Factorial (n!) & Logarithm Calculator
Compute exact factorials (n!) for permutations and evaluate common logarithms (log₁₀) and natural logarithms (ln).
About the Factorial (n!) & Logarithm Calculator
The factorial of a non-negative integer n, denoted n!, is the product of all positive integers less than or equal to n. Factorials grow rapidly and form the foundation of permutations, combinations, and Taylor series.
This calculator evaluates exact factorials up to 20! alongside base-10 common logarithms (log₁₀) and natural logarithms (ln).
Factorial & Logarithm Formulas
Standard definitions for factorials and logarithms:
n! = n × (n − 1) × (n − 2) × ... × 2 × 10! = 1log_b(x) = y ⇔ b^y = xHow to Calculate a Factorial (n!)
- Start with the Integer n: Write out the countdown sequence of integers from
ndown to1. - Multiply Sequentially: Multiply each integer by the running product (or multiply
(n − 1)! × n).
Worked Example: To find 6!, multiply 6 × 5 × 4 × 3 × 2 × 1 = 720.
Frequently Asked Questions (FAQ)
Why is 0! equal to 1?
By the empty product convention in mathematics and combinatorics, there is exactly 1 way to arrange zero objects (doing nothing), and 0! = 1 keeps the recurrence relation n! = n × (n−1)! valid for n = 1.
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