Right Triangle Calculator
Enter the two legs, and find the hypotenuse, both acute angles, area and perimeter — the whole triangle at once.
How to use the right triangle calculator
- Enter the length of leg a (one of the two sides meeting at the right angle).
- Enter the length of leg b.
- The hypotenuse, both acute angles, area and perimeter update automatically.
How is a right triangle solved?
In a right triangle, one angle is always 90°. Given the two legs (the sides meeting at the right angle), the whole triangle can be solved: the hypotenuse is found with the Pythagorean theorem (c = √(a² + b²)), the two acute angles with inverse tangent (A = arctan(a/b)), the area with ½ × a × b, and the perimeter as the sum of all three sides.
Worked example: a right triangle with legs of 3 and 4 has a hypotenuse of √(3² + 4²) = √25 = 5. The angles follow from the tangent: arctan(3 ÷ 4) = 36.87° and arctan(4 ÷ 3) = 53.13°, which sum to 90° as they must in a right triangle. The area is 3 × 4 ÷ 2 = 6 and the perimeter 3 + 4 + 5 = 12.
Frequently asked questions
What's the difference between this and a plain Pythagorean theorem calculator?
A plain Pythagorean theorem calculator only finds the missing side. This calculator solves the entire triangle at once — hypotenuse, both angles, area and perimeter — given the two legs.
Why is arctan (inverse tangent) used to find the angles?
Because the tangent of an angle in a right triangle is the ratio of the opposite to the adjacent leg (tan(A) = a/b). To go the other way — from the ratio to the angle itself — we use the inverse function, arctan.
Does this calculator work if I know the hypotenuse instead?
No, this calculator is designed to start from the two legs. If you instead know the hypotenuse and one leg, you can use the Pythagorean theorem manually to find the other leg first.