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Margin of Error Calculator

Find the margin of error for a survey result.

How it is calculated

For a survey percentage the tool uses MOE = z × √(p × (1 − p) / n). p is the observed share (entered as a percentage and divided by 100), n is the sample size and z depends on the confidence level: 1.282 for 80%, 1.440 for 85%, 1.645 for 90%, 1.960 for 95% and 2.576 for 99%. Any other confidence value falls back to 95%. The result is the margin in percentage points, plus the range from p − MOE to p + MOE. It assumes a simple random sample from a large population, and it covers sampling error only, not biased questions or non-response.

Worked example

A poll of 1,000 people finds 50% in favour, at 95% confidence (z = 1.96). Variance: 0.5 × 0.5 = 0.25. Divide by n: 0.25 / 1000 = 0.00025, whose root is 0.015811. Multiply by z: 1.96 × 0.015811 ≈ 0.0310. The margin of error is 3.10%, so the true share is likely between 46.90% and 53.10%.

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Common mistakes

  • Reading the margin as relative. A margin of 3.10% around 50% means ±3.10 percentage points, not 3.10% of 50.
  • Entering 0.5 for 50%. The proportion field is a percentage.
  • Applying the full-sample margin to a subgroup. Results for a small subgroup, such as one age band, have a much larger margin because n is smaller.
  • Believing the margin covers all error. Wording, who agrees to answer and how the sample was chosen also affect accuracy.

About this calculator

The margin of error (MOE) measures how much a survey's reported percentage could differ from the true value in the full population, given the size of the sample and how confident you want to be in the estimate. For a proportion, it's calculated as MOE = z × √(p(1−p)/n), where z is the critical value from the standard normal distribution for the chosen confidence level (1.96 for 95%, 2.576 for 99%), p is the sample proportion, and n is the sample size.

Pollsters, market researchers, and social scientists report the margin of error alongside every survey result — "62% support the policy, ±3 percentage points" — so readers know the range the true population value likely falls in. Larger samples shrink the margin of error, which is why national polls often use n≈1,000 to get a MOE near 3%, while smaller focus-group surveys carry much wider uncertainty.

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