Diagonal Calculator

A diagonal calculator helps you to determine the length of the longest possible straight line that can be drawn within a shape, connecting opposite corners. It is typically used to find diagonal of a rectangle’s measurements in geometric shapes like rectangles and squares.

What is the Diagonal of a Rectangle?

In Maths,

A rectangle is a two-dimensional and four-sided polygon shape with the same length on both sides and all the angles at 90 degrees.

Whereas,

The diagonal of a rectangle is a straight line that connects two opposite corners or vertices of the rectangle. It passes through the inside of the rectangle and divides it into two congruent right triangles.

Pythagorean Theorem:

Pythagorean theorem states that the square of the diagonal's length is equal to the sum of the squares of the rectangle's length and width. The diagonal length of a rectangle can easily be calculated using the Pythagorean theorem.

Important Parameters of Rectangles:

There are some important parameters that play a crucial part in calculating diagonals such as:

• l  =  length
• w =  Width
• d  =  Diagonal
• α =  Angle between diagonals
• r  =  Circumcircle radius
• A  =  Area
• P  = Perimeter

You can use these parameters to derive the diagonal of a rectangle’s equation.

The Expressions of Diagonal of a Rectangles:

Here is the diagonal formula to find the accurate results:

Diagonal = √(l² + w²)

Where,

• L  =  Length of the rectangle
• W =  Width of the rectangle

Calculations and Examples:

Here’s a real-life example that will help you in getting the answer to the question of how to find the diagonal of a rectangle.

Example:

Let's say you have a rectangular picture frame, and you want to find the diagonal measurement of a rectangle to choose the right-sized picture for it. You can also find these values from the diagonal size calculator.

Suppose the measurements of the length and width of the picture frame are as follows:

Length (l) = 20 inches
Width (w) = 12 inches

Use the formula for the diagonal of a rectangle: Diagonal = √(l² + w²)

Diagonal = √(20² + 12²)
Diagonal = √(400 + 144)
Diagonal = √544
Diagonal =  23.32 

So, the diagonal of your rectangular picture frame is approximately 23.32 inches. This helps you select a picture that fits nicely within the frame without any guesswork.

Steps to Use a Diagonal Calculator:

Using a diagonal calculator doesn't require an advanced degree in mathematics. Here's how you can quickly calculate by having some inputs such as:

What to do:

• Select the parameter you want to calculate
• Enter the values into their particular field
• Press the Calculate button

What you get:

• The diagonal of a rectangle
• The angle of a rectangle
• The Perimeter of a rectangle
• The Area of a rectangle
• The circumcircle of a rectangle

FAQs:

How many diagonals are possible in a rectangle?

The answer is “Two”. Rectangles have four sides, so they have two diagonals. The same as a square so must keep the use of a free rectangle diagonal calculator.

What are the examples of rectangles in real life?

In our everyday life, we see most things as rectangular like TVs, computers, mobile phones,  laptops, CPUs, notice boards, tables, books, walls, magazines, tennis courts, etc.

What is meant by rectangle diameter?

In rectangles, the diameter is equal to the length of a diagonal or two long lines joining opposite corners. There are two identical right-angle triangles that are formed when a rectangle is divided by a diagonal.

References:

Wikipedia.org: Diagonal, Polygons