A confidence interval pairs a point estimate with model-based uncertainty. Repeated samples produce different intervals.
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Confidence Interval for a Proportion. A confidence procedure adds model-based uncertainty around an estimate. Wider confidence levels and noisier or smaller samples generally produce wider intervals.
1Compute the sample estimate2Calculate its standard error3Apply the stated confidence procedure
Method used
Wilson interval uses center (p̂+z²/2n)/(1+z²/n) and its adjusted half-width.
Wilson intervals behave better than the simple Wald interval near zero, one, or modest sample sizes.
What the result cannot establish
A 95% confidence interval does not mean there is a 95% probability that a fixed parameter lies inside this realized interval. The 95% describes long-run coverage of the procedure under its assumptions.
Assumption: Trials must represent independent Bernoulli outcomes with a stable target probability.
Quick guide
How to use this calculator
Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the confidence interval for a proportion calculator works
Wilson interval uses center (p̂+z²/2n)/(1+z²/n) and its adjusted half-width.
Wilson intervals behave better than the simple Wald interval near zero, one, or modest sample sizes.
Worked example
Confidence Interval for a Proportion example
60 successes in 100 trials gives a 95% Wilson interval of about 0.502 to 0.691.
Wilson interval uses center (p̂+z²/2n)/(1+z²/n) and its adjusted half-width.
Supported inputs
Precision and limits
Model and design
Trials must represent independent Bernoulli outcomes with a stable target probability.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Wilson intervals behave better than the simple Wald interval near zero, one, or modest sample sizes.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
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