Deep in probability theory and mathematical physics sits a function most students meet once and never forget the shape of: the beta function, B(x, y), defined by an integral from 0 to 1 of t^(x-1)(1-t)^(y-1) dt. Its party trick is the relationship with the gamma function — B(x, y) = Γ(x)Γ(y) / Γ(x+y) — which turns many impossible-looking integrals into simple factorial arithmetic, since Γ(n) = (n-1)! for positive integers. That makes B(3, 2) = (2! × 1!) / 4! = 2/24 = 1/12, a calculation you can do on a napkin. The beta function is the normalization constant of the beta distribution, the go-to model for probabilities and proportions in Bayesian statistics — conversion rates, click-through rates, anything living between 0 and 1. Physicists meet it in string theory amplitudes. This calculator evaluates the function for you: enter your values in the Variable A and Variable B fields and read the Result.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Beta Function Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.