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Peak Forms margin of error calculator
Enter the number of responses, the observed share and the confidence level, optionally the population size: the calculator shows the margin of error and the range in which the true share lies.
e = z · √(p · (1 − p) / n) · with a known population size N additionally · √((N − n) / (N − 1))
Margin of error
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In percentage points. This is how far the observed share can deviate from the true share by chance.
Confidence interval
–
The true share lies in this range at the chosen confidence level, provided the assumptions are met.
z-value used
1,960
Two-sided quantile of the standard normal distribution for the confidence level.
Assumption: The margin of error only covers random sampling variation. Errors from question wording, the choice of respondents or missing responses are not included.
Method and sources: Normal approximation (Wald interval) with finite population correction following W. G. Cochran, Sampling Techniques, 3rd edition, Wiley 1977, chapter 3. See also NIST/SEMATECH e-Handbook of Statistical Methods.
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What the calculator doesn't answer.
- The margin of error only covers random sampling variation, not bias from question wording or the choice of respondents.
- The formula applies to proportions from a random sample, not to means or to comparing two groups.
- With very few responses or shares close to 0 % or 100 % the approximation is imprecise; the calculator points this out.
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