Margin of Error Calculator
Calculate the margin of error for a survey or poll given sample size and confidence level.
Inputs
Use 0.5 for maximum margin of error
Margin of Error
4.38%
Z Critical Value
1.9600
Lower Bound
45.62%
Upper Bound
54.38%
Step by step
Values used
Sample Size = 500; Proportion (0–1) = 0.5000; Confidence Level (%) = 95
Formula applied
MOE = z × √(p(1−p) / n)
Margin of Error
= 4.38
Z Critical Value
= 1.9600
Lower Bound
= 45.62
Upper Bound
= 54.38
How it works
The margin of error tells you how far your survey results might be from the true population value. It depends on the sample size, the estimated proportion, and the desired confidence level.
Formula
MOE = z × √(p(1−p) / n)
- z
- Critical z-value for confidence level
- p
- Estimated proportion
- n
- Sample size
Frequently Asked Questions
Why use p = 0.5?
p = 0.5 gives the maximum (most conservative) margin of error. If you don't know the true proportion, 0.5 is the safest assumption.
How do I reduce the margin of error?
Increase the sample size. Quadrupling the sample cuts the margin of error in half.