Pythagorean Theorem Formula Explained, With Examples
Every pythagorean theorem 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
c = √(a² + b²).
What each input means
- Side a: the value you enter in the calculator.
- Side b: the value you enter in the calculator.
Example
For example, with these inputs:
- Side a: 3
- Side b: 4
the calculator returns:
- Hypotenuse c: 5
How the result changes
The table keeps the other inputs at their example values and changes side a.
| Side a | Hypotenuse c |
|---|---|
| 3 | 5 |
| 1.5 | 4.272 |
| 2.25 | 4.5894 |
| 3.75 | 5.4829 |
| 4.5 | 6.0208 |
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.
Calculators are best used to check working rather than replace it, especially for exams where method marks count. Work the problem by hand first, then confirm with the calculator.
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.
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.
Related calculations
- Area of an Ellipse Calculator: Calculates the area of an ellipse from the measurements you enter.
- Area of a Rhombus Calculator: Calculates the area of a rhombus from the measurements you enter.
- Area of a Sector Calculator: Calculates the area of a sector from the measurements you enter.
- Circumference of a Circle Calculator: Calculates the circumference of a circle from the measurements you enter.
Use the Pythagorean Theorem Calculator to plug in your own numbers.
Run your own numbers: Pythagorean Theorem Calculator