Contents
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: . By definition, .
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 . 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.
Factorial questions
The notation is short, but zero and large values often need a little context.
What does n! mean?
It means the product of every positive integer from 1 through n.
Why is 0! equal to 1?
The value is defined as 1 so counting formulas and the factorial recurrence remain consistent at zero.
Can I enter a decimal number?
No. This calculator implements the elementary factorial and sequence sums for whole numbers only.
Is the large result rounded?
No. The calculator uses integer arithmetic and displays every digit for inputs up to 5,000.
What is the difference between factorial and a sum?
A factorial multiplies the integers, while the other three modes add selected integers up to n.
Similar calculators
You may find the following calculators on the same topic useful:
- Fibonacci Number Calculator. Enter a non-negative index to get the exact term without scientific notation or rounding.
- Double Factorial Calculator. Enter an integer to multiply numbers of the same parity from n down to 2 or 1.
- Primorial Calculator. Enter a whole-number limit to multiply every prime not greater than n.
- Superfactorial Calculator. Enter a whole number n to multiply all factorials from 1! through n!.
- Prime Number Checker. Enter a whole number to classify it as prime, composite, or an exceptional value.
- Degrees to radians converter. Enter an angle in degrees or radians and see the equivalent value immediately.
- Division with remainder calculator. Enter an integer dividend and a nonzero divisor to calculate the quotient and the unique Euclidean remainder.
- Combinations calculator. Enter the total number of elements and the selection size to get the exact number of possible groups.
- Next prime number calculator. Enter a whole number up to 1,000,000,000,000 to find the first prime number that is strictly greater.
- Digital root calculator. Enter a whole number with up to 10,000 digits to reduce it to one digit and inspect the calculation.
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