Factorial Calculator
Free factorial calculator with exact big-integer results up to 1000!. See the expanded multiplication, digit count and scientific notation instantly.
About the Factorial Calculator
The factorial n! is the product of all positive integers from 1 to n, with 0! defined as 1. Factorials count arrangements: 5 people can line up in 5! = 120 ways, and they sit inside every permutation and combination formula in probability. This free factorial calculator computes exact values using big-integer arithmetic — no rounding — up to 1000!, a number with 2,568 digits.
For small inputs it shows the expanded multiplication (10! = 10 × 9 × … × 1 = 3,628,800); for large ones it adds the digit count, scientific notation and a copyable exact value. Students tackling permutations and combinations in matric, FSc and entry-test prep across Pakistan and India get both the answer and the working, all computed instantly in the browser.
How to Use the Factorial Calculator
- 1Enter a whole number from 0 to 1000.
- 2Read the exact factorial, digit count and scientific notation.
- 3Copy the full exact value for large results with one click.
Frequently Asked Questions
How is a factorial calculated with an example?
Multiply every integer from n down to 1. For n = 6: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720. Each step multiplies the previous factorial by the next integer, so 7! = 7 × 720 = 5,040.
Why does 0! equal 1?
There is exactly one way to arrange zero objects — the empty arrangement. It also keeps formulas consistent: n! = n × (n−1)! only works for n = 1 if 0! = 1, and the combination formula C(n, n) = n! ÷ (n! × 0!) must equal 1.
How large do factorials get?
Explosively large. 10! = 3,628,800; 20! ≈ 2.43 × 10¹⁸ (already past a 64-bit integer); 70! ≈ 1.2 × 10¹⁰⁰, bigger than a googol; and 1000! has 2,568 digits. That is why this calculator uses exact big-integer arithmetic instead of floating point.
Where are factorials used in real problems?
Permutations and combinations: the number of ways to arrange r items from n is n! ÷ (n−r)!, and to choose r items is n! ÷ (r!(n−r)!). For example, picking 3 committee members from 10 people gives 10! ÷ (3! × 7!) = 120 possibilities.
Can I calculate the factorial of a negative or decimal number?
Standard factorials are defined only for whole numbers 0, 1, 2, …, and this calculator enforces that. Mathematics extends the idea to decimals via the gamma function, where Γ(n) = (n−1)!, but negative integers remain undefined even there.