Margin of Error Calculator
Enter your sample size, the response proportion and a confidence level to find the margin of error for a survey or poll. Add a population size for the finite-population correction.
How to calculate the margin of error
- Enter the number of respondents in your sample.
- Set the response proportion (use 0.5 for the most conservative estimate).
- Pick a confidence level and read off the margin of error.
Examples
A typical national poll
n = 1000, p = 0.5, 95% confidence
Margin of error = +/- 3.1%
Frequently asked questions
What is the margin of error?
It is the half-width of the confidence interval around a survey result. A result of 50% with a 3% margin means the true value likely lies between 47% and 53%.
Why is 0.5 the default proportion?
The product p times (1 minus p) is largest at 0.5, so using 0.5 gives the widest, most conservative margin when the true proportion is unknown.
How does the confidence level change the margin?
Higher confidence needs a larger z-value, so the margin grows. 99% confidence gives a wider margin than 95%, and 95% is wider than 90%.
When should I use the population correction?
Use it when your sample is a large share of a small, finite population. The finite-population correction shrinks the margin in that case.
Does a bigger sample always help?
Yes, but with diminishing returns. The margin falls with the square root of the sample size, so cutting it in half needs about four times the respondents.
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