Margin of Error Calculator
Find the margin of error for a survey or poll from its sample size, confidence level, and observed proportion — with an optional finite population correction and the formula worked through with your numbers.
Enter a sample size of at least 2 and a proportion between 0 and 100. If you give a population size, it must be larger than the sample.
Frequently Asked Questions
- What is the margin of error?
- The margin of error is the range around a survey result within which the true population value is likely to fall, at your chosen confidence level. A poll reporting 52% support with a ±3% margin of error means the true figure is likely between 49% and 55%.
- How is the margin of error calculated?
- The calculator uses MOE = z × √(p(1−p)/n), where z is the z-score for your confidence level, p is the observed proportion, and n is the sample size. If you enter a population size, the result is multiplied by the finite population correction √((N−n)/(N−1)).
- How can I reduce my margin of error?
- Increase your sample size — but note the relationship is a square root, so halving the margin of error requires roughly four times the respondents. Lowering the confidence level also shrinks the margin, at the cost of being less certain the interval contains the true value.
- Why is 50% used as the default proportion?
- The term p(1−p) peaks at p = 0.5, so a 50% proportion gives the largest, most conservative margin of error. If you already know the observed proportion from your survey, enter it to get a tighter, more accurate margin.
- What is the finite population correction?
- When your sample is a substantial fraction of a small population, the standard formula overstates the error. The finite population correction √((N−n)/(N−1)) shrinks the margin to account for this. It matters little when the population is large relative to the sample.