Confidence Interval for a Proportion Calculator

This calculator works out a confidence interval for a proportion, the range within which the true population proportion is likely to lie, from a sample. Proportions are everywhere in research and everyday life: the share of voters backing a party, the percentage of customers who are satisfied, the fraction of items that pass a quality check. When you measure a proportion from a sample rather than the whole population, your result is only an estimate, and a confidence interval tells you how precise that estimate is. It is built from the sample proportion plus or minus a margin of error, and the margin depends on the sample size and the confidence level you choose. Larger samples give tighter intervals, and a higher confidence level, say 99 percent rather than 90, gives a wider one, because being more certain means casting a wider net. This tool does the standard calculation. You enter the number of successes, the people or items with the characteristic you are measuring, the total sample size, and the confidence level. The calculator returns the margin of error and the lower and upper bounds of the interval, along with the sample proportion itself. The results update as you type, so you can see how a bigger sample shrinks the margin. Use it to report survey results properly, to judge whether a difference is meaningful, or to plan a sample size. It uses the normal approximation, which is reliable when the sample is reasonably large and the proportion is not too close to zero or one. The familiar margin of error quoted in opinion polls is exactly this calculation at the 95 percent level.

Uses the normal approximation: margin = z x sqrt(p(1-p)/n). Reliable for reasonably large samples. The 95% level is the usual poll margin of error.