Margin of Error Calculator – Proportion
Estimate the normal-approximation margin of error for a sample proportion, in percentage points.
Formula
E = z√[p(100−p)/n], with p entered as a percentage.
Margin (percentage points) ≈ (1.96×sqrt((50)×(100-(50))÷(100)))÷min(1,max(0,ceil(min((50)-500÷(100),100-500÷(100)-(50)))))
How to use
- Enter the observed percentage p.
- Enter sample size and choose confidence.
- Read the approximate margin in percentage points.
Examples
- p = 50%, n = 100, confidence 95%: margin ≈ 9.8 percentage points.
Frequently asked questions
When is this suitable?
Use independent random observations with more than five successes and five failures. Other inputs are rejected; small samples or extreme proportions need another method.
Is 9.8 a relative percentage?
No. A result of 9.8 means add or subtract 9.8 percentage points from p.
Does it include survey bias?
No. It excludes selection bias and finite-population correction. Critical z values are rounded.
Sources
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