to ±1.5 needs four thousand and four times the cost. That is where the value stops justifying the spend.
Does margin of error cover all polling error?
No, and this is the important caveat. It covers sampling error only. A biased sample, a leading question or systematic non-response are not in it, and in practice those are usually the larger problems.
What does 95% confidence actually mean?
That if the same survey were repeated many times, about 95% of the intervals produced would contain the true value. It is a statement about the method's long-run behaviour, not about this one interval.
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