OnlineCalculator360
Result
How the Calculator Works
Enter the length and width of the rectangle and the calculator returns the diagonal length using the Pythagorean theorem: d = √(l² + w²). This is the straight-line distance from one corner to the opposite corner.
The diagonal is longer than either side but shorter than their sum. For a room or panel, it represents the maximum straight dimension, which is useful when you need to know whether something will fit through a gap, lie flat in a space, or serve as the hypotenuse of a structural triangle.
Formula and Worked Example
This is the Pythagorean theorem applied to the two shorter sides of the right triangle formed by the diagonal.
A wardrobe is 1.8 m tall and 0.65 m deep. Can it be tilted flat and moved through a doorway that is 2.1 m tall and 0.9 m wide?
Wardrobe diagonal = √(1.8² + 0.65²) = √(3.24 + 0.4225) = √3.6625 = 1.913 m
Since 1.913 m < 2.1 m (doorway height), the wardrobe can be tilted through the door with room to spare. If the wardrobe had a 0.9 m depth instead, the diagonal would be √(3.24 + 0.81) = 2.01 m, which is just barely too tall to tilt through.
Practical Uses: TVs, Doors, and Structural Bracing
The diagonal measurement comes up in three distinct contexts in home planning and construction:
| Context | What You Calculate | Why It Matters |
|---|---|---|
| TV screen size | Diagonal of visible display | Manufacturer's advertised "size" is always the diagonal |
| Moving furniture | Diagonal of furniture face | Maximum tilt clearance through a doorway |
| Roof truss / pergola brace | Diagonal of rectangular bay | Minimum brace bar length before joint allowance |
| Checking squareness | Both diagonals of an installed frame | Equal diagonals confirm the rectangle is truly square (no racking) |
| TV wall clearance | Diagonal of wall space | Confirms wall area can fit the TV mount plus safe viewing distance |
| Steel gate diagonal brace | Diagonal of gate leaf | Diagonal bar prevents parallelogram deformation over time |
TV Screen Size Guide
TV screens are sold by their diagonal measurement. Below is a reference table for common TV sizes in 16:9 aspect ratio, showing the approximate width and height of the display panel:
| Screen Size (diagonal) | Display Width | Display Height |
|---|---|---|
| 32 inch (81 cm) | 70.1 cm | 39.4 cm |
| 43 inch (109 cm) | 94.2 cm | 53.0 cm |
| 50 inch (127 cm) | 110.7 cm | 62.3 cm |
| 55 inch (140 cm) | 121.8 cm | 68.5 cm |
| 65 inch (165 cm) | 143.9 cm | 80.9 cm |
| 75 inch (190 cm) | 166.1 cm | 93.4 cm |
The physical TV cabinet is slightly larger than the display area due to bezels and stand width. Use these figures for the display; add 5 to 8 cm to each dimension for the full cabinet footprint.
Frequently Asked Questions
Diagonal = √(length² + width²). This is the Pythagorean theorem applied to the right triangle formed by the two sides and the diagonal.
TV screen size is the diagonal of the visible display area. A 55-inch TV has a 55-inch (139.7 cm) diagonal. The actual width and height depend on the aspect ratio (16:9 for most modern TVs).
Calculate the expected diagonal from the frame's width and height. Then measure both physical diagonals of the installed frame. If both diagonals are equal and match the formula, the frame is perfectly square with no racking.
Calculate the diagonal of the wardrobe's face (height and depth). If this diagonal is less than the door opening height, you can tilt the wardrobe flat and move it through. Add a small margin for wall thickness and grip space.
A4 is 210 mm × 297 mm. Diagonal = √(210² + 297²) = √132,309 = 363.7 mm (36.37 cm).
A diagonal brace in a rectangular frame must be cut to the exact diagonal length of the bay. Calculate the diagonal with this calculator, then add your joint allowance at each end before cutting the steel or timber bar.
Yes. Measure the physical TV cabinet width and height, calculate the diagonal of the cabinet, and compare against the bracket's supported size range. Most mounts list a diagonal screen size range.
For a square with side a, the diagonal = a√2. A 2 m × 2 m square has a diagonal of 2 × 1.414 = 2.83 m. Enter equal values in this calculator to verify.