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 two proportions calculator works
(p̂₁−p̂₂)±z*√[p̂₁(1−p̂₁)/n₁+p̂₂(1−p̂₂)/n₂].
The interval describes plausible differences on the absolute proportion scale.
Worked example
Confidence Interval for Two Proportions example
60/100 minus 45/100 gives an estimated difference of 0.15 before uncertainty is added.
(p̂₁−p̂₂)±z*√[p̂₁(1−p̂₁)/n₁+p̂₂(1−p̂₂)/n₂].
Supported inputs
Precision and limits
Model and design
Groups and trials must be independent and sufficiently large for the normal approximation; bounds are clipped to the possible difference range −1 to 1.
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
The interval describes plausible differences on the absolute proportion scale.
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.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
Continue calculating