The most misunderstood idea in statistics, finally made intuitive. Draw fifty samples, build fifty intervals, and watch about 95% of them capture the true mean.
Confidence IntervalsLive
what 95% really means
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A confidence interval is often misread. It does not mean the true value has a 95% chance of being in one interval — it means that if you repeated the experiment many times, about 95% of the intervals would contain the true mean. The red intervals here are the unlucky ones that miss it.
Reading this result: About 0% of these 50 intervals captured the true mean — close to the 95% you asked for. Raising n from 30 tightens each interval (SE = σ/√n) but does not change that hit rate: the confidence level, not the sample size, sets how often you are right.
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How it works
A confidence interval does not say the true value has a 95% chance of lying in one particular interval. It says the procedure produces intervals that, over many repetitions, contain the true parameter about 95% of the time. The red intervals here are the unlucky ones that miss — exactly the fraction the confidence level predicts.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this confidence interval simulator tool really free?▾
Yes. Confidence Intervals runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
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Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.