Right Triangle Calculator
Give two sides of a right triangle to find the third side, both acute angles, and the area.
Leg a
3
Leg b
4
Hypotenuse c
5
Area
6
Area = ½ × a × b. Legs of 3 and 4 give a hypotenuse of 5 and an area of 6.
Angle opposite a
36.8699°
Angle opposite b
53.1301°
How it works
A right triangle has one 90° corner, and its three sides obey the Pythagorean theorem: a² + b² = c², where c is the hypotenuse, the longest side. Give any two sides and the third is fixed.
Enter two of the three lengths and leave the unknown blank. The tool squares and adds (or subtracts) as needed to find the missing side, then uses the arctangent of the legs to report both acute angles, which always add up to 90°.
The area is half the product of the two legs, since the legs meet at a right angle and act as base and height. Classic legs of 3 and 4, for example, give a hypotenuse of 5 and an area of 6.
Frequently asked questions
Which two sides should I enter?
Any two — two legs, or one leg and the hypotenuse. Fill in the two you know and leave the third box empty so the tool can solve for it.
How are the angles worked out?
From the legs. The angle opposite leg a is arctan(a / b), and the other acute angle is whatever's left over to reach 90°. The right angle itself is fixed at 90°.
Why must the hypotenuse be the longest side?
It sits opposite the right angle, the triangle's largest angle, so it's always longer than either leg. If you enter a hypotenuse shorter than a leg, no real triangle exists and the tool asks you to fix it.