The area of a right triangle is half of the rectangle formed by its legs. It is needed for gable walls, triangular garden beds, sails and roof sections.
How to use the Right Triangle Area Calculator
- What do you know?
- Leg a (opposite α)
- Leg b (adjacent to α)
- Hypotenuse c
- Angle α
- Area
Results update as you type, and everything is calculated in your browser.
How it works
Choose what you know; missing legs are computed first and the area is half their product.
Inputs explained
| Field | What to enter |
|---|---|
| What do you know? | Choose one: Legs a and b, Leg a and hypotenuse c, Leg b and hypotenuse c, Angle α and leg a … |
| Leg a (opposite α) | Units: cm, m, mm, in, ft, yd … |
| Leg b (adjacent to α) | Units: cm, m, mm, in, ft, yd … |
| Hypotenuse c | Units: cm, m, mm, in, ft, yd … |
| Angle α | Units: °, rad, π rad, grad, turn |
| Area | Units: cm², m², mm², in², ft², yd² … |
What each result means
- Hypotenuse c = sqrt([Leg a]^2 + [Leg b]^2)
- Angle α = deg(atan([Leg a]÷[Leg b]))
- Angle β = 90 – [Angle α]
- Area = [Leg a]×[Leg b]÷2
- Perimeter = [Leg a] + [Leg b] + [Hypotenuse c]
- Height to the hypotenuse = [Leg a]×[Leg b]÷[Hypotenuse c]
Example values
How the main result changes when Leg a changes and everything else stays at the example values above:
| Leg a (opposite α) (cm) | Area (cm²) |
|---|---|
| 1.5 | 3 |
| 2.25 | 4.5 |
| 3 | 6 |
| 3.75 | 7.5 |
| 4.5 | 9 |
| 6 | 12 |
Formula
Area = a·b/2 = (c²·sin 2α)/4
Worked example
Inputs — What do you know?: Legs a and b; Leg a (opposite α): 3 cm; Leg b (adjacent to α): 4 cm.
Results — Leg a = 3 cm; Leg b = 4 cm; Hypotenuse c = 5 cm; Angle α = 36.869898 °; Angle β = 53.130102 °; Area = 6 cm²; Perimeter = 12 cm; Height to the hypotenuse = 2.4 cm.
Key terms
- Leg
- A side forming the right angle.
Frequently asked questions
What is the area of a right triangle with legs 3 and 4?
6.
Why is it half the product of the legs?
Two copies of the triangle form a rectangle.
Can I find the area from the hypotenuse alone?
No – you need one more value.
Which is the base and which the height?
Either leg can be the base; the other is the height.