Confidence interval for a proportion
From x successes in n trials, the confidence interval for the true proportion — computed both the simple Wald way and the Wilson score way, which stays sensible for small samples or proportions near 0 or 1.
Related tools
All Statistics & probability tools →Need Sample proportion, Wald lower, Wald upper, Wilson lower, Wilson upper? The Confidence interval for a proportion derives it from Successes (x), Sample size (n), Confidence level in one step. For instance, with Successes (x) = 42, Sample size (n) = 100 and Confidence level = 80% it returns Sample proportion = 42%, Wald lower = 35.67% and Wald upper = 48.33%.
How to use it
- Enter your values: Successes (x), Sample size (n), Confidence level.
- Read the result instantly: Sample proportion, Wald lower, Wald upper, Wilson lower, Wilson upper.
Frequently asked questions
How does the Confidence interval for a proportion work?
It takes Successes (x), Sample size (n) and Confidence level and derives Sample proportion, Wald lower, Wald upper, Wilson lower and Wilson upper from them. The calculation is live as you type, so the result updates on every change.
Which values does the calculator ask for?
3 values: Successes (x), Sample size (n) and Confidence level. Nothing else is required — no account, no file upload.
What does a typical calculation look like?
With Successes (x) = 42, Sample size (n) = 100 and Confidence level = 80%, the calculator returns Sample proportion = 42%, Wald lower = 35.67% and Wald upper = 48.33%. Those figures come from running this exact tool, so you can reproduce them by entering the same values.
How much does the result change with different inputs?
It moves a lot. Using Successes (x) = 84, Sample size (n) = 200 and Confidence level = 90% instead, Wald lower goes from 35.67% to 36.26% — which is why it is worth testing a few scenarios rather than trusting a single figure.
Which “Confidence level” option should I choose?
You can pick between « 80% », « 90% », « 95% » and « 99% ». Each one changes what the calculator works out, so switch and compare — the default is « 80% ».
What does it give for smaller values?
Scaled down to Successes (x) = 21, Sample size (n) = 50 and Confidence level = 80%, Wald lower comes out at 33.05%. The relationship is worth checking at both ends before you rely on a single result.
When would I actually use this?
Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.
What is the most common mistake?
Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.
What is the difference between the Confidence interval for a proportion and the Confidence interval calculator?
This one returns Sample proportion and Wald lower; the Confidence interval calculator returns Lower bound and Upper bound. That is the whole difference — open the one whose figure you need.
Is there a tool for the next step?
Proportion calculator is the closest one after this: Solve a proportion a/b = c/x and find the missing value x.