Diagonal of a Rectangle Calculator
Get the corner-to-corner diagonal of any rectangle from its length and width. Enter both sides in the same unit — inches, feet, cm, anything — and you also get area, perimeter, and the angle the diagonal makes with the long side.
Example: with Length (l) 12 · Width (w) 5 → Diagonal: 13 units.
- Area (l × w)60 square units
- Perimeter 2(l + w)34 units
- Diagonal angle22.62° between diagonal and length
Computed by the calculator below using its default values. Change any input to see your own numbers.
d = √(l² + w²) — the Pythagorean theorem, because the diagonal splits a rectangle into two right triangles. 12 × 5 gives exactly 13.
One formula, two everyday jobs
The diagonal of a rectangle is the hypotenuse of the right triangle formed by its two sides, so d = √(l² + w²). That single line answers two very different questions. The first is sizing: TVs, monitors, and picture frames are sold by diagonal, so a 12 × 5 ft wall and a 13 ft ladder are related the same way a 16:9 panel's width, height, and advertised size are.
The second is squareness. Framers and deck builders measure both diagonals of a layout: in a true rectangle they are equal, so if one tape reads longer, the frame is racked into a parallelogram. The classic 3-4-5 check is this formula in reverse — mark 3 ft on one side, 4 ft on the other, and the corner is square exactly when the diagonal between marks is 5 ft.
How it’s calculated
Diagonal d = √(l² + w²) (Pythagorean theorem). Area = l × w; perimeter = 2(l + w); diagonal angle vs the length side = arctan(w/l) converted to degrees (× 180/π). Both inputs must be in the same unit; the diagonal comes back in that unit.
True rectangles only (four 90° corners). For a racked or irregular quadrilateral the two diagonals differ and this single value does not apply.
Handy rectangle diagonals
| Rectangle | Sides | Diagonal |
|---|---|---|
| 3-4-5 layout check | 3 × 4 ft | exactly 5 ft |
| Letter paper | 8.5 × 11 in | 13.90 in |
| Classic 5:12 rectangle | 12 × 5 | exactly 13 |
| Plywood sheet | 48 × 96 in | 107.33 in |
| 16:9 screen shape | 16 × 9 | 18.36 |
Computed with d = √(l² + w²); exact Pythagorean triples noted.
Common mistakes
- Adding the sides and taking the square root — √(l + w) is wrong; square each side first, then add, then root.
- Mixing units, like length in feet and width in inches; convert both to one unit before squaring.
- Assuming the diagonal makes a 45° angle — that only happens in a square. For 12 × 5 it is 22.6°.
- Checking squareness with one diagonal only; you need both diagonals equal (or a verified 90° corner) to confirm a rectangle.
Frequently asked questions
What is the diagonal of a rectangle formula?
d = √(l² + w²), the Pythagorean theorem applied to the right triangle the diagonal creates. A 12 × 5 rectangle has a diagonal of exactly 13.
Are both diagonals of a rectangle equal?
Yes — in a true rectangle the two diagonals are the same length and bisect each other. Builders exploit this: measure both diagonals, and if they differ the frame is out of square.
How do I get the diagonal in feet if I measured inches?
Compute in inches, then divide by 12. A 48 × 96 in sheet has a 107.33 in diagonal, which is 8.94 ft. Never mix units inside the square root.
Can I find the sides from the diagonal alone?
No — infinitely many rectangles share one diagonal. You need the diagonal plus one side (then w = √(d² − l²)) or the aspect ratio, which is how TV width and height are recovered from the advertised size.