Margin of Error Calculator
Calculate the margin of error for a survey sample.
Assumptions used in this calculation
- Simple random sampling: Assumes the sample was drawn via simple random sampling from a large population; it does not account for design effects from stratified or clustered sampling.
About this calculator
Every survey result comes with some uncertainty, and reporting a number like "52% support" without its margin of error hides how much that figure could shift if you polled a different sample, information that's easy to skip because computing it means working through a square root and a critical z-value by hand. This calculator takes a confidence level, sample size, and sample proportion, then computes the margin of error as MOE = z × √(p(1 − p) ÷ n). Because the formula divides by √n, quadrupling the sample size only halves the margin of error, which is why large surveys need proportionally huge samples for small further precision gains. It also depends on the proportion itself through the p(1−p) term, which peaks at p = 50% and shrinks as the result moves toward 0% or 100%, so a landslide result naturally comes with a tighter margin than a close one for the same sample size. It assumes simple random sampling and doesn't account for design effects from stratified or clustered survey methods.
Worked example
95% confidence, n=1000, p=50%
Result: ±3.1%
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