Distribution Calculator: Two-Way Probability and Quantile Lookup
What is the Distribution Calculator?
Statistical inference relies on standard distributions: Z (standard normal), t, chi-square and F for hypothesis tests and confidence intervals, and binomial and Poisson for count-type probabilities. This calculator implements probability density, cumulative probability and quantile (inverse cumulative) lookup in both directions, replacing printed statistical tables. It supports one- and two-tailed settings and inverse operations, reducing manual table-reading errors.
When to Use It
Use it whenever you need a critical value such as t(0.025, n-1), a P-value from a test statistic, or a binomial or Poisson probability for sampling-plan evaluation or defect probability. It is a high-frequency companion for manual verification of hypothesis tests and confidence intervals in quality, research and teaching. Because it runs in the browser, there is no need to carry paper tables.
How to Use It (Step by Step)
Select the distribution, enter the parameters, such as degrees of freedom or n and p for binomial or Poisson, and the value or probability, and choose one- or two-tailed. The tool returns the P-value or critical value instantly, with input validation that flags common errors such as negative degrees of freedom or probabilities outside 0-1. Confirm the tail convention matches your test, and save the distribution, parameters and result together for report traceability.
Key Formulas / Example
For a two-tailed t-test with statistic t = 2.31 and df = 14, the tool returns the two-tailed P-value directly, and the critical value t(0.025, 14) is approximately 2.145 from the inverse CDF. For the binomial distribution, P(X <= k) = sum of C(n, i) * p^i * (1 - p)^(n - i) for i = 0 to k. One-tailed is used when the test direction is specified; two-tailed when only a difference matters, and confidence intervals always use two tails.