Understanding Margin of Error
How we calculate. MoE in percentage points = z × sqrt(p(1−p)/n) × 100, with p as a proportion. The form uses the same arithmetic as the worked examples on this page. See our methodology and accuracy policy.
Real-world scenario: A typical Margin of Error case uses sample proportion (%) 50 and sample size (n) 400. Enter the same figures below to reproduce the worked path.
What is Margin of Error?
A common survey precision metric. Assumes a simple random sample and large-sample normal approximation.
- p as percent in the form (converted internally)
- z ≈ 1.96 for ~95% confidence
- Output is percentage points
The Formula
Worked Example
Common Use Cases
- Poll reporting: ±MoE
- Sample size planning: precision targets
- Survey design: n vs width tradeoffs
Pro Tips
- Use p=50% for conservative MoE
- Finite populations may need corrections
- Design effects can widen MoE
Limitations: Margin of Error results are educational statistics aids—not formal statistical certification. Confirm assumptions (SRS, large-sample approximations, labeling) for your analysis.
FAQ
Is MoE the same as confidence level?
No. Confidence level chooses z; MoE is the resulting half-width in percentage points.
What if n is 0?
MoE is undefined—enter a positive sample size.
Authoritative References
For statistical definitions and survey practice, consult: