Margin of Error Calculator
Calculate the margin of error for a survey or poll given sample size, population proportion, and confidence level.
Results
What is it?
The margin of error (MOE) quantifies the uncertainty in a survey or poll result. It tells you how much the measured proportion could differ from the true population proportion at a given confidence level. For example, a poll showing 52% ± 3% means the true value is likely between 49% and 55% with the chosen confidence.
How to use
Enter your sample size, set the estimated proportion using the slider (use 50% if unknown — it produces the most conservative, widest margin), and select a confidence level. The MOE and confidence interval bounds are displayed instantly.
Example scenario
A national poll of 1,000 people asks about candidate preference. Using p=50%, z=1.96 (95% confidence): MOE = 1.96 × √(0.5 × 0.5 / 1000) = 1.96 × 0.01581 ≈ 3.1%. So if 52% support candidate A, the 95% CI is 48.9% to 55.1%.
Pro tip
To halve the margin of error, you need to quadruple the sample size — it grows with √n. At 50% proportion the MOE is maximised (worst case). Using a known proportion closer to 0% or 100% yields a tighter margin. Most national polls use n ≈ 1,000, giving MOE ≈ ±3% at 95% confidence.