📊Margin of Error Calculator
The margin of error (MOE) quantifies the uncertainty in a survey result. A poll showing 60% support with ±4% MOE means the true population value likely falls between 56–64% at the stated confidence level. MOE shrinks as sample size grows.
Tip: To halve the margin of error, you need to quadruple the sample size — precision is expensive. Doubling n only reduces MOE by about 30%.
- 1MOE = z × √(p(1-p)/n)
- 2z = 1.96 for 95% confidence
- 3p = observed proportion · n = sample size
- 4MOE is the ± value reported alongside poll results
Design effect
Complex survey designs (stratified, cluster sampling) multiply the simple random sample MOE by a design effect factor, typically 1.5–2.0, because observations within clusters are correlated.
Fun Fact
The margin of error in news reports almost always assumes a perfectly random sample — but most online polls use convenience samples, making the stated MOE statistically meaningless.
References