About Confidence Interval Calculator (Means & Proportions)
High-precision confidence interval estimator for empirical research parameters. Computes confidence intervals for sample means using Z-distribution or Student’s t-distribution, and proportion intervals using Wilson Score and Wald methods. Features a dynamic bell curve visualization of the confidence region.
Key Capabilities & Features
- Dual parameter modes: Single sample mean (x̄) and binomial proportion (p̂)
- Exact distribution selection: Automatic Student’s t for unknown σ and Z-distribution for known σ
- Advanced proportion intervals: Wilson Score interval (recommended by NIST) and classic Wald method
- Comprehensive readouts: Lower bound, upper bound, margin of error, standard error, and critical value
- Integrated SVG reference bell curve diagram highlighting point estimate and shaded interval span
How to Use Confidence Interval Calculator (Means & Proportions)
Select Parameter Type
Choose whether you are estimating a numerical Mean or a categorical Proportion.
Enter Sample Data
Provide the sample mean, standard deviation, and sample size (or successes and trials).
Choose Confidence Level
Select 90%, 95%, or 99% confidence level.
Read Interval Bounds
Inspect the resulting [Lower, Upper] interval and margin of error.
Privacy & In-Browser Execution Guarantee
100% Client-Side. Estimation intervals and critical values are computed locally in JavaScript.
Frequently Asked Questions
Why is the Wilson Score interval superior to the Wald interval for proportions?
The Wald interval performs poorly near 0 and 1 or with small sample sizes, whereas the Wilson Score interval uses exact quadratic inversion of the score test, guaranteeing valid coverage probabilities.
What does a 95% confidence interval actually mean?
It means that if the same sampling procedure were repeated across many independent samples, 95% of the calculated intervals would contain the true population parameter.