Free · Arithmetic calculators ➗

Nonnegative Integer Factorial Product

Multiply the positive integers through n, including the empty-product value 0! = 1.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

5! = 5 × 4 × 3 × 2 × 1 = 120.

n! = product of integers 1 through n; 0! = 1

Worked example

Enter these known values and leave the other values blank.

Nonnegative integer n
5
Factorial n!
120

Assumptions and limitations

  • Input is an integer from 0 through 20,000; the bound keeps factorial evaluation responsive.
  • Factorials grow rapidly. This tool calculates the product for nonnegative integers; it does not define noninteger factorials or invert a factorial to find n.
  • Arithmetic uses 64 significant decimal digits. Large counts can be rounded, and scientific notation is approximate; this tool does not certify every digit of an arbitrarily large integer.

Common questions

Why is zero factorial one?

The empty product equals one, consistent with n! = n × (n−1)! at n = 1.

References

Bookify bounds factorial input at 20,000 to keep evaluation responsive.

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