Confidence Interval Calculator

About the Confidence Interval Calculator

A confidence interval gives a range of plausible values for a population parameter based on sample data, along with a confidence level expressing how reliable that estimate is. A 95% confidence interval means that if you repeated your sampling process 100 times, 95 of the resulting intervals would contain the true population parameter. Our calculator computes confidence intervals for population means, using the t-distribution for small samples.

How It Works

CI = x̄ ± (z* or t*) × (s / √n), where x̄ is sample mean, z* or t* is the critical value for your confidence level, s is sample standard deviation, and n is sample size. For large samples (n > 30): use z* values: 90% CI = 1.645, 95% CI = 1.960, 99% CI = 2.576. For small samples: use t* from the t-distribution with (n−1) degrees of freedom. The margin of error is the ± portion of the interval.

Tips & Best Practices

• ✓Wider confidence intervals reflect more uncertainty — caused by smaller samples or higher variability.
• ✓Doubling sample size reduces the margin of error by a factor of √2 ≈ 1.41.
• ✓"95% confident" does NOT mean 95% probability the true value is in this interval — it refers to the long-run procedure.
• ✓Overlapping confidence intervals do not necessarily mean no significant difference exists.
• ✓One-sided CI (used for one-tailed tests) has a different critical value than two-sided.

Who Uses This Calculator

Market researchers presenting survey results with margins of error, clinical trial teams reporting treatment effect estimates, quality engineers defining measurement precision, political pollsters reporting vote shares, and students completing inferential statistics coursework all use confidence intervals.