Diagonal Calculator
How to Find the Diagonal
Finding the diagonal of a rectangle is one of the most useful math skills in real life. It connects geometry to carpentry, technology, and design.
A diagonal line cuts a rectangle into two identical Right Triangles. This means we can use the famous Pythagorean Theorem to solve it.
- d: The Diagonal (Hypotenuse).
- w: The Width (Base).
- h: The Height (Leg).
Construction: Squaring a Foundation
If you are building a deck, laying a foundation, or tiling a floor, having perfect 90-degree corners is critical. If your corners are off, your whole building will be crooked.
Builders use the diagonal to check this.
Measure the Length and Width of your frame. Calculate what the diagonal should be using this calculator.
Then, take a tape measure from corner to corner.
• If your measurement matches the calculation, your corners are Square (90°).
• If your measurement is different, your frame is a Parallelogram (slanted), and you need to adjust it.
The "3-4-5" Method
For smaller layouts, carpenters use the "3-4-5 Rule."
- Measure 3 feet along one wall.
- Measure 4 feet along the other wall.
- The distance between those marks must be exactly 5 feet.
This works because $3^2 + 4^2 = 5^2$ ($9 + 16 = 25$).
TV and Screen Sizes
Why are TVs measured diagonally? Why not just Width x Height?
It dates back to the early days of round CRT tubes. The circular glass tube was measured by its diameter. When screens became rectangular, manufacturers kept measuring the "Diameter" (Diagonal) to make the number sound impressive.
Common Screen Dimensions (16:9 Ratio)
| Screen Size (Diag) | Width | Height |
|---|---|---|
| 32 Inch | 27.9" | 15.7" |
| 55 Inch | 47.9" | 27.0" |
| 65 Inch | 56.7" | 31.9" |
| 75 Inch | 65.4" | 36.8" |
Use our calculator to check if a "75-inch TV" will actually fit on your 60-inch wide TV stand! (Hint: It won't).