Confidence Interval Calculator
Calculate a confidence interval for a mean or proportion. Free tool showing the margin of error, critical value and interval bounds with steps.
About the Confidence Interval Calculator
A confidence interval gives a range of plausible values for a population parameter based on a sample. This free confidence interval calculator builds an interval for either a mean or a proportion at 90%, 95% or 99% confidence, and shows the critical value, the margin of error and both bounds, with the working laid out.
For a mean, the interval is x̄ ± z × (s ÷ √n), using the z critical value for your confidence level (1.645, 1.96 or 2.576). For a proportion it is p̂ ± z × √(p̂(1 − p̂) ÷ n). The margin of error is the ± part; a wider interval means less precision, which you fix by collecting a larger sample.
Students, researchers, pollsters and analysts use confidence intervals to report uncertainty honestly. Everything runs in your browser with no signup.
How to Use the Confidence Interval Calculator
- 1Choose whether you are estimating a mean or a proportion.
- 2Enter the sample statistic (mean and standard deviation, or the proportion) and the sample size.
- 3Select a confidence level: 90%, 95% or 99%.
- 4Read the interval, margin of error and critical value.
Frequently Asked Questions
How do I calculate a 95% confidence interval for a mean?
Use x̄ ± 1.96 × (s ÷ √n). For a sample mean of 50, standard deviation 10 and n = 100, the margin of error is 1.96 × (10 ÷ 10) = 1.96, so the interval is 48.04 to 51.96. The calculator shows every step.
What does a 95% confidence level actually mean?
It means that if you repeated the sampling many times, about 95% of the intervals built this way would contain the true population value. It does not mean there is a 95% probability the true value lies in this one specific interval.
How do I find a confidence interval for a proportion?
Use p̂ ± z × √(p̂(1 − p̂) ÷ n). If 60 of 200 people say yes, p̂ = 0.30, and at 95% the margin is 1.96 × √(0.30 × 0.70 ÷ 200) = 0.0635, giving 23.6% to 36.4%.
How can I make the interval narrower?
Increase the sample size — the margin of error shrinks with √n, so quadrupling the sample halves the margin. Lowering the confidence level (say from 99% to 90%) also narrows the interval, but you accept more risk of missing the true value.
Should I use z or t for the critical value?
Strictly, the t distribution is correct for a mean when the population standard deviation is unknown and the sample is small. For simplicity and large samples this calculator uses z values, which are very close to t once n exceeds roughly 30.