Pythagorean Theorem Calculator: Find the Hypotenuse or a Side
Choose whether you need the hypotenuse or one of the other sides, enter the two you know and see the answer with the working.
- Nothing you type is stored
- Free
- No signup
Hypotenuse c
5cm
Pythagorean triple- Area
- 6 cm²
- Perimeter
- 12 cm
- Angles
- 36.87° · 53.13° · 90°
Show working
- c² = a² + b²
- c² = 3² + 4² = 9 + 16 = 25
- c = √25 = 5 cm
How to use
- Choose "Find hypotenuse" or "Find a side".
- Enter the two known sides and pick a unit.
- Read the missing side, the angles and the steps.
Good to know
In a right-angled triangle, the square of the hypotenuse (the side opposite the 90° angle) equals the sum of the squares of the other two sides: c² = a² + b². You meet it in NCERT Class 7 and again in Class 10.
To find a shorter side, rearrange: b = √(c² − a²). The hypotenuse is always the longest side, so the calculator stops you if it is not.
When all three sides are whole numbers (like 3-4-5, 5-12-13, 8-15-17) it is a Pythagorean triple and a badge says so. Masons use 3-4-5 with a tape to set a corner square.
Questions
What is the hypotenuse?
The side opposite the right angle. It is always the longest side of a right triangle.
How do I find a missing side when I know the hypotenuse?
Subtract the square of the known side from the square of the hypotenuse and take the square root: b = √(c² − a²).
What are Pythagorean triples?
Sets of whole numbers that fit a² + b² = c², such as 3-4-5, 5-12-13, 7-24-25 and 8-15-17.
Does it work for triangles without a right angle?
No. For other triangles use the triangle calculator, which uses the cosine rule.
Is anything I enter stored?
No. The calculation runs in your browser and nothing is sent to a server.