Area of a Right Triangle Calculator

If you are wondering how to find right triangle area, you're in the right place - this area of a right triangle calculator is a tool for you. Whether you're looking for the equation given triangle legs, leg and hypotenuse or side and angle, you won't be disappointed - this calculator has all of them implemented. Scroll down to find out more about area of right triangle formulas or simply give our calculator a try!

The basic equation is a transformed version of a standard triangle height formula (a * h / 2). Because the right triangle legs are perpendicular to each other, one leg is taken as a base and the other is a right triangle height:

area = a * b / 2

Sometimes it's not so obvious - you have other values given, not two legs. Then what?

1. If you have one leg and hypotenuse given, use the Pythagorean theorem to find the missing leg:

   a² + b² = c²

Then take a square root of the transformed equation:

• given a and c we find that b = √(c² - a²):

  area = a * √(c² - a²) / 2

• given b and c we calculate that a = √(c² - b²):

  area = b * √(c² - b²) / 2

2. If you know one angle and hypotenuse, you can use the law of sines:

   a = c * sin(α) b = c * sin(β) = c * sin(90-α) = c * cos(α)

   area = c² * sin(α) * cos(α) / 2

3. Given one angle and one leg, find the area using e.g. trigonometric functions:

   a/b = tan(α) and b/a = tan(β)

   area = b * tan(α) * b / 2 = b² * tan(α) / 2

   area = a * a * tan(β) / 2 = a² * tan(β) / 2

If you've just noticed that your triangle is not a right triangle, check out this general triangle area tool.

Isosceles right triangle is a special right triangle, sometimes called a 45-45-90 triangle. In such triangle the legs are equal in length (as a hypotenuse always must be the longest of the right triangle sides):

a = b

One leg is a base and the other is the height - there is a right angle between them. So the area of an isosceles right triangle is:

area = a² / 2

Let's show the step by step calculation:

1. Pick one option, depending on what you have given. Assume that we know one leg and angle, so we change the selection to given angle and one side.
2. Enter the values. For example, we know that α = 40° and b is 17 in.
3. Watch our area of a right triangle calculator performing all calculations for you! The area of the chosen triangle is 121.25 in².