Right Triangle Calculator

Go back to Calculators page

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

How to Find the Area and Sides 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 $$=\frac{1}{2}\times\text{base}\times\text{height}$$ where a and b are the base and height. If you don’t have those values. Using the information above, Area $$=\frac{1}{2}\times3\times6=9$$. Remember for area, the units are squared.

Some other useful information when dealing with right triangles is knowing the slope or gradient of the triangle. This is calculated using the formula.

$$\frac{y_2-y_1}{x_2-x_1}$$

In a right triangle, the slope of the two lines forming the right angle should equal -1. If they did not, check your work again and see if you accidentally made a mistake.

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

Radians to degrees: multiply by $$\frac{180}{\pi}$$

Angle to degrees: multiply by $$\frac{\pi}{180}$$

Using this calculator will provide you with nearly instant and accurate results. Check your work using the right triangle calculator.