Area of a Right Triangle Calculator

Area of right triangle formulas

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.

How to use the area of a right triangle calculator

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.