Margin of Error Calculator
Calculate the margin of error for your survey results to understand the precision of your data.
Formula: MOE = Z × √((p × (1-p)) ÷ n)
Survey Parameters
Enter your survey details to calculate margin of error.
Number of survey responses collected
Total people you could have surveyed
% who answered a certain way (50% is most conservative)
Margin of Error
The accuracy of your survey results.
±4.9%
Good Precision
Confidence Interval
Range where the true value likely falls.
Lower Bound
45.1%
Observed Value
50%
Upper Bound
54.9%
At 95% confidence, the true value is between 45.1% and 54.9%
Calculation Details
With and without finite population correction.
Standard MOE
±4.99%
without FPC
Adjusted MOE
±4.90%
with FPC
Understanding Margin of Error
Margin of error indicates how much survey results may differ from the true population value.
Key Factors
- Sample size — Larger samples = smaller MOE
- Confidence level — Higher confidence = larger MOE
- Population size — Matters more for small populations
- Response proportion — 50% gives the widest (most conservative) MOE
MOE Guidelines
- ±3% or less — High precision, reliable for decisions
- ±5% — Standard precision, commonly accepted
- ±10% — Directional only, use with caution