Confidence Interval

About this calculator

The Confidence Interval Calculator builds a two-sided confidence interval for a population mean or a population proportion. For a mean it uses the Student-t interval x̄ ± t* · s/√n with df = n − 1; for a proportion it uses the normal (Wald) interval p̂ ± z* · √(p̂(1−p̂)/n). Enter your sample statistics and confidence level to get the margin of error, the lower and upper limits, the critical value, and the standard error, with a number-line diagram of the interval. Useful for statistics, polling, A/B testing, and lab measurements.

How to use the Confidence Interval calculator

1. Enter the values for your problem into the input fields.
2. Read the result — it updates instantly as you type.
3. Check the formula and the visual explanation to follow how the answer was found.
4. Copy the page URL to share the exact calculation.

Common examples

• Mean: x̄ = 50, s = 10, n = 30, 95% → 50 ± 3.73 = [46.27, 53.73]
• Proportion: 45 of 100, 95% → 0.45 ± 0.098 = [0.352, 0.548]
• A higher confidence level (99%) widens the interval; a larger sample (n) narrows it
• Poll of 60%, n = 1000, 95% → 0.60 ± 0.030 = [0.570, 0.630]
• Small sample n = 5 uses a wider t* than the normal z* for the same confidence