Confidence Interval Calculator

A 95% confidence interval implies that the true parameter lies within the bounds...

Any average or percentage you measure from a sample is almost never the exact truth, so this tool reports a range instead of one number. The margin of error is the "give or take" attached to your estimate. Here is the honest trade-off: from the very same data, a 99% interval is wider than a 90% one. More confidence buys less precision, so pick the level your decision actually needs.

For a proportion the standard error is √(p(1−p)/n), and p(1−p) peaks at exactly p = 0.5 (value 0.25). Pollsters exploit this by assuming a 50/50 split as the worst case, which makes the 95% margin roughly 0.98/√n. Plug in n = 1000 and you get about ±3.1% — the classic poll figure. That is also why national polls rarely grow past ~1000 people: reaching ±1.5% would need four times the sample.