Confidence interval calculator
Calculate a Student t interval for a mean or the more stable Wilson interval for a proportion. The result includes the critical value and margin of error.
Your numbers stay in this browser. No account or upload to the server is needed.
How do I use this page?
- Choose a mean or proportion and the confidence level.
- Enter the sample summary: mean, SD and n, or successes x and n.
- Read the bounds, critical value, standard error and formula substitution.
Method and worked example
For a mean, the calculator uses x̄±t*s/√n with n−1 degrees of freedom. It uses tabulated critical values through df=30 and an asymptotic expansion above that.
For a proportion, it uses the Wilson interval. This behaves better than the simple p̂±z√(p̂(1−p̂)/n) interval, especially for small samples or proportions near 0 and 1.
A 95% level means that about 95% of intervals made by this procedure cover the parameter in repeated sampling when the assumptions hold.
Mean example: x̄=72, s=12, n=36 at 95%. The calculator selects t* for 35 degrees of freedom and obtains the margin t*s/√n.