How does the Margin of Error work?

MOE = z × √(p(1-p)/n) Then: z = 1.96 for 95% confidence Then: p = observed proportion · n = sample size Then: MOE is the ± value reported alongside poll results.

Can you give an example of how to use the Margin of Error?

Example: Input n=1,000 · p=0.5 · 95% confidence gives a result of MOE = ±3.1% (1.96×√(0.25/1000)=0.031).

Is the Margin of Error free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Margin of Error?

Our Margin of Error uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Margin of Error

📊Margin of Error Calculator

Sample size n

Proportion % (p)

Confidence

The margin of error (MOE) quantifies the uncertainty in a survey result. A poll showing 60% support with ±4% MOE means the true population value likely falls between 56–64% at the stated confidence level. MOE shrinks as sample size grows.

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Pro Tip

To halve the margin of error, you need to quadruple the sample size — precision is expensive. Doubling n only reduces MOE by about 30%.

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Did You Know?

The margin of error in news reports almost always assumes a perfectly random sample — but most online polls use convenience samples, making the stated MOE statistically meaningless.

References

›Margin of error — Wikipedia

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