Confidence Interval Calculator

When you measure a sample instead of an entire population, the number you get is only an estimate. A confidence interval wraps that estimate in a range of plausible values for the true population parameter, such as a mean or a proportion. Reporting the interval rather than a single point tells your audience how precise the estimate actually is and how much sampling variation it carries.

The math behind the interval follows a simple structure: take your estimate and add and subtract a margin of error, written as Estimate ± (Critical Value × Standard Error). The estimate is the figure straight from your sample, such as the sample mean. The critical value is pulled from a t-distribution or z-distribution table according to the confidence level you choose. The standard error measures how much the sample estimate would bounce around from one sample to the next.

The confidence level is the part people most often read wrong. A 95% confidence interval does not say there is a 95% chance the true value sits inside your particular interval. It says that if you drew sample after sample and built an interval each time, 95% of those intervals would capture the true population parameter. The interpretation only holds when the sample is drawn randomly and represents the population, so a biased sampling method quietly breaks the whole result.