When you want to find out the diagonal of a rectangle, it can be a complicated process to do so by hand. Fortunately, as long as you have the other parameters of a rectangle, you can find the diagonal measurement – and others - using this calculator tool.
To determine the diagonal of a rectangle, you can use the length, width, angle, circumcircle, area, and perimeter measurements. All of these components help to create the shape itself.
The word rectangle is derived from two Latin words – rectus (meaning right or proper) and angulus (meaning angle). From this name, you can determine that a rectangle is a quadrilateral with four right angles – two of which are parallel and of equal length. A rectangle also has two intersecting diagonals which are also the same length.
You may not know that a square is also a particular type of rectangle. It has four sides and two diagonals.
How Do You Find the Diagonal of a Rectangle?
Using a diagonal of a rectangle calculator makes the entire process effortless as long as you have other measurements, but you can also use the diagonal of a rectangle formula.
The formula involves dividing your rectangle into its two congruent right triangles – with at least one 90-degree angle. All triangles will have a length (l) and width (w) and a hypotenuse of (d) for the length.
You also use the Pythagorean theorem to receive an approximate diagonal measurement:
d² = l² + w²
Then, to get the exact formula for finding the diagonal of a rectangle, take a square root.
d = √ (l² + w²)
You can also use the diagonal of a rectangle calculator to measure in various units using SI and imperial.
What is the Formula for Finding the Diagonal of a Rectangle?
You are not always going to have all the appropriate measurements for working out the diagonal of a rectangle handed to you on a plate. Sometimes, you may only get two measurements, and you have to use different formulas to work it out from there.
Firstly, we’ll cover the three equations you will need for the rectangle’s perimeter, area, and the circumcircle radius.
1. Rectangle perimeter: P = 2 x w + 2 x l2. Rectangle area: A = w x l3. Rectangle circumcircle radius: R = d/2
With these formulas, you can now identify various other methods – depending on the measurements you receive, for working out the diagonal of a rectangle. Below, you will see what each formula looks like when you have the following information.
Circumcircle radius: d = 2 * r
Length and width: d = √ (l² + w²)Area and width: d = √ (A²/w² + w²)Area and length: d = √ (A²/l² + l²)Perimeter and width: d = √ (2w² - P*w + P²/4)Perimeter and length: d = √ (2l² - P*l + P²/4))Angle and width: d = w / sin(α/2)Angle and length: or d = l / cos(α/2)Perimeter and area: d = √ (P² - 2*A)Perimeter and angle: d = P / (2*sin(α/2) + 2*cos(α/2))Angle and area: d = √ (2 * A / sin(α))
With all of these formulas, the α refers to the angle between the diagonal measurements. The calculator also assumes that in all measurements, the length is the longer measurement.