Pythagorean theorem calculator: find the missing side
In a right triangle, a² + b² = c², where c is the hypotenuse (the side facing the right angle). Pick the unknown side.
Result
13Hypotenuse c
- c = √(a² + b²) = √(25 + 144) = √169 = 13
- Check: 5² + 12² = 25 + 144 = 169 = 13²
- Perimeter (a + b + c)
- 30
- Area (a × b ÷ 2)
- 30
Inputs
- Side to find
- Hypotenuse c
- Leg a
- 5
- Leg b
- 12
How it is calculated
c² = a² + b², so c = √(a² + b²).
Result
Hypotenuse c
- Perimeter (a + b + c)
- 30
- Area (a × b ÷ 2)
- 30
How it is calculated
- c² = a² + b², so c = √(a² + b²).
- For a leg: a = √(c² − b²).
- The hypotenuse must always be the longest side.
Example
a = 5 and b = 12: c = √(25 + 144) = √169 = 13. Perimeter 30, area 30.
Good to know
- Only valid for a right triangle. For other triangles, use the law of cosines.
- If the hypotenuse is shorter than another side, the triangle is impossible.
- All sides must use the same unit.
Frequently asked questions
What is this tool used for?
In a right triangle, a² + b² = c², where c is the hypotenuse (the side facing the right angle). Pick the unknown side.
How is the result calculated?
c² = a² + b², so c = √(a² + b²).
What should I check before using the result?
Only valid for a right triangle. For other triangles, use the law of cosines.