Updated July 8, 2026
The proportion example below was checked against the calculator's margin-of-error formula, not just against itself.
The margin of error is calculated as the critical z-value multiplied by the standard error of the proportion: MOE = z * sqrt(p * (1 - p) / n). For a 95% confidence level, z = 1.96. A smaller sample produces a larger margin of error.
The formula
MOE = z * sqrt( p * (1 - p) / n )
Where:
- z is the critical value for your confidence level (1.96 for 95%, 2.576 for 99%)
- p is the estimated proportion (use 0.5 if unknown, which gives the widest, most conservative margin)
- n is the sample size
Worked example: finding the margin of error for 95% confidence
You survey 400 people; 52% say yes. What is the margin of error at 95% confidence?
| Step | Calculation | Value |
|---|---|---|
| Identify z for 95% | Standard table | 1.96 |
| p = 0.52, n = 400 | p*(1-p) = 0.52 * 0.48 | 0.2496 |
| Divide by n | 0.2496 / 400 | 0.000624 |
| Take square root | sqrt(0.000624) | 0.02498 |
| Multiply by z | 1.96 * 0.02498 | 0.049 (4.9%) |
The margin of error is plus or minus 4.9 percentage points. The true population proportion is likely between 47.1% and 56.9%.
What does a 2% margin of error mean?
A 2% margin of error means the survey result could be up to 2 percentage points above or below the true value. If 55% of respondents favor a policy, the actual figure in the full population is likely between 53% and 57% at whatever confidence level you chose.
What does 0.05 margin of error mean?
A margin of error of 0.05 (5 percentage points) is common in general-population surveys. To achieve a 5% margin at 95% confidence with p = 0.5, you need n = (1.96^2 * 0.25) / 0.05^2 = 384 people. Achieving a tighter margin requires a larger sample.
What is a good margin of error?
For national opinion polls, plus or minus 3% is standard. For internal business surveys, plus or minus 5% is usually acceptable. Scientific studies targeting real-world decisions often aim for 1% to 2%. The tighter the margin you need, the larger the sample you must collect. Cross-link your result with the confidence interval to understand the full range.
Run your own survey numbers
Enter your sample size and proportion into the margin of error calculator to get the plus-or-minus figure without doing the square root by hand.