Factorial Formula Explained, With Examples
Every factorial result comes from one formula. Once you understand what goes into it, you can sanity-check any figure you are given, whether by an employer, a bank, a teacher or another website.
The formula
n! = 1 × 2 × … × n.
What each input means
- n: the value you enter in the calculator.
Example
For example, with these inputs:
- n: 10
the calculator returns:
- n!: 3,628,800
How the result changes
The table keeps the other inputs at their example values and changes n.
| n | n! |
|---|---|
| 10 | 3,628,800 |
| 5 | 120 |
| 7.5 | 5,040 |
| 12.5 | 479,001,600 |
| 15 | 1.307674e+12 |
Why it matters
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
Each formula has assumptions built in. Area formulas assume flat shapes, volume formulas assume regular solids and statistical measures assume the data you enter is the data you want to describe. Knowing the assumptions helps you pick the right tool.
A quick mental estimate before calculating is a powerful check. If a room's floor area comes out at 4,000 square metres or a percentage comes out above 100% when it should not, you know to look again.
These calculations appear throughout the Singapore syllabus, from primary school percentages and fractions to secondary school algebra and geometry. Understanding the formula makes problem sums easier because you can recognise which quantity is missing.
Related calculations
- Fraction Simplifier: Reduces a fraction to its lowest terms.
- Ratio Simplifier: Simplifies a ratio.
- Decimal to Fraction Converter: Converts a decimal to a fraction.
- Scientific Notation Converter: Writes a number in scientific notation.
Use the Factorial Calculator to plug in your own numbers.
Run your own numbers: Factorial Calculator