Margin of Error Calculator

In short The margin of error for a survey percentage is a critical value times the standard error of a proportion: z × √(p(1−p)/n). At the figure every newspaper uses — 1,000 people, a 50/50 split, 95% confidence — it comes to ±3.10 percentage points. Four hundred people gives ±4.90, and two thousand gives ±2.19, which shows the shape of the trade: the margin falls with the square root of the sample, so buying half the margin costs four times the sample. Two things about that number are widely misread. It is largest at 50%, because p(1−p) peaks there, so a poll quoted as "±3 points" is usually quoting the worst case rather than the margin on the specific figure reported. And the margin on the GAP between two candidates is bigger than the margin on either share, so two results that look separated by more than the quoted margin can still be indistinguishable. The more important limitation is not arithmetic at all. This number measures one thing: how much the answer would bounce if you drew another random sample the same way. It does not include people who refuse to answer, a sampling frame that misses part of the population, question wording, or turnout modelling — and in real polling those are usually the larger errors. A margin of error is a lower bound on how wrong a survey can be, never an upper one.