How to Calculate Rectangle Diagonal

Rectangle Diagonal Calculator

The diagonal length will appear here.

function calculateRectangleDiagonal() { var lengthInput = document.getElementById("rectangleLength").value; var widthInput = document.getElementById("rectangleWidth").value; var resultDiv = document.getElementById("diagonalResult"); var length = parseFloat(lengthInput); var width = parseFloat(widthInput); if (isNaN(length) || isNaN(width) || length <= 0 || width <= 0) { resultDiv.innerHTML = "Please enter valid, positive numbers for both length and width."; resultDiv.style.color = "red"; return; } var diagonal = Math.sqrt(length * length + width * width); resultDiv.innerHTML = "The diagonal length is: " + diagonal.toFixed(2) + " units"; resultDiv.style.color = "#333"; }

Understanding the Rectangle Diagonal

A rectangle is a four-sided polygon where all interior angles are 90 degrees, and opposite sides are equal in length. A diagonal of a rectangle is a line segment connecting two non-adjacent vertices (corners). Every rectangle has two diagonals of equal length that bisect each other.

The Pythagorean Theorem and Rectangles

Calculating the length of a rectangle's diagonal is a classic application of the Pythagorean theorem. If you draw a diagonal across a rectangle, it divides the rectangle into two right-angled triangles. The sides of the rectangle (length and width) become the two shorter sides (legs) of the right triangle, and the diagonal itself becomes the hypotenuse.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is expressed as:

a² + b² = c²

In the context of a rectangle, if 'L' is the length, 'W' is the width, and 'D' is the diagonal, the formula becomes:

L² + W² = D²

To find the diagonal 'D', you simply take the square root of both sides:

D = √(L² + W²)

Why is this useful?

Knowing how to calculate a rectangle's diagonal is useful in various fields:

• Construction and Architecture: To ensure squareness of foundations, walls, or frames. If the diagonals are equal, the corners are 90 degrees. Also, for determining the maximum length of an object that can fit within a rectangular space.
• Design and Engineering: For screen sizes (e.g., TV, monitor, phone screens are measured by their diagonal length), or designing components that fit specific enclosures.
• Mathematics and Geometry: A fundamental concept for understanding spatial relationships and solving geometric problems.

Example Calculation

Let's say you have a rectangular garden plot that is 12 meters long and 9 meters wide. To find the length of its diagonal, you would use the formula:

• Length (L) = 12 meters
• Width (W) = 9 meters
• D = √(12² + 9²)
• D = √(144 + 81)
• D = √(225)
• D = 15 meters

So, the diagonal of the garden plot is 15 meters.

How to Use the Calculator

Our Rectangle Diagonal Calculator simplifies this process for you:

1. Enter Rectangle Length: Input the length of your rectangle into the "Rectangle Length" field. For example, if your rectangle is 10 units long, enter '10'.
2. Enter Rectangle Width: Input the width of your rectangle into the "Rectangle Width" field. For example, if your rectangle is 5 units wide, enter '5'.
3. Click "Calculate Diagonal": Press the button to instantly see the diagonal length.

The calculator will display the diagonal length, rounded to two decimal places, in the result area below the button. This tool is perfect for quick checks in construction, design, or academic work.