Pythagorean Theorem Calculator
Enter any two sides of a right triangle and leave the third blank.
Right triangle
Leave exactly one box empty. c is the hypotenuse (the longest side, opposite the right angle).
The theorem
a² + b² = c²
- a, b
- the two shorter sides (legs)
- c
- the hypotenuse
c = √(a² + b²)
a = √(c² − b²)
Worked example
Legs of 3 and 4
- c² = 3² + 4² = 9 + 16 = 25
- c = √25 = 5
The hypotenuse is 5.
Ladder against a wall
- A 5 m ladder with its foot 1.5 m from the wall
- height = √(5² − 1.5²) = √22.75 ≈ 4.77
It reaches about 4.77 m up the wall.
Pythagorean triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 20 | 21 | 29 |
| 9 | 40 | 41 |
Any multiple of a triple also works: 6, 8, 10 or 30, 40, 50.
Common questions
What if the hypotenuse I enter is shorter than a leg?
That triangle cannot exist — the hypotenuse is always the longest side — so the calculator shows an error instead of a result.