Margin of Error Calculator
What is the margin of error of my survey result?
Single calculationv1.0.0Verified 2026-11-01Runs in your browser
Spec sheet
moe_proportion · v1.0.0Method
Normal-approximation margin of error
- 01
e = z · √(p(1 − p)/n) · √((N − n)/(N − 1)) - 02
CI = p ± e
Limits — read before relying on it
- Normal approximation; for very small samples or proportions near 0 % / 100 % use a Wilson interval.
Sources
- Cochran, W. G. (1977). Sampling Techniques (3rd ed.). Wileytextbook
Worked example
computed by the same formulan = 1,000, 50 %, 95 %
Inputs
- Sample size
- 1000
- Observed proportion
- 50 %
- Confidence level
- 95 %
Result
- Margin of error
- 3.1 %
- Confidence interval
- 46.9 % to 53.1 %
Questions
How is the margin of error calculated?
›
Normal-approximation margin of error. e = z · √(p(1 − p)/n) · √((N − n)/(N − 1)) · CI = p ± e
Example: n = 1,000, 50 %, 95 %?
›
Margin of error: 3.1 %; confidence interval: 46.9 % to 53.1 %.
What does this calculator not cover?
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Normal approximation; for very small samples or proportions near 0 % / 100 % use a Wilson interval.
Where do the numbers come from?
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Sources: Cochran, W. G. (1977). Sampling Techniques (3rd ed.). Wiley. The formula is versioned (moe_proportion v1.0.0) and covered by automated tests.
Is my data stored?
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No. The calculation runs in your browser and nothing is sent unless you choose to save a shareable link.
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