What is Factorial?
Factorial of n (written as n!) is the product of all positive integers up to n. For example, 5! = 5×4×3×2×1 = 120. Factorials are fundamental in counting and probability.
Factorial Calculator
Factorials grow extraordinarily fast — 20! already exceeds 2 quintillion — making manual computation impractical. This calculator handles large factorials precisely, supports double factorials (n!!), and bridges directly into combinatorics through built-in permutation (nPr) and combination (nCr) functions. Common applications include counting arrangements of objects, calculating probability distributions in statistics, evaluating Taylor series expansions in calculus, and solving problems in quantum mechanics and number theory.
star
4.7
calendar_today
Updated:
Factorial Calculator calculator
exclamation
Factorial Calculator
Must be ≤ n
About This Mode
Factorial (n!): Product of all positive integers from 1 to n. Example: 5! = 5×4×3×2×1 = 120
calculate
Result
Expression
5!
Result
120
Step-by-Step
5! = 5 × 4 × 3 × 2 × 1
= 120
Formulas
n! = n × (n-1) × ... × 1
nPr = n! / (n-r)!
nCr = n! / [r!(n-r)!]
lightbulb Tips
- •0! = 1 by definition
- •nPr = n!/(n-r)!
- •nCr = n!/[r!(n-r)!]
- •Max: 170! (float limit)
exclamation Reference
Common Factorials
0! = 16! = 720
1! = 17! = 5,040
2! = 28! = 40,320
3! = 69! = 362,880
4! = 2410! = 3,628,800
5! = 12020! = 2.4×10¹⁸
Key Formulas
n! = n × (n-1)!
nPr = n!/(n-r)!
nCr = n!/[r!(n-r)!]
How to Use the Factorial Calculator
calculate
Select Calculation
Choose factorial, permutation, combination, or other types.
edit
Enter n Value
Input the number for factorial calculation (0-170).
input
Enter r (if needed)
For permutations/combinations, enter the r value.
visibility
View Results
See the result with step-by-step calculation.
The Formula
Factorial multiplies all positive integers up to n. It's used in probability, combinatorics, and calculus.
n! = n × (n-1) × (n-2) × ... × 2 × 1
lightbulb Variables Explained
- n! Factorial of n
- nPr Permutations: n!/(n-r)!
- nCr Combinations: n!/[r!(n-r)!]
tips_and_updates Pro Tips
1
0! = 1 by definition - this is essential for many mathematical formulas
2
Factorials grow extremely fast: 10! = 3,628,800 and 20! has 19 digits
3
For permutations (order matters): nPr = n!/(n-r)!
4
For combinations (order doesn't matter): nCr = n!/[r!(n-r)!]
5
Double factorial n!! multiplies every other number: 7!! = 7×5×3×1 = 105
6
Calculators typically support up to 170! due to floating-point limits
Calculate factorials (n!), double factorials (n!!), permutations (nPr), and combinations (nCr) with step-by-step solutions. Essential for probability and statistics.
Permutations vs Combinations
Permutations count arrangements where order matters (nPr). Combinations count selections where order doesn't matter (nCr). Use permutations for rankings, combinations for groups.