Pythagorean Theorem Calculator
Solve a right triangle with the Pythagorean theorem. Find the hypotenuse from the two legs, or a missing leg from the hypotenuse and the other leg, and see the area, perimeter, and angles.
Hypotenuse (c)
5
Check the highlighted fields to see your result.
- Area
- 6
- Perimeter
- 12
- Acute angles
- 36.87° / 53.13°
Results are estimates for information only and do not constitute financial, medical, or legal advice.
How the theorem works
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. To find the hypotenuse, add the squares of the legs and take the square root. To find a leg, subtract the square of the known leg from the square of the hypotenuse and take the square root.
The formulas
a² + b² = c²
c = √(a² + b²) · b = √(c² − a²)
Worked example
The legs of a right triangle are 3 and 4.
- 3² + 4² = 9 + 16 = 25.
- c = √25 = 5.
- Area: 3 × 4 ÷ 2 = 6. Perimeter: 3 + 4 + 5 = 12.
Frequently asked questions
Does the Pythagorean theorem work for any triangle?
No, only for right triangles, which have one 90° angle. The hypotenuse is always the side opposite that angle, and it is always the longest side.
What are Pythagorean triples?
Sets of three whole numbers that fit a² + b² = c², like 3-4-5, 5-12-13, and 8-15-17. Builders use 3-4-5 to check that a corner is square: measure 3 units on one side and 4 on the other, and the diagonal should be exactly 5.
Can I use it to find a distance?
Yes. The straight-line distance between two points is the hypotenuse of a right triangle whose legs are the horizontal and vertical differences. For example, the diagonal of a 16:9 TV screen.