Understanding Margin of Error
How we calculate. MoE in percentage points = z × sqrt(p(1−p)/n) × 100, with p as a proportion. 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
| Scenario | When to use |
|---|---|
| Percent of a number | Finding a part of a whole (tax, tip, score) |
| Percent change | Comparing old vs new values |
Limitations: Margin of Error results are educational statistics aids—not formal statistical certification. Confirm assumptions (SRS, large-sample approximations, labeling) for your analysis.
Common mistakes
- Swapping part and whole: The denominator must be the full total, not a subset.
- Rounding too early: Carry extra decimal places through multi-step work before rounding the final percent.
- Mixing percent and decimal forms: Enter rates in the format the calculator labels expect.
The worked example for margin of error was verified with the calculator form on this page—enter the same values to confirm the result.
When to use this calculator
- Use this page for margin of error when your question matches the labels on the form above.
- Use the margin calculator when profit must be a percent of selling price.
- Use the markup calculator when profit is measured against cost.
- Use the discount calculator to find a sale price from a list price and percent off.
- After a discount, check the ROI calculator if you need return on what you still spend—or the tip calculator when a discounted bill needs gratuity.
Still unsure about margin of error? Start with the quick answer above, then open the linked calculator that matches your wording.
❓ Frequently Asked Questions
How do I use this margin of error calculator?
For margin of error, enter the values labeled on the form, then press Calculate. Compare the result to the worked example on this page.
What formula does this page use?
See the quick answer and formula box above for margin of error—the same business margin education expression is applied to your inputs.
What if my result looks wrong?
When checking margin of error, re-check part vs whole (or rate vs base), rounding, and whether percents were entered as 25 rather than 0.25 when the form expects percents.
Authoritative References
For statistical definitions and survey practice, consult: