Statistics Calculator

Confidence Interval Calculator

Estimate a two-sided confidence interval for a population mean using a sample mean, sample standard deviation, sample size, and Student’s t distribution.

Free to useRuns in your browserClear formula & method

Enter your data

Confidence Interval inputs

Use the fields below. Results update only when you select the calculate button.

Advertisement

What is a confidence interval calculator?

A confidence interval gives a range produced by a method designed to capture an unknown population mean at a stated long-run rate. It combines the sample estimate with sampling uncertainty.

Use this page for a transparent calculation, then compare the result with the Sample Size Calculator when a different view of the same data would be useful.

How does this confidence interval calculator work?

The calculator finds the standard error, obtains the two-sided Student’s t critical value for n − 1 degrees of freedom, and adds and subtracts the resulting margin of error.

Before interpreting spread or position, it can help to check the center with the Average Calculator. Every tool states its assumptions so results can be reproduced.

x̄ ± t* × (s / √n), with df = n − 1

How to use this calculator

  1. Enter the requested numbers in the labeled fields.
  2. Review unit, sample, confidence, or test choices when shown.
  3. Select Calculate Confidence Interval.
  4. Read the main result, supporting facts, and method note.
  5. Use Copy, Download, or Print when you need to keep the result; select Reset to start over.

If you edit any input after calculating, the old result is marked stale and hidden until you calculate again.

Advertisement

How should you interpret the result?

A 95% confidence level describes the repeated-sampling performance of the method. It does not mean there is a 95% probability that the fixed population mean is inside one completed interval.

For another useful perspective, open the Standard Deviation Calculator; it answers a related question without changing the values you entered here.

Assumptions and limitations

The calculation assumes independent observations and a setting where a one-sample t interval is suitable. Biased sampling or severe nonnormality in small samples can invalidate the interval.

Consider the Z-Score Calculator for a complementary summary and the Chi-Square Calculator when your question involves another statistical property. No single statistic describes every important feature of a data set.

Scope: Results are educational calculations, not a substitute for an appropriate study design, subject-matter expertise, or professional statistical review.

Frequently asked questions

A confidence interval gives a range produced by a method designed to capture an unknown population mean at a stated long-run rate. It combines the sample estimate with sampling uncertainty.
Use the labeled fields in the calculator and enter finite numeric values. The page validates missing, impossible, and mismatched inputs before showing a result.
x̄ ± t* × (s / √n), with df = n − 1
A 95% confidence level describes the repeated-sampling performance of the method. It does not mean there is a 95% probability that the fixed population mean is inside one completed interval.
The calculation assumes independent observations and a setting where a one-sample t interval is suitable. Biased sampling or severe nonnormality in small samples can invalidate the interval.
Yes. The calculator and BMI-style result panel are responsive for phones, tablets, laptops, and desktop screens.
No. Calculations run in your browser. This page does not require an account, and the entered values are not sent to a calculation server.
No. It is an educational tool for transparent calculations and quick checks. Important research, clinical, legal, financial, or policy decisions should use an appropriate study design and qualified review.

Sources and methodology

The formulas and cautions on this page are documented so the calculation can be checked against authoritative statistical guidance.

Advertisement