What makes a right triangle special
A right triangle has exactly one 90° corner. The side facing that corner is the hypotenuse and is always the longest; the two sides forming the right angle are the legs.
Because one angle is already fixed at 90°, the triangle is completely solved as soon as you know any two of its three sides. That is why this calculator only asks for two of leg a, leg b and the hypotenuse.
How the missing parts are found
Given two sides, the rest follow from two well-known relationships:
- The third side comes from the Pythagorean theorem: c² = a² + b².
- Each acute angle comes from the arctangent of the opposite over the adjacent leg.
- The two acute angles always add to 90°, since the third angle uses up the rest of the 180°.
- Area is ½·a·b — half the product of the two legs — and the perimeter is the three sides added together.
Things to watch for
The hypotenuse must be longer than either leg. If you enter a hypotenuse that is shorter than a leg, no such triangle exists and the calculator will flag it.
Keep both entered sides in the same unit. The angles are unit-independent, but the side, area and perimeter outputs inherit whatever unit you typed in.
Formula
c = √(a² + b²); A = atan(a / b); B = atan(b / a); area = ½·a·b.Frequently asked questions
- How many fields do I fill in?
- Exactly two of leg a, leg b and the hypotenuse. The calculator finds the third side and both acute angles.
- Why must the hypotenuse be the largest side?
- It sits opposite the 90° angle, so it is always longer than either leg. The calculator rejects a hypotenuse that is not.