Welcome to the Statistics hub. Proportions are the foundation of inference about percentages: polls, surveys, medical trials and A/B tests all ask whether a sample proportion is far from a claim, or what range of values is plausible. Below are all of our free statistics proportion tools, each with a working calculator, the formula, a worked example and a step-by-step guide.
Proportion Statistics Calculators
Sample Proportion — Find p̂ = x/n, its standard error and a 95% confidence interval, and check the conditions for the normal approximation.
One-Proportion Z-Test — Test a claim about a single proportion: enter p0, x and n to get the z-statistic, the p-value and the decision.
Two-Proportion Z-Test — Compare two independent proportions with a pooled z-test, for A/B tests and treatment comparisons.
Proportion Confidence Interval — Build a 90%, 95% or 99% confidence interval for a population proportion, with the margin of error shown.
Two-Proportion Confidence Interval — Estimate the difference p1 − p2 with an unpooled confidence interval, and learn how to read it.
Sample Size for Proportion — Work out how many people to survey for a chosen margin of error and confidence level.
How Proportion Inference Works
All six tools share one idea: the sample proportion p̂ varies from sample to sample, roughly normally, with standard error √(p(1 − p)/n). A z-test asks whether p̂ is surprisingly far from a claimed value; a confidence interval turns p̂ and its standard error into a range of plausible values for p. Check the conditions every time — random samples, at least 10 successes and 10 failures, and samples smaller than 10% of the population — and the normal approximation will serve you well. For the basic math of proportions, see the Math hub.
Statistics Hub FAQs
Should I use a z-test or a confidence interval?
Use a z-test when you have a specific claim to test (p = 0.5?). Use a confidence interval when you want a range of plausible values for the true proportion.
Are these statistics calculators free?
Yes — every calculator on this site is free, with no sign-up and no limits. All calculations run in your browser.