Right Triangle Calculator (Pythagorean Theorem)
Solve a right triangle's missing side, area, perimeter, and angles from either its two legs or its hypotenuse and one leg.
- Leg A
- 3
- Leg B
- 4
- Hypotenuse
- 5
- Area
- 6
- Perimeter
- 12
- Angle opposite Leg A
- 36.87°
- Angle opposite Leg B
- 53.13°
How it works
The Pythagorean theorem relates a right triangle's sides as a² + b² = c², where c is the hypotenuse (the side opposite the right angle) and a, b are the two legs. Given two legs, the hypotenuse is c = √(a² + b²); given the hypotenuse and one leg, the other leg is the rearranged form, a = √(c² − b²).
From the three sides, area = ½ × leg A × leg B and perimeter is the sum of all three sides. The two non-right angles are found with inverse sine (the angle opposite a leg has sine = that leg ÷ hypotenuse) and always add up to 90°, since all three angles of any triangle sum to 180° and one of them here is already 90°.
FAQ
Why does the calculator ask for 'the known leg' when solving from the hypotenuse?
Given only the hypotenuse and one leg, the Pythagorean theorem determines the other leg uniquely — that known leg must be shorter than the hypotenuse, since the hypotenuse is always a right triangle's longest side.