How this calculator works
In a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.
Hypotenuse: c = √(a² + b²). Missing leg: b = √(c² − a²); the hypotenuse must be the longest side.
Area is a × b ÷ 2, because the two legs are the base and height.
The angles come from trigonometry: one acute angle is arctan(a ÷ b), and the two acute angles add up to 90°.
Worked example
Legs of 3 and 4
- c = √(9 + 16) = √25 = 5.
- Area: 3 × 4 ÷ 2 = 6. Perimeter: 12.
- Angles: 36.87°, 53.13° and 90°.
Questions people ask
How do builders check for a square corner?
With the 3-4-5 rule: measure 3 units along one side and 4 along the other; if the diagonal is exactly 5, the corner is 90°.
Does it work for non-right triangles?
No. For other triangles use the law of cosines, c² = a² + b² − 2ab·cos(C).
What is a Pythagorean triple?
Three whole numbers that fit the theorem, such as 3-4-5, 5-12-13 and 8-15-17.
How do I find a TV or screen diagonal?
Treat width and height as the two legs. A screen 48 inches wide and 27 inches high has a diagonal of √(48² + 27²) ≈ 55 inches.
Last reviewed October 2, 2026