Margin of Error Calculator
Enter a survey's sample size, confidence level and (optionally) the response proportion to get the ± margin of error.
Quick answer: For a proportion, margin of error = z·√(p(1−p) ÷ n). A poll of n = 1,000 at 95% (z = 1.96) with p = 0.5 has MoE = 1.96 × √(0.25 ÷ 1000) = ±3.1%.
The margin of error tells you how far a survey's reported percentage might sit from the true value in the whole population, at a given confidence level. It's why polls quote a result "± a few points." It depends on the sample size, the confidence level and how split the responses are.
The formula
Margin of error = z · √( p(1 − p) ÷ n )
z: 90% = 1.645 · 95% = 1.96 · 99% = 2.576
z: 90% = 1.645 · 95% = 1.96 · 99% = 2.576
Worked example
A survey of 600 people at 95% confidence with p = 0.5: MoE = 1.96 × √(0.25 ÷ 600) = 1.96 × 0.0204 = 0.04 = ±4.0%.
Frequently asked questions
How do I calculate margin of error?
Multiply the z-value for your confidence level by the square root of p(1 − p)/n.
Why use p = 0.5?
p(1 − p) is largest at p = 0.5, so it gives the widest, most conservative margin when you don't know the true split.
How can I reduce the margin of error?
Increase the sample size. Because n is under a square root, cutting the margin in half needs about four times the sample.
Does population size matter?
For large populations, no. A finite-population correction only matters when the sample is a big fraction of the whole.
Related calculators
For general and educational use. Proportion (survey) margin of error.