Pythagorean Theorem Calculator
Pythagorean theorem calculator: find the hypotenuse or a missing leg of a right triangle, plus its area and perimeter, step by step.
Editorial review: Farrow (pseudonym; identity and professional credentials are not disclosed). This page is for educational purposes, not professional advice.
Your inputs
Results update as you type. Nothing you enter leaves your device.
Results
- Area
- 6
- Perimeter
- 12
Example with the starting values
These results use the calculator's initial inputs. Change the values above to calculate your own estimate.
Inputs
- Find the
- Hypotenuse (c)
- Side a (leg)
- 3
- Side b (leg, or hypotenuse when finding a leg)
- 4
Results
- Hypotenuse c
- 5
- Area
- 6
- Perimeter
- 12
How does the Pythagorean Theorem Calculator work?
In a right triangle with legs a and b and hypotenuse c, a² + b² = c². To find the hypotenuse, c = √(a² + b²). A 3-4 triangle gives √(9 + 16) = 5.
To find a missing leg, enter the known leg as side a and the hypotenuse as side b, then b² − a² = (missing leg)². The hypotenuse must be longer than the leg, or there is no triangle.
Frequently asked questions
How do I find the hypotenuse?
Square both legs, add them, and take the square root. Legs 5 and 12 give √(25 + 144) = 13.
How do I find a missing leg?
Subtract the squared known leg from the squared hypotenuse, then take the square root. With c = 13 and a = 5, the other leg is √(169 − 25) = 12.
What are common Pythagorean triples?
3-4-5, 5-12-13, 8-15-17 and 7-24-25 are whole-number right triangles. Any multiple of a triple also works, such as 6-8-10.
Does the theorem work for any triangle?
No, only right triangles, which have one 90 degree angle. For other triangles use the law of cosines, c² = a² + b² − 2ab·cos(C).