Confidence Interval Calculator
Enter a sample mean or a count of successes and get the confidence interval and margin of error, using the t distribution for means and the Wilson method for proportions.
Updated · By Bibin XavierData 90 × 12
| IDtext · 90 levels | Grouptext · 3 levels | Gendertext · 2 levels | Agenumeric | Hours_Studynumeric | Anxietynumeric | Motivationnumeric | Pre_Scorenumeric | Post_Scorenumeric | Exam_Scorenumeric | Passednumeric · coded | Satisfactionnumeric · coded |
|---|---|---|---|---|---|---|---|---|---|---|---|
| S001 | Control | Male | 23 | 11.2 | 29 | 4.6 | 60 | 62 | 67 | 1 | 2 |
| S002 | Workshop | Female | 23 | 3.9 | 28 | 3.5 | 54 | 70 | 54 | 0 | 2 |
| S003 | Online | Female | 18 | 10.1 | 32 | 4 | 55 | 57 | 66 | 0 | 3 |
| S004 | Control | Male | 26 | 13.6 | 41 | 3.5 | 52 | 55 | 59 | 0 | 3 |
| S005 | Workshop | Female | 22 | 9.7 | 27 | 3.6 | 56 | 63 | 65 | 0 | 4 |
| S006 | Online | Female | 20 | 7.9 | 32 | 3.8 | 65 | 82 | 65 | 0 | 2 |
| S007 | Control | Female | 20 | 6.3 | 28 | 3 | 72 | 83 | 61 | 0 | 3 |
| S008 | Workshop | Male | 22 | 8 | 29 | 3.1 | 64 | 72 | 62 | 1 | 3 |
Variables and options
Results
Calculated in your browserInterval estimates
| Method | Critical value | Margin of error | Lower | Upper |
|---|---|---|---|---|
| t distribution (recommended) | 1.971 | 1.57 | 70.83 | 73.97 |
| z distribution (known σ) | 1.960 | 1.56 | 70.84 | 73.96 |
Interpretation
We can be 95% confident that the population mean lies between 70.83 and 73.97.
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Confidence Interval Calculator [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/confidence-interval-calculator/
BibTeX
@software{xavier_confidenceintervalcalculator_2026,
author = {Xavier, Bibin},
title = {Confidence Interval Calculator},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/confidence-interval-calculator/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Confidence Interval Calculator tool on FreeStatisticalTools.com (Xavier, 2026).”
What is a confidence interval?
A confidence interval gives a range of plausible values for a population mean or proportion. Enter your sample mean, standard deviation and sample size, or a count of successes, and the calculator returns the interval, the margin of error and the critical value.
When to use a confidence interval
Use a confidence interval to show the precision of an estimate. The margin of error is half the width of the interval.
How to use this calculator
- Enter the values. Fill in estimate, sample mean, standard deviation and sample size (n).
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report a confidence interval in APA style
Report the estimate with its interval, for example “M = 72.4, 95% CI [70.8, 74.0].”
Frequently asked questions
What does a 95% confidence interval mean?
If you repeated the study many times and built an interval each time, about 95% of those intervals would contain the true population value.
Why use the t distribution instead of z?
When the population standard deviation is unknown and estimated from the sample, the t distribution gives the correct interval width. With large samples t and z give almost the same answer.
Why is the Wilson interval recommended for proportions?
The simple Wald interval can be too narrow and can go below 0 or above 1 when the proportion is near the extremes or the sample is small. The Wilson score interval keeps its coverage close to the stated level.
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