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Calculation Machine

Margin of Error Calculator

The ± figure behind any poll or survey result.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Margin of error
± 3.1 percentage points
Confidence interval
48.9% to 55.1%
Is a 50% result inside the interval?
Yes — result is a statistical tie

Quick answer

Margin of error is z × √(p(1−p)/n) — the range within which the true population value likely falls.

The formula

MOE = z·√(p(1−p) ÷ n)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Sample size1000
  • Observed percentage52 %
  • Confidence level95%

Result

  • Margin of error± 3.1 percentage points
  • Confidence interval48.9% to 55.1%
  • Is a 50% result inside the interval?Yes — result is a statistical tie

How to use the Margin of Error Calculator

  1. 1Enter your sample size.
  2. 2Enter the percentage you observed.
  3. 3Pick the confidence level.

Frequently asked questions

Why do polls say ±3?

That is the margin at 95% confidence for a sample of about 1,067 — the industry's standard cost-accuracy compromise.

Does margin of error cover bias?

No. It only measures sampling randomness. Non-response and bad question wording add error it cannot detect.

About this calculator