Construct confidence intervals for means and proportions. Visualize how sample size and confidence level affect interval width.
Confidence Interval Builder turns a sample mean or observed proportion into an interval at a chosen confidence level, then shows how sample size and confidence level affect interval width. Mean intervals also depend on the sample's spread, while proportion intervals depend on the observed fraction and sample count. The common surprise is interpretive: a 95% confidence interval does not assign a 95% probability to the parameter being inside this particular interval. The percentage describes the long-run coverage of the interval procedure under its assumptions.
For a mean, the interval is centered on the sample mean. Its half-width, called the margin of error, combines a confidence multiplier with the standard error determined by sample spread and sample size. The lower and upper limits subtract and add that margin. With spread and confidence fixed, increasing the sample size reduces the standard error and narrows the interval.
For a proportion, the calculation uses the observed fraction and the number of observations to obtain two confidence limits. The visualization lets you examine how those limits move as sample size or confidence changes. Established proportion-interval methods can produce different limits, especially with small samples or proportions near zero or one, so the selected method matters when interpreting the endpoints.
Higher confidence requires an interval procedure that captures the population parameter more often across repeated samples. With the estimate, sample size, and variability unchanged, that requires extending the limits farther from the estimate. A 99% interval is therefore wider than a 95% interval calculated from the same sample using the same method.
Not reliably. Visual overlap is only a rough diagnostic and does not directly calculate uncertainty in the difference between groups. A valid comparison depends on whether observations are independent or paired, the variability within each group, and the appropriate model. Use a confidence interval or hypothesis test designed for the difference itself.
The behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate percentages, percentage change, and what percent one number is of another with step-by-step breakdowns.
Calculate tips and split bills between multiple people with customizable tip percentages and rounding options.
Calculate monthly payments, total interest, and generate amortization schedules for loans and mortgages.
Calculate Body Mass Index from height and weight with category classification and healthy range guidance.
Calculate sale prices, savings amounts, and final costs after single or stacked percentage discounts.
Compute mean, median, mode, standard deviation, variance, and other descriptive statistics from a data set.