Factorial Calculator

A factorial is the product of every positive whole number up to n, written n!, so five factorial is 1 × 2 × 3 × 4 × 5 = 120. It counts the ways to arrange n distinct items in order, which is why it turns up throughout probability, combinations and permutations.

There is exactly one way to arrange an empty set — the empty arrangement — so the count is 1, not 0. It also keeps the formulas consistent: the recurrence that turns n factorial into n × (n − 1) factorial makes one factorial equal 1 × zero factorial, which only works out if zero factorial is 1.

The number of distinct ways to put n different items in a row. Three books have six possible shelf orders, five runners have 120 possible finishing orders.

Faster than any exponential. Five factorial is only 120, but ten factorial is already 3,628,800 and twenty factorial is over 2.4 quintillion. Each step multiplies by the next integer, so the value explodes.

Because 22 factorial is the first one a standard number can no longer write out digit for digit: it prints as 1,124,000,727,777,607,700,000 when the true value ends in 680,000. Larger factorials need arbitrary-precision arithmetic, so the calculator stops where every printed digit is still true.