Right triangle calculator
Enter any two values, sides or angles, and get the rest of the right triangle: all sides, both acute angles, area, perimeter and the height to the hypotenuse.
Special right triangles
SOH CAH TOA
- sin A = opposite / hypotenuse = a / c
- cos A = adjacent / hypotenuse = b / c
- tan A = opposite / adjacent = a / b
- a² + b² = c²
The 30-60-90 triangle is half an equilateral triangle, which is why its hypotenuse is exactly twice the short leg. The 45-45-90 triangle is half a square, so its hypotenuse is the square’s diagonal, x√2.
Not a right triangle? Use the triangle calculator. Just need the hypotenuse? The Pythagorean theorem calculator shows the tile-square proof.
Show me the steps
An AI tutor walks through the working for this exact result. The answer above is computed in your browser; the explanation is optional and is the only thing that leaves your device.
Solve the right triangle given Leg a = 5 and Hypotenuse c = 13 = Leg a = 5; Leg b = 12; Hypotenuse c = 13; Angles A / B / C = 22.6198649° / 67.3801351° / 90°
Questions people ask
How do I solve a right triangle?
You need two values, at least one of them a side. With two sides, use the Pythagorean theorem for the third and an inverse trig function for the angles. With a side and an angle, use SOH CAH TOA: sin A = a/c, cos A = b/c, tan A = a/b.
What is the 45-45-90 rule?
In an isosceles right triangle, the two legs are equal and the hypotenuse is a leg times √2 (about 1.414). A square cut along its diagonal makes two of them.
What are the side ratios of a 30-60-90 triangle?
1 : √3 : 2. The side opposite 30° is the shortest (x), opposite 60° is x√3, and the hypotenuse is 2x. It is half of an equilateral triangle.
How do I find the 3 sides of a triangle?
For a right triangle, any two values with at least one side determine the rest; enter them above. For other triangles you need three values; use the general triangle calculator, which applies the law of sines and cosines.
How do I find an angle from two sides?
Use the inverse function that matches the sides you know: A = sin⁻¹(a/c), A = cos⁻¹(b/c) or A = tan⁻¹(a/b). The other acute angle is 90° − A.