How Do You Calculate Diagonal of a Rectangle

Rectangle Diagonal Calculator

Enter the length of the rectangle (e.g., 10).

Enter the width of the rectangle (e.g., 5).

function calculateRectangleDiagonal() { var lengthInput = document.getElementById("rectangleLength").value; var widthInput = document.getElementById("rectangleWidth").value; var length = parseFloat(lengthInput); var width = parseFloat(widthInput); var resultDiv = document.getElementById("diagonalResult"); if (isNaN(length) || isNaN(width) || length <= 0 || width <= 0) { resultDiv.innerHTML = "Please enter valid, positive numbers for both length and width."; resultDiv.style.color = "#dc3545"; // Red for error return; } var diagonal = Math.sqrt(Math.pow(length, 2) + Math.pow(width, 2)); resultDiv.innerHTML = "The diagonal of the rectangle is: " + diagonal.toFixed(4) + " units"; resultDiv.style.color = "#0056b3"; // Blue for result }

Understanding the Diagonal of a Rectangle

A rectangle is a four-sided polygon where all four angles are right angles (90 degrees). Opposite sides are equal in length and parallel. The diagonal of a rectangle is a line segment connecting two non-adjacent vertices (corners).

How to Calculate the Diagonal

The calculation of a rectangle's diagonal is a classic application of the Pythagorean theorem. When 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 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 take the square root of both sides:

D = √(L² + W²)

Example Calculation

Let's say you have a rectangle with a length of 12 units and a width of 5 units. To find its diagonal:

1. Square the length: 12² = 144
2. Square the width: 5² = 25
3. Add the squared values: 144 + 25 = 169
4. Take the square root of the sum: √169 = 13

So, the diagonal of a rectangle with a length of 12 and a width of 5 is 13 units.

Using the Calculator

Our Rectangle Diagonal Calculator simplifies this process. Simply enter the length of your rectangle into the "Rectangle Length" field and the width into the "Rectangle Width" field. Click the "Calculate Diagonal" button, and the calculator will instantly display the diagonal length, saving you time and ensuring accuracy.

This tool is useful in various fields, from construction and engineering to design and geometry problems, whenever you need to quickly determine the longest distance across a rectangular shape.