Pythagorean Theorem Calculator
Enter any two sides of a right triangle. Get the third, exact and in decimals.
How it works
In a right triangle, a² + b² = c², where c is the hypotenuse, the side across from the right angle and always the longest. It only works on right triangles.
Example
A right triangle has legs 5 and 12. Find the hypotenuse.
c = 13
Steps
- a² + b² = c²: 5² + 12² = 25 + 144 = 169.
- Take the square root: c = √169 = 13.
More examples
A 10 ft ladder reaches 8 ft up a wall. How far is its foot from the wall?
b = 6
Steps
- b² = c² − a²: 10² − 8² = 100 − 64 = 36.
- Take the square root: b = √36 = 6.
A right triangle has legs 1 and 1. Find the hypotenuse.
c = √2 ≈ 1.4142
Steps
- a² + b² = c²: 1² + 1² = 1 + 1 = 2.
- Take the square root: c = √2 = √2 ≈ 1.4142.
Common mistake
To find a leg, subtract: a² = c² − b². Adding gives a “leg” longer than the hypotenuse, which can’t happen.
Questions
What are Pythagorean triples?
Whole-number sides that fit the theorem: 3-4-5, 5-12-13, 8-15-17 and 7-24-25. Multiples work too, like 6-8-10.
How can I tell if a triangle has a right angle?
Check a² + b² = c² with c as the longest side. For 7, 24 and 25: 49 + 576 = 625, so it does.
Does it work in 3D?
Yes, used twice. The diagonal of a 3 × 4 × 12 box is √(9 + 16 + 144) = 13.