Factorial Calculator

How the factorial calculator works

Choose factorial or one of the three sum modes, then enter a whole number from 0 to 5,000. The calculator returns an exact integer rather than scientific notation or a rounded estimate.

Factorial multiplies every integer from 1 through n

The exclamation mark is part of the notation: $n!=\prod_{k=1}^{n}k$. By definition, $0!=1$.

Factorials count arrangements. If five distinct books can occupy five shelf positions, there are 5! possible orders.

Small values make useful checks

5! = 120. Multiplying 1 × 2 × 3 × 4 × 5 gives the default result and the number of orders for five distinct objects.

10! = 3,628,800. The jump from 9! to 10! is a factor of 10, showing how quickly factorials grow.

0! = 1. This convention keeps permutation and combination formulas valid when a group contains no selected elements.

The menu also calculates three sequence sums

The natural-number mode uses $\sum_{k=1}^{n}k=\frac{n(n+1)}{2}$. For n = 10, the answer is 55.

The even mode adds 2 + 4 + … up to n, while the odd mode adds 1 + 3 + … up to n. With n = 10, those results are 30 and 25.

Only non-negative whole numbers are accepted

The elementary factorial is not defined here for negative numbers or fractions. Values above 5,000 are blocked so the page remains responsive even though the arithmetic uses exact integers.

A large exact result can contain thousands of digits. Copy it when you need every digit; for estimates or asymptotic work, a logarithm or Stirling’s formula is often easier to handle.

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