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Margin of Error Calculator

Calculate margin of error, confidence intervals, and required sample sizes for surveys, polls, and statistical studies. Supports proportions, means, and finite populations.

Proportion / Poll MOE

For survey results where responses are yes/no or categorical (e.g. approval ratings, polls)

Leave blank or enter 50 for maximum (worst-case) MOE

Enter for finite population correction (FPC)

Common Scenarios

Real-world survey and polling examples

Result

Confidence Interval Visualizer

How the CI width changes across confidence levels

MOE vs. Sample Size Table

See how MOE changes with different sample sizes

Sample SizeMOE (90%)MOE (95%)MOE (99%)CI Width (95%)

Interpretation & Notes

Result Summary

Enter your data and click
Calculate

Z-Score Reference

80% CIz = 1.282
90% CIz = 1.645
95% CIz = 1.960
98% CIz = 2.326
99% CIz = 2.576
99.9% CIz = 3.291

Formula Reference

Proportion MOE
E = z × √(p̂(1−p̂)/n)
Mean MOE
E = z × (σ / √n)
Sample Size (n)
n = (z/E)² × p̂(1−p̂)
FPC (finite pop)
× √((N−n)/(N−1))

MOE Quick Reference

n = 100±9.8%
n = 250±6.2%
n = 500±4.4%
n = 1,000±3.1%
n = 2,000±2.2%
n = 5,000±1.4%
n = 10,000±1.0%

95% CI, p̂ = 50%