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Factorial Calculator

Compute n! and multifactorials n!!, n!!!, n!!!! with arbitrary precision.

Factorial formulas

Factorialn! = n × (n − 1) × … × 2 × 1, 0! = 1
Double factorialn!! = n × (n − 2) × (n − 4) × …
Triple factorialn!!! = n × (n − 3) × (n − 6) × …
Stirling's approximationn! ≈ √2πn (n / e)n

Worked examples

  1. Compute 5! and 10!.

    1. 5! = 5 × 4 × 3 × 2 × 1 = 120
    2. 10! = 10 × 9 × … × 1

    Answer: 120 and 3,628,800

  2. Compute 7!!, 8!! and 10!!!.

    1. 7!! = 7 × 5 × 3 × 1 = 105
    2. 8!! = 8 × 6 × 4 × 2 = 384
    3. 10!!! = 10 × 7 × 4 × 1 = 280

    Answer: 105, 384, 280

  3. Estimate 10! with Stirling's formula.

    1. √20π × (10 / e)10 ≈ 7.927 × 453,999

    Answer: ≈ 3,598,696 (0.83% below the true value)

Tips & common mistakes

  • n! counts the ways to arrange n different things in a row — 52! deck shuffles is about 8 × 10⁶⁷.