Margin of Error Calculator
The margin of error for a mean at a chosen confidence level.
Result
Margin of error
2.9400
How it works
The margin of error is the "±" attached to every serious survey result: margin = z · (σ ÷ √n), where z encodes the confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), σ is the spread of the data and n the sample size. "52% ± 3" means the true value plausibly sits between 49 and 55. The √n in the denominator is the law that rules polling economics: to cut the margin in half you must quadruple the sample. That is why national polls settle around 1,000 respondents — enough for roughly ±3% at 95% confidence, and each extra point of precision gets increasingly expensive. Remember what it covers: sampling randomness only. Biased questions, unrepresentative samples or dishonest answers are not inside the ±, which is why two methodologically different polls can disagree by more than their combined margins.
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Frequently asked questions
What shrinks the margin of error?
A bigger sample size, a smaller standard deviation, or a lower confidence level.
Is a smaller margin always better?
It means more precision, but it usually requires a larger, costlier sample.
Why does quadrupling the sample only halve the margin of error?
Because the margin shrinks with the square root of n. Multiplying n by 4 multiplies √n by 2, so the margin divides by 2 — precision grows much slower than sample size.
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