Confidence Interval Calculator

How to use

1. 1Pick a mode: Mean (t-interval) for the realistic case with sample s, Mean (z-interval) when sigma is known, Proportion for a binomial sample p, or From dataset to compute the rest from a list of numbers.
2. 2Choose a confidence level. 95 percent is the standard for survey research and A/B tests; the preset row covers 80, 90, 95, 99, and 99.9 percent, and Custom accepts any value between 0 and 100 percent.
3. 3Fill in the inputs (mean and s and n, or successes and n, or paste the dataset). Load sample fills realistic values; Clear resets the inputs.
4. 4Read the highlighted confidence interval, the standard error, the critical value, the margin of error, and the step-by-step working underneath.
5. 5Use Copy summary to paste the full result into a report or assignment, and consult the reference tables of z and t critical values at the bottom of the page for a sanity check.

About this tool

Confidence Interval Calculator builds the lower and upper bounds for a population parameter from sample evidence and runs the math entirely in your browser. Four modes cover the cases that actually show up in coursework, surveys, A/B testing, and lab work. The t-interval for a mean takes the sample mean, the sample standard deviation s, and the sample size n; degrees of freedom are n - 1 and the critical t is looked up from Hill's 1970 inverse Student t algorithm so the answer matches a printed t-table to three decimals at the common confidence levels. The z-interval for a mean takes the sample mean, the known population standard deviation sigma, and the sample size, and is appropriate when sigma is genuinely known or when n is large enough that s and sigma agree to a working approximation. The proportion mode takes successes x and sample size n and returns two intervals at once: the Wald (normal approximation) interval everyone is taught first, and the Wilson score interval, which keeps coverage close to the nominal confidence level even when p is near 0 or 1 or n is small. The dataset mode parses a column of numbers, computes the sample mean and the sample standard deviation with Bessel's correction (n - 1), and then runs the t-interval directly. Every mode shows the full working: the standard error, the critical value with its degrees of freedom, the margin of error, and the interval itself, formatted alongside a step-by-step explanation suitable for a homework page or methodology section. Confidence presets cover 80, 90, 95, 99, and 99.9 percent, and a custom field accepts any value strictly between 0 and 100 percent. A built-in reference table lists the standard two-tailed and one-tailed z critical values plus two-tailed t critical values across the most common degrees of freedom, so a quick sanity check is always one glance away. The normal CDF uses the Abramowitz and Stegun 26.2.17 series (accuracy about 7.5e-8) and the inverse normal uses Peter Acklam's rational approximation (accuracy about 1.15e-9), more precision than any classroom z-table offers. Useful for statistics students, survey designers, A/B testers, quality engineers, clinical researchers, and anyone who needs a defensible interval estimate with the working written out. Everything runs locally; the numbers you type stay on your device.

Free to use. Works in your browser. No signup, no login.