Right Triangle Calculator
Provide 2 values below to calculate all other values of a right triangle. If radians are selected, values like pi/4 are accepted for angles.
Key formulas
a² + b² = c²
α + β = 90°
A = ½ab
α + β = 90°
A = ½ab
Right triangle
A right triangle has one 90° angle. The side opposite the right angle is the hypotenuse (c). The other two sides are legs (a and b). Right triangles are central to trigonometry and the Pythagorean theorem.
Pythagorean theorem
a² + b² = c²
Example: If a = 3 and b = 4, then c = √(9+16) = 5.
Trigonometry in right triangles
sin(α) = a/c | cos(α) = b/c | tan(α) = a/b
Angles α and β are complementary: α + β = 90°.
Area, perimeter, and altitude
Area = ½ × a × b
Perimeter = a + b + c
Altitude to hypotenuse: h = ab/c
How to use this calculator
- Enter any two known values (e.g. legs a and b, or leg a and hypotenuse c).
- Leave unknown fields blank.
- Click Calculate — all sides, angles, area, perimeter, and altitude are computed.
Frequently Asked Questions
Side c is the hypotenuse — the longest side, opposite the right angle.
You need at least one side length (or area with a side) to determine scale. Two angles alone only fix shape, not size.