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Confidence Interval Calculator

Compute interval estimates with estimate, standard error, critical value, margin, and bounds.

Input

Configure inputs first. Final results, visuals, downloads, and copy summary remain hidden until Calculate Interval succeeds.

Interval methodConfidence level

Values

What This Tool Does

The Confidence Interval Calculator reports interval bounds only after Calculate Interval is clicked and explains that a confidence interval does not prove a hypothesis.

Method

Mean intervals use z or t critical values. Wilson intervals use the score interval form for a binomial proportion.

Worked Example

For values 1, 2, 3, 4, 5, a t interval centers on the sample mean and uses df = 4.

Common Mistakes

Saying a specific interval has a 95% probability of containing the true mean.
Using z when sigma is not known.

Limitations

Coverage depends on method assumptions.
Bootstrap intervals are out of scope.

References

NIST e-Handbook: Confidence Limits for the Mean: NIST/SEMATECH e-Handbook of Statistical Methods, confidence limits and one-sample t-test for the mean.

What does a 95% confidence interval mean?

Over repeated samples, the interval procedure would contain the true parameter about 95% of the time under its assumptions.

What is a Wilson interval?

It is a score-based binomial proportion interval that behaves better than the simple Wald interval in many small-sample cases.

Does an interval prove a hypothesis?

No. It estimates a range of plausible parameter values under the method assumptions.

Why does sample size change width?

Standard error decreases as sample size increases, narrowing many intervals.

Does the Confidence Interval Calculator calculate automatically while I type?

No. Inputs and CSV previews never produce final statistics until the explicit calculate button is clicked.

Are CSV files uploaded?

No. Selected CSV files are processed locally in the browser. ScholarTool does not upload the file to a third-party calculation or data-analysis API.

Can a p-value prove a hypothesis?

No. A p-value is evaluated against the selected alpha level under stated assumptions; it does not prove the null or alternative hypothesis.

Engineering disclaimer

This statistics tool is intended for education, planning, and preliminary analysis. Review assumptions, study design, and professional statistical judgement before using results in research, engineering, safety, regulatory, or compliance decisions. ScholarTool does not prove hypotheses or replace qualified analysis.

Need Professional Support?

ScholarTool is powered by ScholarEase Consultancy Services LLP. Professional engineering, simulation, research, and technical documentation support is available through the connected services website.

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Last reviewed: 2026-07-07

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Engineering disclaimer

Confidence Interval Calculator

Input

What This Tool Does

Method

Worked Example

Common Mistakes

Limitations

References

Related Tools

Engineering disclaimer

Need Professional Support?

Confidence Interval Calculator

Input

What This Tool Does

Method

Worked Example

Common Mistakes

Limitations

References

Related Tools

Engineering disclaimer

Need Professional Support?