Right Triangle Calculator
Calculate sides, angles, area, and trig ratios of a right triangle from any two known values.
Right triangle
Enter any 2 valuesFormula
- a, b
- Legs of the triangle — the two sides that form the 90° angle
- c
- Hypotenuse — the side opposite the right angle (always the longest)
- A, B
- Acute angles at vertices a and b. Sum: A + B = 90°
- Enter any 2 values to see the full solution.
Once any 2 values are set, the remaining 3 are derived from the Pythagorean theorem and inverse trig. The two acute angles always sum to 90°.
Examples
How It Works
The Pythagorean theorem (a² + b² = c²) relates the three sides. If you know any two sides, you can find the third. The acute angles are found using trigonometric ratios: sin A = opposite/hypotenuse = a/c, cos A = adjacent/hypotenuse = b/c, tan A = opposite/adjacent = a/b.
The area of a right triangle is simply ½ × a × b (half the product of the two legs), and the perimeter is a + b + c. This calculator also shows all six trig ratios (sin, cos, tan) for each acute angle.
Tips & Best Practices
Frequently Asked Questions
How do I find the hypotenuse?
Use the Pythagorean theorem: c = √(a² + b²). Square both legs, add them, then take the square root.
How do I find a leg if I know the hypotenuse and the other leg?
Rearrange the Pythagorean theorem: a = √(c² − b²). Square the hypotenuse, subtract the square of the known leg, then take the square root.
How do I find an angle from two sides?
Use inverse trig functions. For example, if you know the opposite side (a) and hypotenuse (c), angle A = arcsin(a/c). Convert from radians to degrees if needed.
What are Pythagorean triples?
Pythagorean triples are sets of three positive integers (a, b, c) where a² + b² = c². Common examples: (3,4,5), (5,12,13), (8,15,17), (7,24,25). Any multiple of a triple is also a triple.