Permutation & Combination Calculator · Practical guide
How to Calculate the Factorial of Large Numbers
Factorials grow faster than almost anything else in everyday math — here is what that looks like.
At a glance
What a Factorial Is
The factorial of n, written n!, is the product of every whole number from 1 up to n: n! = n × (n − 1) × ... × 2 × 1. So 5! = 5 × 4 × 3 × 2 × 1 = 120, and 10! = 3,628,800. By convention, 0! = 1, which keeps formulas like nCr valid when r equals n.
Interactive tool
Permutation & Combination Calculator
Enter your own values, then compare the result with the examples below.
Results
Formulas:
nPr = n! / (n - r)!
nCr = n! / (r! × (n - r)!)
How Fast Factorials Grow
| n | n! |
|---|---|
| 5 | 120 |
| 10 | 3,628,800 |
| 15 | 1,307,674,368,000 |
| 20 | 2,432,902,008,176,640,000 (≈ 2.43 × 10^18) |
| 25 | ≈ 1.55 × 10^25 |
| 50 | ≈ 3.04 × 10^64 |
Doubling n from 10 to 20 does not double the result — it multiplies it by about 670 billion. That is why factorials outgrow calculators so quickly.
How This Calculator Handles Big Results
The tool above computes n! directly and shows the full number with thousands separators up to about 10^15. Beyond that it switches to scientific notation, so 20! displays as roughly 2.432902e+18 rather than a wall of digits. Standard floating-point arithmetic tops out at 170!; anything larger is beyond what ordinary number formats can represent.
Why It Matters for Permutations
Factorials are the engine behind counting: the number of ways to arrange n distinct items is n!. Ten books on a shelf can be ordered 10! = 3,628,800 ways, and shuffling a 52-card deck produces 52! ≈ 8.07 × 10^67 possible orders — more than the number of atoms on Earth, which is why a well-shuffled deck has almost certainly never existed before.
Frequently Asked Questions
Why is 0! equal to 1?
By convention — there is exactly one way to arrange zero items (do nothing). It also keeps formulas like nCr = n! ÷ (r!(n−r)!) valid when r = n.
What is scientific notation?
A compact way to write huge numbers: 2.43 × 10^18 means 2.43 followed by 18 digits' worth of magnitude. This calculator switches to it for results above about 10^15.
Why do factorials grow so fast?
Each step multiplies by a bigger number than the last. Going from 19! to 20! multiplies by 20, from 99! to 100! by 100 — the growth accelerates with every step.
What is the largest factorial this calculator shows?
Up to 170!, the largest factorial within standard floating-point range (about 7.26 × 10^306). Beyond 170!, the value overflows to infinity.