Pythagorean Theorem Calculator
Choose which side is unknown and enter the other two. The calculator applies a² + b² = c² and reports the remaining properties of the triangle.
Result
- Area
- 6
- Perimeter
- 12
- Angle opposite side a
- 36.8699°
- Angle opposite side b
- 53.1301°
- Working
- c = √(3² + 4²) = √25
Formula
- a² + b² = c²
- c = √(a² + b²)
- a = √(c² − b²)
- Area = a × b ÷ 2
How the Pythagorean Theorem Calculator works
In a right triangle, the square on the longest side equals the sum of the squares on the other two. The longest side, opposite the right angle, is the hypotenuse.
The theorem is the basis for measuring diagonals, checking that corners are square, and finding distances between points. Builders use the 3-4-5 triangle to lay out right angles.
Worked example
With legs of 3 and 4: c = √(3² + 4²) = √(9 + 16) = √25 = 5. The area is 3 × 4 ÷ 2 = 6 and the angles are 36.87° and 53.13°.
Frequently asked questions
How do I find the diagonal of a rectangle?
Treat the length and width as the two legs. A 12 by 16 rectangle has a diagonal of √(144 + 256) = 20.
What are Pythagorean triples?
Sets of three whole numbers that satisfy the theorem, such as 3-4-5, 5-12-13, 8-15-17 and 7-24-25.
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