Right Triangle Calculator
A right triangle with legs of 3 and 4 has a hypotenuse of 5. This right triangle calculator solves a triangle from its two legs. Enter the two shorter sides and it returns the hypotenuse using the Pythagorean theorem, plus the area, the perimeter, and both acute angles in degrees. It is built for right triangles, where one angle is exactly 90 degrees.
Quick answer
A right triangle has one 90-degree angle, and the side opposite it is the hypotenuse.
What this tells you
- •A right triangle has one 90-degree angle, and the side opposite it is the hypotenuse.
- •The two legs are the sides that form the right angle.
- •The hypotenuse comes from the Pythagorean theorem, a squared plus b squared equals c squared.
- •The two acute angles always add up to 90 degrees.
How to Use
- 1Enter the length of the first leg (side a).
- 2Enter the length of the second leg (side b) in the same units.
- 3Click Calculate to get the hypotenuse, area, perimeter, and both acute angles.
How It Works
Formula
c = sqrt(a^2 + b^2), area = (a x b) / 2, perimeter = a + b + cThe hypotenuse uses the Pythagorean theorem: square both legs, add them, and take the square root. The area of a right triangle is half the product of the two legs. The acute angles come from the inverse tangent of the leg ratio. For legs of 3 and 4, the hypotenuse is 5, the area is 6, and the angles are about 36.87 and 53.13 degrees.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
The 3-4-5 right triangle
Square the legs (9 and 16), add to get 25, and take the square root for a hypotenuse of 5. The area is 3 x 4 / 2 = 6, and the angles are about 36.87 and 53.13 degrees.
Equal legs of 1 (a 45-45-90 triangle)
When both legs are equal, the hypotenuse is the square root of 2, about 1.4142, and the two acute angles are each 45 degrees.
Common Right Triangles
Leg pairs and the resulting hypotenuse, area, and angles.
| Legs (a, b) | Hypotenuse | Area | Acute Angles |
|---|---|---|---|
| 3, 4 | 5 | 6 | 36.87 and 53.13 |
| 6, 8 | 10 | 24 | 36.87 and 53.13 |
| 5, 12 | 13 | 30 | 22.62 and 67.38 |
| 1, 1 | 1.4142 | 0.5 | 45 and 45 |
Common mistakes
- Using the hypotenuse as one of the legs. Enter the two shorter sides that form the right angle, not the long side opposite it.
- Forgetting to square the legs before adding. The Pythagorean theorem adds the squares of the legs, not the legs themselves.
- Mixing units. Both legs must be in the same unit, so convert before calculating if one is in feet and one is in inches.