Margin of Error Calculator
Calculate the margin of error for a survey or sample. Enter confidence level, sample size, and proportion to find the margin of error.
Use 0.5 if unknown (maximum MOE)
Enter values to calculate the margin of error.
Margin of Error Formula
MOE = z × √(p̂(1 − p̂) / n)
Where z is the z-score for the chosen confidence level, p̂ is the sample proportion, and n is the sample size.
Common Z-Scores
| Confidence Level | Z-Score |
|---|---|
| 90% | 1.645 |
| 95% | 1.960 |
| 99% | 2.576 |
Example: n = 1000, confidence = 95%, p̂ = 0.5
MOE = 1.96 × √(0.5 × 0.5 / 1000)
MOE = 1.96 × 0.01581 = ±3.1%
MOE = 1.96 × √(0.5 × 0.5 / 1000)
MOE = 1.96 × 0.01581 = ±3.1%
How to Reduce Margin of Error
- Increase sample size (most effective).
- Lower the confidence level (less certain but tighter interval).
- Proportions near 0 or 1 naturally have smaller MOE.
FAQ
What does margin of error mean?
A margin of error of ±3% at 95% confidence means that if the survey were repeated many times, 95% of the results would be within 3 percentage points of the true population value.
Why use 0.5 for the proportion?
When the true proportion is unknown, 0.5 gives the largest (most conservative) margin of error because p(1−p) is maximized at p = 0.5.
Related Calculators
Last updated: 2026-08-08