Ā± Margin of Error Calculator
Calculate the margin of error for an estimated population proportion.
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Please enter valid values.
Formula and Explanation
Calculate the margin of error for an estimated population proportion.
| Concept | Formula or rule |
|---|---|
| Margin of Error Calculator | E = zā[p(1āp)/n] |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: For n=400 and p=50% at 95% confidence, Eā4.9%.
ā Margin of error ā Ā±4.9 percentage points
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
ā ļø
Calling it total error
Margin of error covers sampling uncertainty under the model, not bias or poor measurement.
Margin of error covers sampling uncertainty under the model, not bias or poor measurement.
ā ļø
Ignoring design effects
Clustered or weighted samples may have larger uncertainty.
Clustered or weighted samples may have larger uncertainty.
ā ļø
Mixing percentage and proportion formats
This page expects a percentage.
This page expects a percentage.
Practice Questions
1. If n quadruples, what happens to margin of error?
Answer: It halves.
2. Does 99% confidence increase or decrease E?
Answer: Increase.
3. What p gives the largest E?
Answer: 50%.
Frequently Asked Questions
What reduces margin of error?ā¾
A larger sample size or lower confidence level.
Does population size always matter?ā¾
Mostly when the sample is a substantial share of a finite population.
Is Ā±5% the same as 5% relative error?ā¾
No. It usually means 5 percentage points for a proportion.