Go back to Calculators page

Right Triangle Calculator

To find the area and sides of a right triangle, use this handy right triangle calculator.

Given two sides of a right triangle, the right triangle calculator will determine the length of the third side. The hypotenuse calculator is also handy to solve for the hypotenuse of a right triangle. The right triangle calculator will also fine the area of a right triangle.

The side opposite the right angle is the hypotenuse. The Pythagorean theorem is used to solve for the length of the hypotenuse. If a right triangle has legs measuring a and b with hypotenuse c, the Pythagorean theorem is a² + b² = c². Solving for c is as simple as taking the square root of both sides of the equation.

Let's try an example to solve for the hypotenuse.

Suppose the legs have lengths 3 and 6.  Substitute 3 for a and 6 for b in the equation.

3^2 + 6^2 = c^2

9 + 36 = c^2

45 = c^2

c = 6.71 (rounded to two decimal places)

Next, we will find the area of a right triangle.  The formula is simple, it's just Area = (1/2)(base)(height) where a and b are the base and height. If you don't have those values. Using the information above, Area = (1/2)(3)(6) = 9. Remember for area, the units are squared.

Some other useful pieces of information when dealing with right triangles. The sides of a triangle have a certain amount a slope or gradient. This is simply calculated using the formula.

(y₂ - y₁)/(x₂ - x₁)

In a right triangle, the slopes of the two lines forming the right angle will multiply to -1. If they did not, your manual calculations are incorrect.

If you need to convert from degrees to radians or vice versa, simply use the following formulas:

If angle is in radians, multiply by 180/π

If angle is in degrees, multiply by π/180

Use of this calculator will provide you with nearly instant and accurate results. Checking your work or doing all of your work using the right triangle calculator is fast and convenient.