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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.

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