Margin of Error Calculator
Margin of error calculator for polls and surveys from sample size, proportion and confidence level.
E = z · √(p(1 − p) / n)
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
E = z·√(p(1 − p)/n). Use z = 1.645 for 90 %, 1.96 for 95 % and 2.576 for 99 % confidence.
Use p = 50 % when the proportion is unknown: it gives the largest, most cautious margin.
Formula
E = z · √(p(1 − p) / n)
| Symbol | Quantity | Units |
|---|---|---|
| z | Z value (1.96 = 95 %) | — |
| p | Sample proportion | %, × |
| n | Sample size | — |
| E | Margin of error | %, × |
Worked example
Given: z = 1.96 · p = 30 % · n = 1 000
E = z √(p(1 − p)/n)
Result: E = 2.84031 %
Frequently asked questions
Margin of error for 1 000 respondents and 30 %?
1.96 × √(0.3 × 0.7 / 1000) ≈ ±2.84 points.