Statistics and research
Margin of error calculator
Margin of error for a survey proportion or a mean at any confidence level, with the finite population correction.
Runs in your browser. What you enter stays on this page and is not uploaded.
Leave blank for a large or unknown population.
Results
Margin of error±3.099 pointsConfidence95%
- Standard error √(p(1 − p)/n)
- 0.015811388 (1.58114 points)
- Critical z
- 1.959964
- Margin of error
- ±3.09898 percentage points
- Interval around the proportion
- 46.901% to 53.099%
Use 50% when the proportion is unknown: it gives the largest margin for a given n.
Method and limits
How to use it
Enter the number of completed responses and the observed percentage (use 50% for the worst case), or the standard deviation for a mean. Add the population size if the sample is a noticeable share of it.
Formulas
- Proportion: E = z √(p(1 − p) / n).
- Mean: E = z σ / √n.
- Finite population correction: multiply by √((N − n) / (N − 1)).
Assumptions and limits
- Covers random sampling error only — not non-response, coverage or question-wording bias.
- For a proportion near 0% or 100% or a small n, use a Wilson or exact interval (confidence interval calculator).
- The margin for a difference between two subgroups is larger than the margin of either one.
Worked example
A poll of 1,000 people finds 50%: E = 1.95996 × √(0.25 / 1000) = 0.0310, so ±3.1 percentage points at 95% confidence (46.9% to 53.1%).
References
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