Wilson Proportion Interval
Use the Wilson score interval for a binary success count.
Your numbers
Lower confidence limit
Independent binary trials; confidence describes the method’s repeated-sample coverage, not a probability assigned to a fixed true proportion.
Scenario comparison
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Formula
Use Wilson centre C = (p+z²/(2n))/(1+z²/n) and half-width H = z√[p(1−p)/n+z²/(4n²)]/(1+z²/n). p is successes divided by trials, n is trials, and z is the two-sided standard-normal critical value. Bounds are C−H and C+H, displayed as percentages.
Use the Wilson score interval for a binary success count.
Worked example
- Successes
- 50
- Trials
- 100
- Confidence level (%)
- 95
- Lower confidence limit
- 40.3831530366 %
- Upper confidence limit
- 59.6168469634 %
- Observed proportion
- 50 %
Scope and limitations
Independent binary trials; confidence describes the method’s repeated-sample coverage, not a probability assigned to a fixed true proportion.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 1dc9681ceb58 · Example checked: