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Margin of Error Calculator
Find the margin of error of a survey percentage. Enter the sample size, the percentage observed and the confidence level to get the “plus or minus” figure and the resulting interval, with an optional correction for a small population.
- Interval lower bound
- 46.9%
- Interval upper bound
- 53.1%
- Standard error
- 1.5811%
- Critical value (z*)
- 1.96
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Your recent calculations
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Formula
How to use it
- Enter the number of people who responded.
- Enter the percentage you observed, or leave it at 50% for the largest (most cautious) margin.
- Choose the confidence level.
- Enter the population size only if the sample is a noticeable share of it.
Worked examples
A poll of 1,000 people at 95% confidence
- Margin of error (±)
- 3.1%
- Interval lower bound
- 46.9%
- Interval upper bound
- 53.1%
- Critical value (z*)
- 1.96
A poll of 400 people at 95% confidence
- Margin of error (±)
- 4.9%
Surveying 250 of a 1,500-person workforce
- Margin of error (±)
- 5.66%
Reference values
At 95% confidence and a 50% result: a sample of 100 has a margin of ±9.8 points, 400 has ±4.9, 600 has ±4.0, 1,000 has ±3.1, 1,500 has ±2.5 and 2,400 has ±2.0. To halve the margin of error you need four times as many responses.
What it does and does not cover
The margin of error only measures random sampling variation. It says nothing about question wording, people who did not respond, or a sample that does not represent the population.
It applies to the full sample. A subgroup — respondents under 30, say — is a smaller sample with a larger margin. And the margin on the gap between two results from the same poll is larger than the margin on either one alone.
Questions people ask
What is the margin of error for a poll of 1,000 people?
About ±3.1 percentage points at 95% confidence, from 1.96 × √(0.25 ÷ 1000).
What is the margin of error for a sample of 400?
About ±4.9 percentage points at 95% confidence.
How do I cut the margin of error in half?
Quadruple the sample size. Going from ±4.9 to roughly ±2.5 takes about 1,600 responses instead of 400.