Confidence Interval Calculator
Calculate confidence intervals for a sample mean or sample proportion at any confidence level (90%, 95%, 99%, etc.).
How to use the Confidence Interval Calculator
- Enter your inputs into the Confidence Interval Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The confidence interval formulas
For mean: x̄ ± z × (σ/√n) · · · For proportion: p̂ ± z × √(p̂(1−p̂)/n)
z is the critical value for the chosen confidence (1.96 for 95%, 2.576 for 99%). The interval estimates where the true population value likely lies.
Worked example
Sample of 100 heights with mean 170 cm, SD 8 cm. 95% CI: 170 ± 1.96 × (8/10) = 170 ± 1.57 = (168.4, 171.6). We're 95% confident the population mean falls in this range.
Frequently asked questions
What does "95% confidence" mean exactly?
If we repeated the sampling process many times, 95% of resulting intervals would contain the true population value. It does NOT mean "there's a 95% chance the true value is in this specific interval."
When do I use t-distribution instead of z?
When the population SD is unknown and you're estimating it from the sample. For small samples (n < 30), t-distribution is meaningfully wider than z; for large samples they converge.
How does sample size affect CI width?
CI width shrinks with √n. Quadrupling the sample size halves the interval width — diminishing returns on precision per dollar of data collection.