How to use the wilson score interval calculator
Find a 95 percent confidence interval for a proportion that works well even with small samples or extreme proportions. Enter successes, trials in the fields above; the observed proportion, wilson lower bound (95%), wilson upper bound (95%) are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “Wilson score interval”, “confidence interval proportion”, “binomial confidence interval”, “calculate wilson score interval”, “find observed proportion”.
Formula
Variables
- s — Successes
- n — Trials
Worked example
With successes = 42, trials = 100, the calculator gives observed proportion ≈ 42 %; wilson lower bound (95%) ≈ 32.79822 %; wilson upper bound (95%) ≈ 51.79369 %.
Frequently asked questions
What is the wilson score interval calculator used for?
Find a 95 percent confidence interval for a proportion that works well even with small samples or extreme proportions. It helps with questions such as “Wilson score interval”, “confidence interval proportion”, “binomial confidence interval”.
What is the formula for the wilson score interval calculation?
Observed proportion (%) = s / n × 100. Wilson lower bound (95%) (%) = 100 × ((s / n+3.8416 / (2 × n))-1.96 × √((s / n) × (1-s / n) / n+3.8416 / (4 × n × n))) / (1+3.8416 / n). Wilson upper bound (95%) (%) = 100 × ((s / n+3.8416 / (2 × n))+1.96 × √((s / n) × (1-s / n) / n+3.8416 / (4 × n × n))) / (1+3.8416 / n). Here s is successes, n is trials.
What inputs do I need for the wilson score interval calculator?
You need successes, trials. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the wilson score interval calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the wilson score interval result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.