Right triangle calculator
Solve a right triangle: every side and angle, the area and perimeter from two values.
About this calculator
This right triangle calculator solves the whole triangle from any two values: two sides, or one side and one angle.
It gives both legs, the hypotenuse, both angles, the area, the perimeter and the height to the hypotenuse.
How it works
With the right angle at C, a² + b² = c², sin A = a ÷ c, cos A = b ÷ c and tan A = a ÷ b. The other two angles add up to 90°, so any two values, at least one of them a side, fix the whole triangle.
Last reviewed:
Worked example
- I know: Both legs, a and b
- Leg a: 3
- Leg b: 4
Hypotenuse c: 5
Common questions
How do I find the missing side of a right triangle?
With two sides, use a² + b² = c². With one side and an angle, use sine, cosine or tangent.
How do I find the angles of a right triangle?
Use the inverse functions, such as A = tan⁻¹(a ÷ b). In a 3-4-5 triangle the angles are about 36.87° and 53.13°.
What are special right triangles?
The 45-45-90 triangle has sides in the ratio 1 : 1 : √2, and the 30-60-90 triangle has sides in the ratio 1 : √3 : 2.
Sources and further reading
The story behind it
Where the idea came from: A Babylonian clay tablet known as Plimpton 322, written around 1800 BC, lists the sides of right triangles more than a thousand years before Pythagoras.
Carpenters still use the 3-4-5 triangle to check that corners are square. Trigonometry, from the Greek for measuring triangles, grew out of solving right triangles like these.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
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