Write 1 at the top of a page, then build each new row from the two numbers above it — 1, then 1 1, then 1 2 1, then 1 3 3 1 — and you have drawn Pascal's triangle, a number pattern that has fascinated mathematicians from 11th-century China to Blaise Pascal's 1653 treatise. Its magic is that every entry is the sum of the two entries diagonally above it, yet the rows secretly count combinations: row n, read left to right, lists C(n,0), C(n,1), C(n,2), and so on.

That makes the triangle a probability cheat sheet. Row 4 reads 1 4 6 4 1, which tells you that flipping four coins yields one way to get all heads, four ways to get three heads, six ways to get two heads, and so on. The entries also expand binomials — (x + y)³ = 1x³ + 3x²y + 3xy² + 1y³ — and along the diagonals hide the Fibonacci numbers, triangular numbers, and powers of 2 in the row sums. This calculator evaluates single entries: the binomial coefficient C(n,k) equals the falling product n × (n−1) × … divided by k!. Type the falling product n × (n−1) × … × (n−k+1) in the Variable A box and 1/k! in the Variable B box, and the Result box returns C(n,k).

With the pre-filled defaults — Variable A 10, Variable B 5 — the Pascal Triangle 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.