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.
How to use this calculator
- Enter the requested numbers in the labeled fields.
- Review unit, sample, confidence, or test choices when shown.
- Select Calculate Confidence Interval.
- Read the main result, supporting facts, and method note.
- 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.
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.
Frequently asked questions
Sources and methodology
The formulas and cautions on this page are documented so the calculation can be checked against authoritative statistical guidance.