Exact Binomial Confidence Interval
Compute a conservative Clopper–Pearson interval for a success proportion.
Your numbers
Lower bound
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
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Formula
Use L = B⁻¹(α/2;k,n−k+1) and U = B⁻¹(1−α/2;k+1,n−k). k is successes and n is trials. For confidence-level fraction c, set α = 1−c; B⁻¹ is the beta quantile. Handle boundaries k = 0 → L = 0 and k = n → U = 1.
Compute a conservative Clopper–Pearson interval for a success proportion.
Worked example
- Successes
- 5
- Trials
- 10
- Confidence level (%)
- 95
- Lower bound
- 18.7086028447 %
- Upper bound
- 81.2913971553 %
- Observed proportion
- 50 %
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
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: e318a0d0d050 · Example checked: