What Is the Margin of Error Calculator?
A margin of error calculator determines the statistical radius of uncertainty around survey sample statistics.
How Does the Margin of Error Calculator Work?
Applies standard normal sampling error propagation to determine confidence bounds.
Margin of Error Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
MOE = Z × √[p(1 - p) ÷ n] × FPC
Multiplies critical Z value by the standard error of the proportion, with finite population correction factor if population size is known.
How to Use the Margin of Error Calculator
- Input completed sample size, desired confidence level, and observed proportion.
Step-by-Step Example Calculation
500 respondents at 95% Confidence
Input Values:
sampleSize:500
confidenceLevelPct:95
observedProportionPct:50
Understanding Your Result
Shows ± error percentage and the lower and upper bounds of the resulting confidence interval.
Factors That Affect the Result
- Sample size (n) and the variance of the observed proportion.
When Should You Use This Calculator?
- Interpreting election polls, academic studies, marketing questionnaires, and quality audits.
Assumptions & Limitations
- Assumes unbiased random sampling without systematic sampling defects.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard asymptotic normal approximation for binomial proportions.