This margin of error calculator converts a survey percentage, confidence level, and sample size into a ± error band.
Statistics
Margin of Error Calculator
Compute the margin of error for a proportion estimate.
Calculator
About this calculator
Formula notes
MOE = z·√(p(1−p)/n). Worst case uses p = 0.5, which maximizes p(1−p).
Worked examples
- Example: 95% confidence (z = 1.96), p = 0.5, n = 100 gives MOE = 1.96·√0.0025 ≈ 9.8 points, i.e. 40.2% to 59.8% around 50%.
- For a 50% estimated proportion and n = 1,000, the approximate 95% margin of error is about 3.1 percentage points before finite-population correction.
How to use it
- Enter the observed percentage (or 50% for worst case).
- Enter the sample size and confidence level.
- Read the plus-or-minus margin and interval bounds.
Frequently asked questions
Why use p = 0.5 for planning?
p(1−p) peaks at 0.5, so it gives the most conservative (largest) margin.
Does population size matter?
Only for small populations; then a finite-population correction shrinks the margin.
Limits and interpretation
- The formula describes random sampling error under its assumptions and does not include nonresponse, coverage, wording, weighting, or measurement bias.
- Small samples or proportions near 0 or 1 may make the normal approximation inappropriate.