This free Confidence Interval Calculator helps you compute confidence intervals for a mean (Z or t distribution) and for a proportion. Simply enter your data (mean, standard deviation, sample size or successes/trials) and choose a confidence level (80%, 90%, 95%, 99%, or custom). The calculator instantly shows the margin of error and the lower and upper bounds of the interval.
In statistics, a confidence interval (CI) is a range of values that is likely to contain the true population parameter (mean or proportion).
$$ CI = \bar{x} \; \pm \; Z_{\alpha/2} \times \frac{\sigma}{\sqrt{n}} $$
$$ CI = \bar{x} \; \pm \; t_{\alpha/2, df} \times \frac{s}{\sqrt{n}} $$
$$ CI = \hat{p} \; \pm \; Z_{\alpha/2} \times \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} $$
For smaller samples (n < 30), use the t-distribution instead of Z.
Q: What does a 95% confidence interval mean?
A: It means we are 95% confident that the true population parameter lies within the calculated range.
Q: When do I use Z vs t distribution?
A: Use Z if population σ is known and n ≥ 30. Use t if σ is unknown or n is small.
Q: Can a confidence interval include negative values?
A: Yes, depending on the data — especially with means near zero.
Q: Why are Wilson intervals recommended for proportions?
A: They give more accurate coverage than the simple Wald method, especially for small n.