Math

Free Confidence Interval Calculator

Confidence interval for a sample mean.

  • Free Forever
  • No Registration Required
  • Instant Results
  • Downloadable Reports
  • Mobile Friendly

Inputs

Result

95% confidence interval

95.351 to 104.649

Margin of error4.6485
Standard error2.3717

Your result is ready.

Download your free detailed report — inputs, result, formula and explanation included.

Estimates only. Verify with a professional for consequential decisions.

  • Always Free
  • No Hidden Costs
  • No Account Required
  • Unlimited Calculations
  • Instant Reports

Short answer

Confidence interval for a sample mean.

What is the Confidence Interval Calculator?

Confidence interval for a sample mean.

How does the Confidence Interval Calculator work?

Enter the inputs above and read the result.

Formula

CI = mean ± z × (s ÷ √n)

Variables

  • zCritical value for confidence level
  • sSample standard deviation

Explanation

The interval is expected to contain the true population mean with the stated confidence, assuming a roughly normal sampling distribution.

Examples

Applications

    Advantages

      Limitations

        Common mistakes

          Tips

            Related concepts

            The Confidence Interval Calculator sits inside the Math Calculators hub, in the statistics & probability cluster. Describing data and quantifying uncertainty. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.

            distributiondispersionsignificancesamplepopulationexpected value

            Practical use cases and industry applications

            Understanding Confidence Interval

            Confidence interval for a sample mean. Within math calculators, confidence interval belongs to the statistics & probability cluster, where it shares terminology and assumptions with closely related tools.

            Learning how confidence interval is calculated

            The interval is expected to contain the true population mean with the stated confidence, assuming a roughly normal sampling distribution. Working through the variables one at a time — z, s — makes the result reproducible by hand and easier to sanity-check.

            Using confidence interval to make a decision

            Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.

            How confidence interval compares with related measures

            distribution, dispersion, significance, sample all describe adjacent aspects of statistics & probability. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.

            Frequently asked questions

            Related calculators

            More statistics & probability tools

            We value your privacy

            We use cookies to run the site, remember your preferences, and — with your permission — show relevant ads and measure traffic. See our Cookie Policy.