Margin of Error Calculator
Find the margin of error of a survey proportion.
Results update as you type.
About this calculator
The margin of error tells you how far a survey result is likely to be from the true population value. For a proportion it is z*·√(p(1 − p) / n), where p is the sample proportion, n the sample size and z* the critical value for your confidence level. The default 50% proportion gives the most conservative (largest) margin, which is why pollsters often quote it.
Frequently asked questions
Why does a bigger sample lower the margin of error?
The margin shrinks with the square root of the sample size, so quadrupling n halves the margin of error. This diminishing return is why very large samples are needed to push the margin below one or two percentage points.
Why is 50% the default proportion?
The quantity p(1 − p) is largest at p = 0.5, so assuming a 50/50 split produces the widest, most conservative margin of error. Using it guarantees the true margin is no larger than reported.
Results are estimates for general guidance only, not financial, medical or tax advice.