Diagonal Calculator 2026
Instantly calculate the diagonal length of rectangles, squares, cubes & cuboids. Perfect for construction, design, and geometry projects with step-by-step formulas.
Shape & Dimensions
Select a shape and enter its measurements
All sides of a square are equal
Calculates the space diagonal (corner to opposite corner)
Diagonal Results
Length with formulas and breakdown
Select a shape, enter dimensions, then click Calculate Diagonal to see your results with step-by-step working.
Diagonal Formulas
Quick reference for the diagonal formulas of common shapes. All formulas use the Pythagorean theorem and its 3D extensions.
| Shape | Diagonal Formula | Key Variables |
|---|---|---|
| ▭ Rectangle | d = √(l² + w²) | l = length, w = width |
| ◻ Square | d = a√2 | a = side length |
| 🟦 Cube (space diagonal) | d = a√3 | a = side length |
| 📦 Cuboid (space diagonal) | d = √(l² + w² + h²) | l = length, w = width, h = height |
Diagonal Calculator FAQ
Learn more about diagonal calculations, formulas, and real-world applications for construction, design, and geometry.
The diagonal of a rectangle is calculated using the Pythagorean theorem: d = √(l² + w²), where ‘l’ is the length and ‘w’ is the width. This formula works because the diagonal creates a right triangle with the length and width as the two sides.
The diagonal of a square is calculated using the formula d = a√2, where ‘a’ is the side length. Since all sides of a square are equal, the diagonal is approximately 1.414 times the side length. This comes from applying the Pythagorean theorem to a square.
The space diagonal of a cube (the diagonal that goes through the center from one corner to the opposite corner) is calculated using d = a√3, where ‘a’ is the side length. This is approximately 1.732 times the side length.
A face diagonal is the diagonal across one face of a 3D shape (like the diagonal on one side of a cube). A space diagonal goes through the interior of the shape from one corner to the opposite corner. For a cube with side ‘a’, the face diagonal is a√2 and the space diagonal is a√3.
Diagonal calculations are essential in construction for ensuring square corners (checking if a room or foundation is perfectly square), calculating material lengths for diagonal bracing, determining screen sizes, and verifying that structures are built to correct specifications.