How to use the Confidence Interval Calculator
- 1. Choose what to estimatePick a mean with sample SD, a mean with known SD, or a proportion.
- 2. Enter your sampleType the mean and SD (or successes) and the sample size.
- 3. Read the intervalSee the lower and upper limits and the margin of error.
Formula and worked example
For a mean with a sample standard deviation: CI = x̄ ± t* × s ÷ √n, where t* comes from the t-distribution with n − 1 degrees of freedom. When the population SD is truly known, z* replaces t*. For a proportion: p̂ ± z* × √(p̂(1 − p̂) ÷ n).
Example: a sample of 25 students has a mean score of 50 and an SD of 10. The standard error is 10 ÷ √25 = 2. For 95% confidence with 24 df, t* = 2.0639, so the margin is 4.1278 and the interval is 45.8722 to 54.1278. Using z = 1.96 instead would give a slightly narrower, over-confident range.
What the interval does and does not mean
A 95% interval means the method captures the true value in about 95 of every 100 samples. It does not mean 95% of individual values fall inside it. Three things make an interval narrower: a bigger sample, less spread in the data, and a lower confidence level.
- t vs z: use t whenever the SD comes from your own sample. The difference matters most below about 30.
- Proportions: the simple Wald interval misbehaves when successes or failures are few. The Wilson interval shown alongside is the better choice then.
- Polls: a reported "±3%" margin is half the width of a 95% interval.
Planning a survey? Work out how many responses you need with the sample size calculator.
Frequently asked questions
Which confidence level should I use?
95% is the usual default. Use 99% when a wrong conclusion is costly, and 90% for early exploration.
Is the t value exact?
Yes. It is computed from the t-distribution itself, not read from a rounded table.
Is the Confidence Interval Calculator free?
Yes, the Confidence Interval Calculator is free. The first time you see your first result, you are asked for your name and WhatsApp number once. After that, this and every other Uncodemy tool opens straight away without the form.