Double Factorial Calculator
Compute the double factorial n!! — the product of every other integer down from n — with its ordinary factorial and digit count.
How it works
n!! = n · (n − 2) · (n − 4) · … down to 1 (odd n) or 2 (even n) · 0!! = 1!! = 1
The double factorial n!! multiplies together every second integer, not every one — so 9!! skips the evens and takes 9 × 7 × 5 × 3 × 1. It is not the factorial applied twice. Double factorials appear throughout combinatorics and calculus: the number of ways to pair up 2k objects is (2k − 1)!!, and integrals of powers of sine and cosine collapse into double-factorial ratios. By convention both 0!! and 1!! equal 1.
Worked example
For n = 9 (odd): 9!! = 9 × 7 × 5 × 3 × 1 = 945. Compare the ordinary factorial 9! = 362,880, which multiplies every integer 9 × 8 × 7 × … × 1. The double factorial 945 is a three-digit number, far smaller because it uses only half the factors.
Sources: Double factorial — Wikipedia
Frequently asked questions
Is n!! the same as (n!)!?
No. The double factorial n!! skips every other integer, so 9!! = 9 × 7 × 5 × 3 × 1 = 945. Taking the factorial of a factorial, (n!)!, would be astronomically larger and is a completely different operation.
What is 0!! and why?
By definition 0!! = 1, matching the empty-product convention (multiplying no numbers leaves the identity 1). It keeps identities like (2k)!! = 2ᵏ·k! consistent at k = 0, and 1!! = 1 as well.
Where are double factorials used?
They count perfect matchings — (2k − 1)!! is the number of ways to pair 2k items — and they show up in reduction formulas for integrals of sinⁿx and cosⁿx, and in series for the gamma function at half-integers.
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This calculator is for educational purposes. Double-check important results before acting on them.