Fisher Exact Test Calculator

About this calculator

The Fisher exact test computes the exact probability of observing a particular 2×2 contingency table of counts, given the table’s fixed row and column totals, rather than relying on the chi-square test’s large-sample approximation. For a table with cells a, b, c, d (and totals n = a+b+c+d), the exact hypergeometric point probability of that specific table is P = [(a+b)!(c+d)!(a+c)!(b+d)!] / [a!·b!·c!·d!·n!], derived from the hypergeometric distribution that describes how counts fall into cells when the margins are held fixed.

This point probability is the building block of the full Fisher exact test p-value (which sums this quantity over all tables as extreme or more extreme than the one observed), and it’s paired here with the odds ratio — (a·d)/(b·c) — which measures the strength and direction of the association between the two categorical variables. Biostatisticians and researchers reach for Fisher’s exact test instead of chi-square specifically when sample sizes are small or any expected cell count falls below about 5, a very common situation in clinical trials, case-control studies, and rare-event data; this calculator returns the exact probability of the entered 2×2 table along with its total and odds ratio.