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Hypotenuse formula
Square each leg, add the squares, then take the square root of the total.
c = √(a² + b²)
Worked example
For legs 5 and 12, c = √(25 + 144) = √169 = 13.
Use the longest side as a reasonableness check
The hypotenuse must be longer than either individual leg, but shorter than the sum of the two legs.
Common mistakes
- Adding the legs before squaring them.
- Forgetting the final square root.
- Calling a shorter leg the hypotenuse.
Frequently asked questions
What is the hypotenuse?
It is the longest side of a right triangle and sits opposite the 90° angle.
Does this work for every triangle?
No. The Pythagorean theorem in this form applies to right triangles.
What is the hypotenuse of a 5-12-13 triangle?
13.