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Margin of Error Calculator

How much a survey result could swing, in either direction, from sampling alone.

Survey details

Margin

Margin of error -
Confidence interval -
Z-value -

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Quick answer

Margin of error is the plus-or-minus figure attached to a survey result: "52%, margin of error 3 points" means the true figure in the full population is probably somewhere between 49% and 55%. It comes from the formula z times the square root of p times one minus p, divided by n. Bigger samples shrink it because n sits under a square root; the confidence level you pick sets how cautious the z multiplier is.

What a bigger sample actually buys you

The relationship is not a straight line. Doubling your sample does not halve your margin of error; you need to quadruple it. Here is the margin at p = 50% and 95% confidence across a few common survey sizes, from this calculator's own formula:

Sample size (n)Margin of error at 95%
100±9.80%
400±4.90%
1,000±3.10%
2,000±2.19%
4,000±1.55%

The 1,000-respondent row is close to why so many national polls settle on roughly that size: it lands the margin near ±3 points, a rough industry standard, without the cost of chasing a much bigger sample for a small further gain. See the sample size calculator to work this table backward from a target margin.

Good to know

FAQs

Is margin of error the same thing as the confidence interval?

No, margin of error is half the width of the interval. Add and subtract it from your sample proportion and you get the confidence interval; this page reports both so you don't have to do that step by hand.

Why do pollsters always seem to quote the margin at 50%?

Because p times one minus p is largest when p equals 50%, which makes the margin of error largest too. Quoting the 50% figure is the conservative, worst-case number, valid no matter which way the actual result leans.

My margin of error came out huge. What's wrong?

Usually a small sample size. Margin of error shrinks with the square root of n, so quadrupling your sample only halves the margin; this calculator does not apply a finite-population correction, so it will overstate the margin slightly for a small, fully-surveyed population.

Does this account for people who didn't respond to the survey?

No. This figure only reflects random sampling error, the noise you would expect from a truly random sample of that size. It has nothing to say about nonresponse bias, wording effects, or a sample that was not actually random, all of which can matter more than the number itself.