Survey margin of error

Enter an unweighted sample size and an estimated survey share. The fixed 95% two-sided Wilson score interval is approximate and has no continuity or finite-population correction. Fractional n×share is allowed as a continuous approximation for a reported or planning percentage; it is not a claim of an exact observed integer success count. For raw counts, use the binomial confidence-interval tool.

The main results are separate lower and upper distances from the entered share, in percentage points (pp). They are generally asymmetric. The optional half-width is symmetric around the adjusted Wilson center, not necessarily around the entered share. For n=100 and share=0%, the interval is about 0–3.70%: downward distance 0pp, upward 3.70pp, center and half-width about 1.85. Do not report 0%±1.85pp from that half-width.

Independent observations with a common probability are assumed. Nonresponse, selection bias, clustering, survey weights or design effects are not covered, and a confidence interval does not establish representativeness. Confidence describes repeated-sampling coverage, not a probability that a fixed true proportion lies in this particular interval. Small positive values use scientific notation and near-100% bounds use their complement. Results update directly as you type or press Enter. Raw input drafts, including unfinished values, remain in local browser storage through navigation and reload. Only inputs are stored; the interval is recomputed. ≈0% marks a positive lower bound below floating-point range, while ≈100% marks a rounded upper bound below true certainty. The point marks the entered share. The line shows the Wilson interval on a labeled scale that adjusts to the interval width.