A right triangle has one 90° corner.
About this calculator
A right triangle has one 90° corner. The side opposite that corner — the hypotenuse — is always the longest. The Pythagorean theorem links the three sides: a² + b² = c². Give any two sides and this calculator finds the third, both acute angles, the area, and the perimeter.
Leave the unknown side as 0. The classic 3-4-5 triangle has legs 3 and 4 with hypotenuse 5. If you know the hypotenuse and one leg, the calculator uses c² − a² = b² to find the missing leg — but the hypotenuse must be longer than either leg or the triangle is impossible.
Right triangles appear everywhere: ladder against a wall, roof pitch, diagonal screen size, GPS distance on flat maps. For the pure Pythagorean step-by-step proof use the [[pythagorean]] calculator. For general triangles (not necessarily 90°) try the [[triangle]] calculator. For distance between two coordinate points use the [[distance]] calculator.
Common uses
- Find hypotenuse length from two known legs — construction and layout work
- Find a missing leg when you know the hypotenuse and one side
- Compute roof pitch angles or ladder reach problems
- Verify 3-4-5 or 5-12-13 triples in carpentry squares
- School geometry — area and perimeter from two given sides
Frequently asked questions
How do I find the hypotenuse of a 3-4-5 triangle?
Enter leg a = 3, leg b = 4, leave hypotenuse as 0. The calculator returns c = √(9 + 16) = 5. Area = 6 square units and the two acute angles are about 36.87° and 53.13°.
What happens if I enter all three sides?
The calculator needs exactly two known sides. If all three are positive it may not know which one to solve. Leave the unknown side as 0 and fill in the other two.
Can the hypotenuse be shorter than a leg?
No. If your inputs imply c ≤ a or c ≤ b, the triangle is invalid — the calculator shows a warning. The hypotenuse must always exceed both legs in a right triangle.
How are the angles calculated?
Once all three sides are known, angle A = arctan(a/b) and angle B = arctan(b/a). They always sum to 90° because the third angle is the right angle.
What if I only know the hypotenuse and one leg?
Enter the hypotenuse in side c and the known leg in side a or b. Leave the other leg as 0. The calculator subtracts squares: b = √(c² − a²). Example: c = 13, a = 5 gives b = 12.