Confidence interval calculator
Calculate the confidence interval for a mean (with Student's t or the normal distribution) or a proportion, from summary data or a pasted list of numbers.
How to useConfidence interval for a mean and a proportion
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Confidence interval calculator: what it is for
Calculate the confidence interval for a mean from the mean, standard deviation and sample size, or paste a list of numbers and let the tool calculate everything. When the standard deviation comes from the sample, it uses Student's t distribution with n − 1 degrees of freedom. For proportions, it shows the classic interval and the Wilson interval, more reliable with small samples.
The calculations run in your browser; no data you type is sent to servers.
How to use
- Choose mean or proportion.
- Enter the data or paste the list.
- See the interval, margin of error and critical value.
When to use it
- Analyzing experiment results.
- Reporting research in theses and papers.
- Studying inferential statistics.
Frequently asked questions
How is the confidence interval for a mean calculated?
Mean ± critical value × standard error, where the standard error is the standard deviation divided by the square root of the sample size. When the standard deviation comes from the sample itself, Student's t with n − 1 degrees of freedom is used; when the population standard deviation is known, the normal z is used.
What does 95% confidence mean?
That if the study were repeated many times the same way, about 95% of the calculated intervals would contain the true value. It doesn't mean there's a 95% chance that the value is in this specific interval.
When should I use t instead of z?
Whenever the standard deviation comes from the sample, especially with fewer than 30 observations. With large samples, both values are practically the same.
Is it really free?
Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.