Right Triangle Calculator
From the two legs of a right triangle, get the hypotenuse, both acute angles, the area and the perimeter.
How it works
c = √(a² + b²) · A = tan⁻¹(a ÷ b) · B = 90° − A · Area = ½ · a · b · Perimeter = a + b + c
A right triangle is fully determined by its two legs. The hypotenuse comes from the Pythagorean theorem, and each acute angle comes from the tangent of the opposite leg over the adjacent leg. Because the right angle already uses 90°, the two acute angles always add up to the remaining 90°. The area is half the product of the legs, since the legs are a perpendicular base and height.
Worked example
Legs a = 3 and b = 4: hypotenuse c = √(9 + 16) = √25 = 5 — the classic 3-4-5 triangle. Angle A = tan⁻¹(3 ÷ 4) ≈ 36.87°, so angle B ≈ 53.13°. Area = ½ × 3 × 4 = 6 and perimeter = 3 + 4 + 5 = 12.
Sources: Right triangle — Wikipedia
Frequently asked questions
Why do the two non-right angles add to 90°?
Every triangle’s angles sum to 180°. The right angle takes 90°, leaving exactly 90° for the other two, so they are complementary — as one grows, the other shrinks by the same amount.
What if I know the hypotenuse and one leg instead?
Use the Pythagorean Theorem Calculator, which solves for a missing leg from the hypotenuse and the other leg. This calculator starts from the two legs.
How is the area half the product of the legs?
The two legs meet at the right angle, so one is a base and the other is the perpendicular height. Area = ½ × base × height becomes ½ × a × b with no extra trig needed.
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This calculator is for educational purposes. Double-check important results before acting on them.