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Confidence Interval for a Proportion — result sheet
Wald 95/90/99% interval for a population share from successes and trials.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: p-hat = x/n; SE = sqrt(p-hat(1-p-hat)/n); interval = p-hat +/- z* x SE.
The Wald interval centers on the sample proportion with a normal critical value. It misbehaves near 0/1 or tiny n; those cases are flagged, not silently reported.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Successes — minimum 0; maximum 1000000000
- Trials — Successes cannot exceed trials.; minimum 1; maximum 1000000000
- Confidence level — 3 choices
Worked example
| Input | Value |
|---|---|
| Successes | 240 |
| Trials | 400 |
| Confidence level | 95 |
95% interval (0.5520, 0.6480); margin 0.0480.
Assumptions and limits
- Random sample; need n*p-hat and n*(1-p-hat) both >= 5.
- Two-sided Wald interval; whole-number counts with x <= n.
- Boundary proportions 0/1 give zero width and a warning.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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