How to use the Pythagorean Theorem Calculator
Enter the lengths of the two shorter sides of a right triangle in the same unit. The result is the hypotenuse, the side opposite the right angle.
Worked example
A ladder reaches 4 m up a wall with its foot 1 m out from the wall. The ladder length is √(4² + 1²) = √17, about 4.12 m. The famous 3, 4, 5 triangle works the same way: 3² + 4² = 9 + 16 = 25, and √25 = 5.
Checking a corner is square
Builders use the 3, 4, 5 rule to check right angles. Measure 3 units along one wall and 4 along the other. If the diagonal between those marks is exactly 5, the corner is square. Scale it up to 6, 8 and 10 for larger rooms. To find a missing short side, use b = √(c² − a²).
The formula
c = √(a² + b²)
Examples
- Legs 3 and 4
Hypotenuse: 5
- Legs 5 and 12
Hypotenuse: 13
- Legs 8 and 15
Hypotenuse: 17
Limitations and assumptions
Only for right angled triangles. For other triangles, use the law of cosines.
Frequently asked questions
What is the Pythagorean theorem?
In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
How do I find a missing leg?
Rearrange to a = √(c² − b²). Use the hypotenuse and the known leg.
What is a Pythagorean triple?
Three whole numbers that satisfy the theorem, such as 3-4-5, 5-12-13 and 8-15-17.
Does it work for any triangle?
Only right triangles, which have one 90 degree angle.