Margin of Error Calculator
Calculate margin of error for surveys and statistical studies with confidence intervals
Survey Margin of Error Calculator
Use FPC when sample size is 5% or more of the total population
Z-score: 1.96
Number of people surveyed
Proportion as decimal (e.g., 0.57 for 57%)
Calculated Sample Proportion (p̂): 0.5000 (50.00%)
Example Calculation
Survey Scenario
Population: 5,000 people
Sample: 400 people surveyed
Responses: 260 people answered "yes"
Confidence Level: 96%
Calculation
Sample Proportion: 260/400 = 0.65
Z-score (96%): 2.05
FPC needed: 400/5000 = 8% (>5%)
Margin of Error: ±4.69%
Interpretation: 96% confident the true proportion is 65% ± 4.69%
Common Confidence Levels
95% is most commonly used in social sciences
MOE Guidelines
When to Use FPC
Use FPC when:
Sample ≥ 5% of population
Effect:
Reduces margin of error for finite populations
Formula:
FPC = √((N-n)/(N-1))
Understanding Margin of Error
What is Margin of Error?
Margin of error indicates how many percentage points your survey results may differ from the true population value. It's a measure of the uncertainty in your sample estimates due to random sampling variation.
Key Applications
- •Political polling and election predictions
- •Market research and customer satisfaction
- •Quality control and manufacturing
- •Medical and clinical research studies
Factors Affecting MOE
Sample Size
Larger samples reduce margin of error. MOE decreases proportionally to the square root of sample size.
Confidence Level
Higher confidence levels increase margin of error. 99% confidence requires a larger margin than 95%.
Population Proportion
MOE is largest when proportion is near 50% (0.5), and smallest near 0% or 100%.
Important Considerations
- • Margin of error only accounts for random sampling error, not bias
- • Assumes random sampling from the target population
- • Does not account for non-response bias or measurement errors
- • FPC should be used when sample is ≥5% of finite population