Margin of Error Calculator

What the margin of error means

When a poll reports "48% support, ±3% margin of error at 95% confidence", it means the 95% confidence interval is 45%–51%. The true population proportion is estimated to fall in this range 95% of the time under repeated sampling.

The margin of error does not capture non-sampling errors — biased questions, self-selection, non-response, or measurement errors. A technically correct margin of error on a flawed survey is still misleading. The MOE only quantifies random sampling uncertainty.

What affects the margin of error

Three inputs drive the margin of error: sample size (n), confidence level (z), and the expected proportion (p). Larger samples produce smaller margins of error — MOE shrinks by 1/√n, so quadrupling sample size halves the MOE. Higher confidence levels (e.g. 99% vs. 95%) produce larger MOEs because the interval must be wider to be more confident.

The proportion p = 50% produces the maximum margin of error for any given sample size and confidence level. Using 50% is conservative and common when the true proportion is unknown. If you know the proportion will be near 20%, the MOE will be smaller.

Margin of error vs. sample size

For n=100, p=50%, 95% confidence: MOE ≈ ±9.8%. For n=1,000: MOE ≈ ±3.1%. For n=10,000: MOE ≈ ±1.0%. National polls with n=1,000 are sufficient for ±3% precision, which is why major news polls typically use samples in the 800–1,500 range.