Confidence Interval Calculator

About this tool

A survey reports a mean of 72.5. That single number says nothing about precision until it comes with a range such as 69.4 to 75.6. A larger sample or tighter data narrows the interval.

Mean 72.5, standard deviation 12.8, 64 observations and 95% confidence give a standard error of 1.6, a margin near 3.14 and an interval of 69.36 to 75.64. The comparison table shows that moving to 99% raises z from 1.960 to 2.576 and widens the interval to roughly 68.38 to 76.62.

What it does

• ComparisonFour confidence levels compared Every number shown here maps to a field on the form, so changing one value recomputes the rest. The units are printed next to each input, which saves most of the usual mistakes.
• PrecisionStandard error scales with sample size The main figures sit at the top of the result panel and the breakdown sits below it, so you can read the conclusion first and audit the steps afterwards. Nothing you type leaves the browser.
• BoundsBoth bounds at once All arithmetic runs locally in the page. There is no request to a server, no account, and no saved history once the tab is closed. Use the example button if you want a set of values that is known to work.
• Critical valueBuilt-in z critical values Intermediate quantities are kept in the detail table. When a total looks wrong, tracing back through those rows is much quicker than staring at the headline number alone.
• AssumptionsStates when the approximation holds The formula is written out in the notes rather than hidden behind a label, so you can check it against a spreadsheet or a textbook. Values are rounded only for display.
• BreakdownAll four levels tabulated Inputs are validated before any calculation starts. Empty or impossible values produce a short explanation instead of a zero, a NaN, or a made-up answer.

How to use it

1. Start by filling inenter the sample mean The main figures sit at the top of the result panel and the breakdown sits below it, so you can read the conclusion first and audit the steps afterwards. Nothing you type leaves the browser.
2. Next, setenter the sample standard deviation All arithmetic runs locally in the page. There is no request to a server, no account, and no saved history once the tab is closed. Use the example button if you want a set of values that is known to work.
3. Then pressenter the sample size Intermediate quantities are kept in the detail table. When a total looks wrong, tracing back through those rows is much quicker than staring at the headline number alone.
4. Read thechoose a confidence level The formula is written out in the notes rather than hidden behind a label, so you can check it against a spreadsheet or a textbook. Values are rounded only for display.
5. Finally, usepress Calculate and read the comparison Inputs are validated before any calculation starts. Empty or impossible values produce a short explanation instead of a zero, a NaN, or a made-up answer.

Things to keep in mind

• Negativestandard deviation cannot be negative All arithmetic runs locally in the page. There is no request to a server, no account, and no saved history once the tab is closed. Use the example button if you want a set of values that is known to work.
• Sample sizesample size must be at least 2 Intermediate quantities are kept in the detail table. When a total looks wrong, tracing back through those rows is much quicker than staring at the headline number alone.
• Small nsmall samples need a t distribution The formula is written out in the notes rather than hidden behind a label, so you can check it against a spreadsheet or a textbook. Values are rounded only for display.
• Interpretationwidth is not the size of a mistake Inputs are validated before any calculation starts. Empty or impossible values produce a short explanation instead of a zero, a NaN, or a made-up answer.
• Biasonly sampling error is covered Every number shown here maps to a field on the form, so changing one value recomputes the rest. The units are printed next to each input, which saves most of the usual mistakes.