Factorial Calculator

Result

n!2432902008176640000
Digits19
Trailing zeros4
Expansion1 × 2 × … × 20

No exponent notation, no rounding

The exact value of n! using arbitrary-precision arithmetic, the number of digits, and how many zeros it ends with.

Factorials grow alarmingly fast. 10! is still in the millions, 20! is over two quintillion, and 100! is a 158-digit number. Ordinary calculators give up and switch to exponent notation, discarding everything after the first few digits.

This one uses arbitrary-precision arithmetic, so the answer is exact to the last digit. It also counts the trailing zeros, which is decided entirely by how many fives appear among the factors.

What this calculator shows

The exact factorial in full
How many digits it has, the quickest sense of scale
How many zeros it ends with and why there are that many

What to keep in mind

Factorials are defined for non-negative integers; 0! is one by a convention that keeps combinatorial formulas continuous.
The upper bound is 2000, past which the answer stops fitting on a screen.

FAQs

Why is 0! equal to one?

It is the only value that keeps n! = n × (n−1)! working. Combinatorially, there is exactly one way to arrange an empty set.

How are trailing zeros counted?

Add n/5, n/25, n/125 and so on, discarding remainders. For 100! that gives 20 + 4 = 24 zeros.

Where are factorials actually used?

Combinatorics: n items can be arranged in n! orders. From there they run through combinations, permutations, probability and Taylor series.

Is there a factorial of a fraction?

Through the gamma function, where Γ(n+1) = n!. It is defined for fractional and complex arguments, but the plain factorial only takes integers.

Worked example

Twenty factorial

Input: n = 20

Output: 2,432,902,008,176,640,000 — 19 digits, 4 trailing zeros

Note: The four zeros come from the fives among the factors: 5, 10, 15 and 20 contribute one each. Twos are always more plentiful, so there is never a shortage of pairs.

Useful links

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Factorial Calculator

Result

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