Right Triangle Calculator

Enter both legs, or one leg and the hypotenuse. The page returns the third side, both acute angles, area (unit²) and perimeter (unit).

How it works

The right angle sits between the legs. The hypotenuse is √(a²+b²). The angle opposite a is arctan(a/b); the other acute angle is 90° minus that, so they add to 90°. Area is ½ab — a length² — while the sides stay in the length unit.

The hypotenuse must be longer than a known leg.

Formula

c = √(a² + b²)
∠A = arctan(a / b),  ∠B = 90° − ∠A
Area = ½ab
Perimeter = a + b + c

Worked examples

Legs 3 and 4
a = 3, b = 4 → c = 5, area 6, angles ≈ 36.87° and 53.13°
Leg and hypotenuse
leg 3, hypotenuse 5 → other leg 4

Useful notes

This assumes the 90° angle is between a and b.
For a non-right triangle, use the triangle calculator.

FAQ

How do I solve a right triangle from two legs?: Hypotenuse is √(a²+b²). Area is ½ab. The acute angles are arctan(a/b) and its complement.
Why are area and sides in different units?: Sides are lengths. Area is length times length. A 3 cm by 4 cm triangle has a 5 cm hypotenuse and a 6 cm² area.
Is this the same as the Pythagorean page?: Pythagoras finds one missing side. This page also reports angles, area and perimeter.

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