Right Triangle Calculator
Solve a right triangle from two legs, a leg and the hypotenuse, or one side and an angle: every side, both angles and the area.
Result
Area: 6 ft²
A measurement, not a material estimate. Nothing is added for waste.
- Hypotenuse c
- 5 ft (60 in, 1.524 m)
- Leg a
- 3 ft (36 in, 0.9144 m)
- Leg b
- 4 ft (48 in, 1.2192 m)
- Angle A
- 36.8699 °
- Angle B
- 53.1301 °
- Perimeter
- 12 ft (144 in, 3.6576 m)
- Altitude to the hypotenuse
- 2.4 ft (28.8 in, 0.7315 m)
- Inscribed circle radius
- 1 ft (12 in, 0.3048 m)
https://calcgallery.com/geometry/right-triangle-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Right Triangle Calculator
- Choose what you know. Both legs, a leg and the hypotenuse, a leg and the angle opposite it, or the hypotenuse and an angle.
- Enter the two values. The legs are the two sides that meet at the right angle. The hypotenuse is the long side opposite it.
- Read the area, then both legs, the hypotenuse, both acute angles and the other measurements below it.
What makes a right triangle easier
A right triangle has one angle of exactly 90 degrees, so only two more parts are needed to solve it. Any two sides will do, or one side and one of the other angles. The two acute angles always add up to 90 degrees, so knowing one gives the other.
The four cases
| You know | The rest |
|---|---|
| Both legs, a and b | c = √(a² + b²) |
| A leg a and the hypotenuse c | b = √(c² − a²) |
| A leg a and its opposite angle A | c = a ÷ sin A, b = a ÷ tan A |
| The hypotenuse c and an angle A | a = c × sin A, b = c × cos A |
In every case the page finds both legs first and calculates everything from them, so the outputs always agree with each other.
Sine, cosine and tangent
For the acute angle A, which is opposite leg a:
sin A = opposite ÷ hypotenuse = a ÷ ccos A = adjacent ÷ hypotenuse = b ÷ ctan A = opposite ÷ adjacent = a ÷ bThat is all trigonometry means on a right triangle: the ratios between its sides, named by the angle they belong to.
Where it turns up
- Rafters. The run and the rise are the legs, and the rafter is the hypotenuse, before any overhang. The roof pitch calculator works in rise per 12.
- Stairs. The total rise and the total run are the legs, and the stringer is the hypotenuse.
- Squaring a layout. A 3-4-5 triangle has an exact right angle, which is how builders check a corner without a large square.
- Ramps and slopes. The angle and the rise give the length of ramp needed. The slope calculator gives the grade as a percentage.
Building codes set limits for stairs, ramps and roofs, and they vary from place to place. This page does the geometry only, so check your local requirements.
With your numbers
- c = √(a² + b²) = √(3 ft² + 4 ft²) = 5 ft
- A = asin(a ÷ c) = 36.8699 °, B = 90° − A = 53.1301 °
- Area = ½ × 3 ft × 4 ft = 6 ft²
Quick reference
A measurement, not a material estimate. Nothing is added for waste.
| Example | Area |
|---|---|
| Legs 3 and 4 ft | 6 ft² |
| Legs 5 and 12 ft | 30 ft² |
| Legs 1 and 1 m | 0.5 m² |
| Leg 6 m, hypotenuse 10 m | 24 m² |
| Leg 6 m opposite 30° | 31.1769 m² |
| Hypotenuse 10 ft at 30° | 21.6506 ft² |
| Rise 4 ft over a 12 ft run | 24 ft² |
Common questions about the Right Triangle Calculator
- Which side is the hypotenuse?
- The side opposite the right angle, which is always the longest side. On a roof it is the rafter, on a ladder against a wall it is the ladder, and on a staircase it is the stringer. If the number you have for it is not longer than both other sides, one of the measurements is wrong, and the page gives no result until it is fixed.
- Can I solve a right triangle from two angles?
- No. Two angles fix the shape but not the size: a 30-60-90 triangle can be any size at all. You need at least one side as well, and the page offers each side with an angle.
- How do I check that a corner is square?
- Use the 3-4-5 rule. Measure 3 units along one wall and 4 along the other, and the diagonal between the two marks should be exactly 5. Any multiple works, such as 6, 8 and 10 feet or 0.9, 1.2 and 1.5 m. A longer diagonal means the corner is wider than 90 degrees, and a shorter one means it is tighter.
- What are the altitude and the inscribed circle radius?
- The altitude is the shortest distance from the right angle to the hypotenuse, ab ÷ c. The inscribed circle is the largest circle that fits inside the triangle, touching all three sides; its radius is (a + b − c) ÷ 2. For a 3-4-5 triangle they are 2.4 and exactly 1.