Factorial Calculator

What is a Factorial Calculator?

A factorial calculator takes a non-negative integer n and returns n!. Factorials are defined as the product n × (n-1) × (n-2) × ... × 1, and they appear constantly in permutations, combinations, probability, and algorithm practice.

Small values look like ordinary multiplication, but the result grows extremely fast. For example, 10! is 3,628,800, while 20! already has 19 digits and 100! stretches to 158 digits.

This tool highlights the main result first, then lets you review the exact integer, the expansion, the digit count, and the trailing-zero count in one place. If you also want to reduce numerators and denominators in combination formulas, the Fraction Calculator is a useful follow-up step.

When this tool is useful

Factorials show up in school math, probability and statistics, algorithm training, combinatorics, and counting problems of all kinds. Because the value explodes so quickly, it helps to see the exact result and the scale summary together. If your workflow moves from a ratio setup into a counting formula, the Proportion Calculator can help you organize the inputs before you check the factorial terms.

• Permutation and counting problems – Check how many ways distinct items can be arranged
• Combination formula review – Verify the numerator and denominator pieces of nCr and nPr
• Programming practice – Compare iterative, recursive, and BigInt outputs
• Trailing-zero patterns – See how often a factor of 10 appears in large factorials
• Large-number intuition – Compare the scale of 50!, 100!, and 500!

Key features

This factorial calculator does more than return a single answer. It packages the extra context you need to interpret large values quickly, especially when the exact integer becomes too long to read at a glance.

• Exact results from 0! to 5,000! – Calculates the full integer inside the browser
• Scientific-notation summary – Shows the scale of very large answers immediately
• Digits, trailing zeros, and last non-zero digit – Highlights the structure of the number
• Multiplication expansion – Shows the full product for small inputs and a shortened version for large ones
• Neighboring factorial comparison – Organizes (n-1)!, n!, and (n+1)! side by side
• Copy result – Sends the exact value and summary to notes, homework drafts, or chat in one click

How to use it

Type one integer and the result updates immediately. The example buttons also make it easy to jump through common checkpoints such as 0!, 10!, and 100!.

1. Enter an integer n – Type any integer from 0 to 5,000.
2. Read the top card first – Check the n! value, the digit count, and the trailing zeros.
3. Review the exact value – Look at the full integer in the exact-value panel below.
4. Use the expansion and table to verify – Confirm the product structure and the neighboring factorial changes.
5. Copy if needed – Paste the result into notes, homework drafts, or chat.

How the calculation works

The core definition is n! = n × (n-1)!. That relationship makes it easy to see how much larger the current value is than the previous factorial, and the comparison table follows that logic directly.

The reason both 0! and 1! equal 1 is that this convention keeps the recursive definition and the combination formulas consistent. It lets you keep using n! = n × (n-1)! without a break.

The trailing-zero count tells you how many factors of 10 appear in the product. Because there are always more factors of 2 than factors of 5, you only need to count the 5s with ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + .... If you also want to compare nearby square-root or cube-root scales around perfect powers, the Root Calculator gives you another way to read the size of the number.

As the value grows, the exact integer becomes difficult to scan in one line, so this tool also provides a scientific-notation summary at the top. That makes very large answers such as 100!, 500!, and 1000! easier to interpret quickly.

• Digit count – Shows how many digits the result contains
• Trailing-zero count – Shows how many factors of 10 appear in the product
• Last non-zero digit – Shows the final non-zero digit after the trailing zeros are removed
• Neighboring factorial comparison – Summarizes how the current value connects to the previous and next factorial

Frequently asked questions