🎓 Statistics & Data • Inferential Statistics
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Margin of Error Calculator
Calculates the margin of error (MOE) at 90%, 95%, or 99% confidence levels for sample proportions.
Presets:
0.50 gives worst-case conservative MOE
Applies FPC if specified
Calculated Margin of Error (95% CL)
±3.10%
Decimal: ±0.0310
Sample Size vs. Margin of Error CurveLaw of Diminishing Returns
Formula & Adjustments
Standard Error (SE): 0.0158
Critical Value (z*): 1.96
Population assumed infinite (no FPC correction needed)
MOE = z* × SE × FPC = ±3.10%
What is the Margin of Error?
The margin of error expresses the maximum expected difference between true population parameters and sample estimates in random surveys.
Formula & Step-by-Step Calculation
MOE = z* · √[ p(1 - p) / n ]
Critical z value times standard error of the proportion.
Worked Step-by-Step Examples
Example 1
Survey of 1,000 voters with 50% proportion at 95% confidence
Solution: Margin of Error = ±3.10%
• 1.96 × √[(0.5 × 0.5) / 1000] = 1.96 × 0.0158 = ±0.0310 (±3.10%)
Common Real-World & Academic Use Cases
- ✓ Election political polling accuracy disclosures
- ✓ Consumer market research survey reliability
- ✓ Corporate employee sentiment sampling
How to Use the Margin of Error Calculator
1
Select Confidence Level
Choose 90%, 95%, or 99%.
2
Enter Sample Size n
Input number of respondents.
3
Read Margin of Error
Inspect ± percentage.
Frequently Asked Questions
Q: Why does doubling sample size not halve the margin of error?
Because sample size is inside a square root: reducing MOE by half requires quadrupling the sample size.