confidence interval calculator: method, formulas and interpretation

The confidence interval calculator uses a dedicated calculation path for this exact problem rather than a generic input-and-output shell. Inputs are normalized before the formula is applied, and the result panel exposes the assumptions needed to audit the answer.

Mean and proportion methods

The confidence interval calculator uses the selected normal critical value for a mean when a standard deviation is supplied. Proportion mode uses Wilson score bounds, which stay within zero and one and behave better than the simple p ± z√(p(1−p)/n) expression near extreme proportions or modest sample sizes.

Sampling assumptions and finite populations

The confidence interval calculator assumes observations are collected through an appropriate independent sampling process. The optional finite-population correction reduces standard error only when sampling without replacement from a known finite population and the sample is a meaningful fraction of it. Design effects, clustering, weighting and nonresponse require methods beyond this calculator.

Worked use and validation

The confidence interval calculator rejects missing, non-finite or physically impossible values with a specific message. Load the worked example to inspect the complete calculation and compare it with a manual result before relying on a planning estimate.

How to read the output

The confidence interval calculator separates the primary result from supporting quantities, unit conversions and limitations. Display rounding does not replace the unrounded values used inside later steps. Use consistent inputs and preserve the stated model when comparing scenarios.