# Right Triangle Area Calculator

URL: https://speedycalculator.com/calculators/math/right-triangle-area/
Last updated: 2026-10-30

> The right triangle area calculator finds the area of a right triangle from two legs, a leg and the hypotenuse, or a side and an acute angle.

## Inputs

- What do you know?
- Leg a (opposite α) (cm, m, mm, in, ft, yd, km, mi)
- Leg b (adjacent to α) (cm, m, mm, in, ft, yd, km, mi)
- Hypotenuse c (cm, m, mm, in, ft, yd, km, mi)
- Angle α (°, rad, π rad, grad, turn)
- Area (cm², m², mm², in², ft², yd², km², ha, acre)

## Results

- Leg a
- Leg b
- Hypotenuse c
- Angle α
- Angle β
- Area
- Perimeter
- Height to the hypotenuse

## Formula

```
Area = a·b/2 = (c²·sin 2α)/4
```

## Explanation

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

FieldWhat to enterWhat 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 cUnits: cm, m, mm, in, ft, yd …Angle αUnits: °, rad, π rad, grad, turnAreaUnits: 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)1.532.254.5363.757.54.59612

## 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.

## FAQ

**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.


## Sources

- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)