Right Triangle Solver
Enter the two legs of a right triangle and get the hypotenuse, both acute angles, area and perimeter in one step.
How it works
c = √(a² + b²) · A = arctan(a/b) · B = arctan(b/a) · Area = ½·a·b
A right triangle is fully determined by its two legs. The hypotenuse follows from the Pythagorean theorem, and each acute angle is the arctangent of its opposite leg over the adjacent leg. Because one angle is fixed at 90°, the two acute angles always sum to 90° (they are complementary). The area is half the product of the two legs, since they meet at a right angle.
Worked example
For legs a = 3, b = 4: c = √25 = 5, angle A = arctan(3/4) ≈ 36.87°, angle B = arctan(4/3) ≈ 53.13° (and 36.87 + 53.13 = 90), area = ½·3·4 = 6, perimeter = 3 + 4 + 5 = 12.
Sources: Right triangle — Wikipedia
Frequently asked questions
Why do the two non-right angles add to 90°?
The angles of any triangle sum to 180°. One angle here is 90°, so the other two must share the remaining 90° — they are complementary.
Can I solve the triangle from one leg and one angle instead?
Yes in general, using trig ratios, but this calculator is built for the two-legs case, which needs no angle input and avoids ambiguity.
Why is the area just ½·a·b?
The two legs are perpendicular, so one leg is the base and the other is the height. Area of a triangle is ½·base·height.
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This calculator is for educational purposes. Double-check important results before acting on them.