Factorial Calculator

Calculate factorial (n!) and double factorial (n!!). Useful for permutations, combinations, and mathematical calculations.

Factorial multiplies every whole number from n down to 1, and this calculator switches between two entirely different methods depending on how large n is. Up through 170, it multiplies the numbers together directly in a loop; above 170, the loop is abandoned in favor of Stirling's approximation, a formula built from square roots and powers of e that estimates enormous factorials without ever multiplying the full chain of integers, trading exactness for a result that stays computable at any size. That 170 cutoff is an overflow boundary, not an accuracy one: 171! is too large for a standard floating-point number to represent at all and would come back as Infinity, so direct multiplication stops just short of that. The loop's results stop being mathematically exact numbers well before then, though — 18! is 6,402,373,705,728,000, still inside the range where every integer is represented exactly, but 19! already exceeds that range at over 121 quadrillion, so from n = 19 onward the direct-multiplication loop is still running and still avoiding overflow, but the specific integer it returns can no longer be trusted to be exactly correct down to the last digit. The Double Factorial output multiplies only every other integer down from n — for the default value of 5, that is 5 times 3 times 1, giving 15, not the 120 that ordinary factorial produces from the same input — and it uses the same direct-multiplication approach regardless of how large n gets, since it was not given the Stirling fallback the way ordinary factorial was. Negative numbers are converted to their positive equivalent before either calculation runs, via an absolute-value step, so entering negative 5 quietly returns the same answer as entering 5 rather than reporting an error or leaving factorial mathematically undefined the way it technically is for negative integers.