Home/Math/Right Triangle Calculator – Sides, Angles & Area

📐Right Triangle Calculator

Find missing sides and angles of a right triangle instantly. Enter any two values and get the rest — hypotenuse, legs, angles, area, and perimeter. Free online tool with step-by-step solutions.

Angle Unit:

Please provide 2 values below to calculate the other values of a right triangle.

∠α

∠β

A (area)

P (perimeter)

Right Triangle

A right triangle has one 90° angle. The side opposite the right angle is the hypotenuse (c), the longest side. The altitude (h) is the length from the right angle vertex to the hypotenuse, dividing the triangle into two smaller similar triangles.

Pythagorean triples are right triangles with integer sides: 3-4-5, 5-12-13, 8-15-17, etc.

Special Right Triangles

30°-60°-90° Triangle

Ratio: 1 : √3 : 2
Given 60° side = 5: a = 5/√3, c = 10/√3
Used for evaluating trig functions of π/6.

45°-45°-90° Triangle

Ratio: 1 : 1 : √2 (isosceles right triangle)
Given c = 5: a = 5/√2
Used for evaluating trig functions of π/4.

Key Takeaways

Hypotenuse is longest

Side c is always the longest side, opposite the 90° angle.

Angles sum to 180°

α + β + 90° = 180°, so α + β = 90° (complementary).

Pythagorean Triples

Common integer triples: 3-4-5, 5-12-13, 7-24-25, 8-15-17.

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