📏Confidence Interval Calculator
Calculate a confidence interval for a mean or proportion, with the margin of error and critical value shown step by step.
Free Confidence Interval Calculator
Need a confidence interval for a mean or proportion? Our free Confidence Interval Calculator computes the margin of error and interval bounds instantly, choosing the right method automatically — a z-interval when the population standard deviation is known, or a t-interval when it isn't.
Enter your sample mean or proportion, sample size, and standard deviation, pick a confidence level (90%, 95%, 99%, or a custom value), and get the full interval along with the critical value and standard error used to build it. Every step is shown, from the critical value lookup to the final margin-of-error formula, so you can follow — or verify — the calculation by hand.
Built for statistics students and researchers who need accurate, transparent results without a textbook z-table or t-table. Free, with no sign-up and no limits. See the About page or the FAQ for more.
About the Confidence Interval Calculator
Features
Three modes
z-interval, t-interval, and proportion interval, selected with a single toggle.
Accurate critical values
Computed via the regularized incomplete beta function, not a limited lookup table.
Custom confidence levels
90%, 95%, 99%, or any custom percentage in between.
Step-by-step working
Standard error, critical value, and margin-of-error substitution shown for every result.
Frequently Asked Questions
What is a confidence interval?
A range of values, calculated from sample data, that's likely to contain the true population parameter at a given confidence level.
When should I use a z-interval vs a t-interval?
Use a z-interval when the population standard deviation is known; use a t-interval when you only know the sample standard deviation, which is the more common real-world case.
How is a confidence interval calculated?
As the sample statistic ± the margin of error, where the margin of error is the critical value times the standard error.
What confidence levels can I choose?
90%, 95%, and 99% are built in, plus a custom percentage.
Can I calculate a confidence interval for a proportion?
Yes, switch to proportion mode and enter your observed proportion and sample size.
What is the critical value?
The z* or t* value corresponding to your chosen confidence level and (for t) degrees of freedom; it's shown alongside your result.
What sample size do I need?
Any n ≥ 2 works for a t-interval; larger samples generally give a narrower, more precise interval.
Does it show the calculation steps?
Yes, the standard error, critical value, and margin-of-error formula are all shown.
Is my data stored?
No, all calculations run client-side in your browser.
Is it free?
Yes, completely free with no sign-up or limits.