How to use Confidence Interval Calculator

Choose a mean or proportion method.
Enter the sample summary and confidence level.
Review the bounds, critical value and assumptions.

Example: Confidence Interval Calculator

Confidence Interval Calculator: 95% interval: 9.17444057535 to 10.8255594247.

You add

Interval method: t Confidence level (%): 95 Sample mean: 10 Standard deviation: 2 Sample size n: 25 Success count: 12

You get

95% interval: 9.17444057535 to 10.8255594247. Method: Mean, Student t with sample SD Confidence level: 95% Sample size: 25 Sample estimate: 10 Critical value: 2.06389856163 Degrees of freedom: 24 Interval center: 10 Half-width: 0.825559424651 Lower limit: 9.17444057535 Upper limit: 10.8255594247 The confidence level describes long-run coverage when repeating this sampling method. It is not a probability that this particular fixed parameter lies in this computed interval. Mean intervals assume independent observations and a normal population or a suitable sample size; unknown-SD t uses n−1 degrees of freedom. Wilson uses independent binary trials. No weighting, clustering or finite-popul Method | Mean, Student t with sample SD Confidence level | 95% Sample size | 25

Options

Deviation source: Use Student t when the mean calculation uses a sample standard deviation. Select z only for a known population deviation under that method’s assumptions.
Wilson proportion: Use the observed success count and total sample count. They describe the entered sample rather than a forecast of future outcomes.

Supported inputs and limits

Specified mean and Wilson proportion methods only. Mean summaries need appropriate sampling and distribution assumptions; an estimated deviation uses a t critical value. Confidence describes the long-run method, not the probability that one fixed interval contains the parameter.

Where your input is processed

This tool processes your input in this browser. Your text and files are not uploaded to UseFreeTools. Check this tool's limits for anything it may save on your device.

Confidence belongs to the repeated-sampling method

A 95% procedure is intended to cover the fixed parameter in about 95% of repeated samples under its assumptions. It does not assign a 95% probability to the parameter being inside this already computed interval. Nonrepresentative sampling and measurement bias are not repaired by a narrow interval.

Questions about Confidence Interval Calculator

When should I use the t method?

Use the estimated-deviation method when the population deviation is unknown and your sample provides its estimate, subject to the stated assumptions.

Does 95% confidence assign a probability to these fixed bounds?

No. It describes how the interval method performs over repeated suitable samples.

Why use Wilson bounds for proportions?

They remain within zero and one and account for the sample size, including all-success or no-success samples.

Project manager: Tony Hines · Content updated 4 October 2026 · Report a problem

Confidence Interval Calculator

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