Last updated
Stirling's Approximation for Large Factorials
n! ≈ √(2πn) × (n/e)^n
For n = 100:
Exact: 9.332622 × 10^157
Stirling: 9.324848 × 10^157
Error: 0.083% (very accurate for large n)
The Factorial Calculator on TechConverter.me computes exact factorials for any non-negative integer, shows step-by-step multiplication, and supports double factorials, subfactorials, and Stirling's approximation — making it a complete reference for factorial-related calculations.
Examples
Example 1: Basic Factorial Computation
Computing 7! with step-by-step breakdown:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
Step by step:
7 × 6 = 42
42 × 5 = 210
210 × 4 = 840
840 × 3 = 2,520
2,520 × 2 = 5,040
5,040 × 1 = 5,040
7! = 5,040
Example 2: Large Factorials
The calculator handles arbitrarily large numbers using exact arithmetic:
10! = 3,628,800
20! = 2,432,902,008,176,640,000
50! = 30,414,093,201,713,378,043,612,608,166,979,581,188,299,763,898,377,856,000,000,000,000
100! = 9.332622 × 10^157 (exact: 158-digit number)
Number of digits in n!:
10! → 7 digits
20! → 19 digits
100! → 158 digits
1000! → 2,568 digits
Example 3: Combinatorics — Permutations and Combinations
Factorials are the foundation of counting problems:
How many ways can 5 people sit in 5 chairs?
P(5,5) = 5! = 120 arrangements
How many ways can you arrange the letters in "HELLO"?
5 letters, but L repeats twice: 5! / 2! = 120 / 2 = 60 arrangements
How many ways can you choose 3 items from 10?
C(10,3) = 10! / (3! × 7!)
= 3,628,800 / (6 × 5,040)
= 3,628,800 / 30,240
= 120 combinations
Lottery: choose 6 numbers from 49
C(49,6) = 49! / (6! × 43!)
= 13,983,816 possible combinations