How is this different from the Pythagorean theorem calculator?

The Pythagorean theorem calculator returns only the one missing side. This right triangle calculator goes further, also giving both acute angles, the area, and the perimeter from the same two inputs.

Which two sides can I enter?

Any two of the three: the two legs, leg a with the hypotenuse, or leg b with the hypotenuse. When you supply a leg and the hypotenuse, the hypotenuse must be the longer of the two.

How are the acute angles found?

Angle A is the inverse tangent of leg a divided by leg b, converted to degrees. Because the three angles of a right triangle sum to 180° and one is 90°, angle B is simply 90° minus angle A.

Right Triangle Calculator

Enter any two values to solve the triangle.

Side a

Side b

Hypotenuse (c)

Area6.0000

Side a3.0000

Side b4.0000

Hypotenuse5.0000

Perimeter12.0000

Angle A36.87deg

Angle B53.13deg

A right triangle has one 90° angle, and knowing any two of its three sides fully determines the rest. This calculator takes two known sides (two legs, or one leg and the hypotenuse) and solves for the missing side, both acute angles, the area, and the perimeter. It is a complete right-triangle solver rather than a single-formula tool.

Formula

c = √(a² + b²); angle A = atan(a / b); area = ½·a·b

a, b: The two legs that meet at the right angle
c: The hypotenuse, opposite the right angle
angle A, angle B: The two acute angles, summing to 90°

How it works

Enter exactly two of the three sides: leg a, leg b, or the hypotenuse. The calculator fills in the third side with the Pythagorean theorem.
It then finds angle A as the inverse tangent of a divided by b, sets angle B to 90° minus angle A, computes the area as half the product of the two legs, and adds all three sides for the perimeter.

Worked example

A right triangle has legs a = 3 and b = 4.

Hypotenuse c = √(3² + 4²) = √25 = 5.
Angle A = atan(3 / 4) ≈ 36.87°, so angle B = 90 - 36.87 ≈ 53.13°.
Area = ½ × 3 × 4 = 6; perimeter = 3 + 4 + 5 = 12.

c = 5, angle A ≈ 36.87°, angle B ≈ 53.13°, area = 6, perimeter = 12.

Frequently asked questions

How is this different from the Pythagorean theorem calculator?: The Pythagorean theorem calculator returns only the one missing side. This right triangle calculator goes further, also giving both acute angles, the area, and the perimeter from the same two inputs.
Which two sides can I enter?: Any two of the three: the two legs, leg a with the hypotenuse, or leg b with the hypotenuse. When you supply a leg and the hypotenuse, the hypotenuse must be the longer of the two.
How are the acute angles found?: Angle A is the inverse tangent of leg a divided by leg b, converted to degrees. Because the three angles of a right triangle sum to 180° and one is 90°, angle B is simply 90° minus angle A.

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Pythagorean Theorem Calculator Triangle Calculator Parallelogram Calculator Distance Calculator