What is the Right Triangle Side and Angle Calculator?
This calculator solves a right triangle when you know its two legs (the sides that form the 90° angle). From legs a and b it instantly returns the hypotenuse c, both acute angles A and B, the area, and the perimeter. It is a universal geometry tool that works in any units (cm, m, inches, feet) as long as both legs use the same unit.
How to use it
Enter the length of side a (the leg opposite angle A) and side b (the leg opposite angle B), then read off the results. There is no need to enter the right angle — it is always 90° by definition of a right triangle.
The formulas explained
The hypotenuse comes from the Pythagorean theorem, $$c = \sqrt{\text{a}^{2} + \text{b}^{2}}$$ The acute angles come from basic trigonometry: $$A = \tan^{-1}\!\left(\frac{\text{a}}{\text{b}}\right)$$ because the tangent of an angle equals opposite over adjacent. Since the three interior angles of any triangle sum to 180° and one is 90°, the remaining angle is $$B = 90^{\circ} - A$$ The area of a right triangle is half the product of its legs, \(\tfrac{1}{2}\cdot\text{a}\cdot\text{b}\), and the perimeter is \(\text{a} + \text{b} + c\).
Worked example
Take the classic 3-4-5 triangle with a = 3 and b = 4. The hypotenuse is $$\sqrt{9 + 16} = \sqrt{25} = 5$$ Angle \(A = \tan^{-1}(3/4) \approx 36.87^{\circ}\), and angle \(B = 90 - 36.87 = 53.13^{\circ}\). The area is $$\tfrac{1}{2} \times 3 \times 4 = 6$$ and the perimeter is \(3 + 4 + 5 = 12\).
FAQ
Which leg is a and which is b? It does not matter for the hypotenuse, area, or perimeter. The labels only determine which acute angle is called A versus B.
What units does it use? Any unit you like — just keep both legs in the same unit. The hypotenuse and perimeter come out in that unit and the area in its square.
Can I enter decimals? Yes, any positive decimal value works for either leg.
