Plus or minus three point one points. That is the margin of error a poll of a thousand people typically carries, printed at the bottom of nearly every election survey, and it is one of the most reported and most misread numbers in any report built on a poll. Margin of error explained simply comes down to one question: how far can a single sample drift from the truth, purely by the luck of who got asked.
Margin of error explained: what the number is actually promising
Somewhere out there sits a true value the poll is trying to measure, a share of an electorate, an opinion held by some fraction of a population, a number no single poll can ever observe directly. A pollster draws a random sample instead, asks the same question of everyone in it, and reports a share. That one sample almost never lands exactly on the true value. It lands somewhere close, and the margin of error describes, in advance, how close “close” tends to be.
Run the same poll a hundred times, each time with a thousand new randomly chosen people, and roughly ninety-five of those hundred samples will land within about three point one points of the true value. That is the confidence interval a ninety-five percent margin actually promises: not that any single reported number is correct, but that roughly ninety-five in a hundred such intervals, built the same way, would contain the truth. It is a statement about the reliability of the method across many repeats, not a guarantee attached to the one poll sitting in front of a reader.
Confidence interval, in plain terms
A confidence interval is simply the poll’s reported share with the margin added and subtracted on either side, paired with the confidence level, almost always ninety-five percent, used to calculate it. A poll reporting fifty-two percent with a margin of three point one points is reporting an interval running from roughly forty-nine to fifty-five, and the ninety-five percent confidence level describes how often intervals built this exact way would actually capture the true value, across an imagined series of repeated polls, rather than describing how likely this specific interval is to be right.
Sample size vs precision: why smaller polls need bigger margins
Sample size decides how wide the margin has to be, and the relationship is unforgiving. A poll of one thousand people carries a margin of about three point one points, calculated from the worst-case fifty-fifty split pollsters generally publish, since that split produces the widest possible margin for any given sample size. Cut the sample to four hundred people and the margin grows to about four point nine points. Cut it further, to a hundred people, and the margin nearly triples from the thousand-person figure, reaching about nine point eight points. Precision is expensive because the margin shrinks only with the square root of the sample size rather than the sample size itself: cutting a sample to a quarter of its size roughly doubles the margin, not quadruples it, but the cost still adds up fast at the smaller end.
That square-root relationship is worth sitting with for a moment, because it explains a pattern that otherwise looks strange: pollsters rarely survey more than about a thousand or fifteen hundred people, even for a national poll covering hundreds of millions. Doubling a sample from a thousand to two thousand only shrinks the margin from about three point one points to roughly two point two, a real but modest gain that usually is not worth the doubled cost of fielding the survey. Below a few hundred respondents, though, every additional person bought matters far more, which is exactly why a poll of a hundred people, the kind a local newsroom or a small campaign might actually be able to afford, carries a margin wide enough to make most close results essentially unreadable.
Margin of error explained for a lead, not just a single share
Where this number gets misapplied most often is inside a close race. A poll reporting fifty-one percent to forty-nine carries a margin of about three point one points on each candidate’s own share, and it is tempting to read a two-point lead as real given that margin. But the lead is the difference between two numbers, each with its own sampling error moving in opposite directions, so the margin on that gap runs roughly double the margin on either single share, about six point two points rather than three point one. Re-run a poll like that a hundred times on a race that genuinely sits at fifty-one to forty-nine, and the candidate shown trailing still leads or ties in close to a third of those hundred re-polls. A two-point lead inside a six-point margin is not really a lead in any meaningful sense, even though headlines built on it rarely say so.
What a margin of error cannot see
The margin only ever measures one kind of error: the luck of a random draw. It has nothing to say about who actually chose to answer. An opt-in online panel where one side’s supporters are even modestly more likely to participate can produce a result that clusters several points away from the truth in the same direction every single time, while the printed margin stays exactly the same, since that number was never built to account for who showed up to answer in the first place. That distinction matters enough that the American Association for Public Opinion Research maintains a formal statement on it: a genuine margin of sampling error applies to a real random probability sample, and an opt-in panel, not drawn that way, reports a model-based credibility interval instead, a related idea built on different assumptions rather than a stricter version of the same thing.
An interactive margin of error explainer walks through this entire progression step by step, from one sample to a hundred repeated samples to the effect of an opt-in panel, using a seeded simulation so the same numbers appear on every visit. Pew Research Center has its own accessible explanation covering much of the same ground, including the doubled margin on a lead between two candidates. None of it changes the underlying lesson: a margin of error is a real, useful, precisely calculated number, and it answers a much narrower question than most headlines built on top of it assume it does.
Reading a poll’s margin of error is really one instance of a broader habit covered in how to read a report: checking what a number can and cannot support before treating it as settled. A margin of error can tell a reader exactly how much random scatter to expect from a well-run random sample. It cannot tell a reader whether the sample was random to begin with, whether the question was worded fairly, or whether the people who declined to answer differ in some systematic way from the people who did. Those questions sit in the methodology section of whatever report the poll appears in, not in the plus-or-minus figure printed underneath it, and a reader who checks only the margin has checked the easiest part of the number, not the most important one.