How to Calculate Pythagorean Theorem: A Step-by-Step Guide
Finds the hypotenuse of a right triangle.
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.
What you need
- Side a
- Side b
Step by step
- Enter the side a.
- Enter the side b.
- The results update as you type, or press Calculate.
- Read the hypotenuse c first, then the supporting figures below it.
The formula
c = √(a² + b²).
Worked example
For example, with these inputs:
- Side a: 3
- Side b: 4
the calculator returns:
- Hypotenuse c: 5
A second example
Now change the inputs to:
- Side a: 3.75
- Side b: 4
the calculator returns:
- Hypotenuse c: 5.4829
Practical tips
- Round only at the final step to avoid accumulated rounding errors.
- Estimate the answer roughly first so you can spot a result that is clearly wrong.
- For exam work, show your method; marks are often given for working, not just the answer.
- When numbers are very large or small, scientific notation makes them easier to compare.
Background
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.
In everyday life the same maths shows up in discounts, recipe scaling, renovation measurements and comparing prices per unit. Being comfortable with it saves money and avoids costly measuring mistakes.
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.
Want to skip the arithmetic? The free Pythagorean Theorem Calculator does all of this instantly and updates as you type.
Run your own numbers: Pythagorean Theorem Calculator