Diagonal Size Calculator
Enter the width and height, and a depth if it is a box. The calculator gives the diagonal, its angles, the space diagonal of a box, the aspect ratio and the 3-4-5 figures for setting out square corners.
- Diagonal length
- Angle
- Square check
Use the same unit for every side.
The diagonal of a rectangle comes from the right-angle rule. It is the square root of width squared plus height squared. A 4 × 3 m frame has a diagonal of exactly 5 m. When both diagonals of a frame match, every corner is square.
Diagonal chart
Common rectangles. Search for a size.
| Width | Height | Diagonal | Angle |
|---|---|---|---|
| 3 | 4 | 5 | 53.1° |
| 4 | 3 | 5 | 36.9° |
| 6 | 8 | 10 | 53.1° |
| 5 | 12 | 13 | 67.4° |
| 16 | 9 | 18.36 | 29.4° |
| 8 | 10 | 12.81 | 51.3° |
| 10 | 10 | 14.14 | 45.0° |
| 12 | 6 | 13.42 | 26.6° |
Rounded to two places.
Width and diagonal
3 m high. Slide the width.
The rectangle is drawn with both diagonals and the angle.
How to find a diagonal
Right-angle rule. Step through it.
Width
Measure.
For big layouts, measure diagonals with a long tape pulled tight and level.
2D diagonal, box diagonal or 3-4-5
Diagonal uses. Compare them.
Flat.
Solid.
Setting out.
Multiples like 6-8-10 and 9-12-15 work just as well as 3-4-5 for bigger layouts.
Before you set out
Square checks. Tick each item.
Tick each item as you go.
Adjust the frame by pushing along the longer diagonal until both match.
What you get
Diagonal sizing. Each tile explains one result.
Length.
Both.
Space diagonal.
Aspect.
Figures.
The space diagonal tells you the longest pole that fits inside a box.
Frequently Asked Questions
No question matches that search.
How do I calculate a diagonal?
Square the width and the height, add them and take the square root.
How do I check a frame is square?
Measure both diagonals. If they are equal, the corners are square.
What is the three four five rule?
A triangle with sides three, four and five has a right angle, which builders use to set out corners.
What is the diagonal of a box?
The square root of width squared plus height squared plus depth squared.
What angle does the diagonal make?
The angle whose tangent is the height divided by the width.
Does a square have a special diagonal?
Yes, it is the side times about one point four one four.
How long is the diagonal of a sixteen by nine rectangle?
About eighteen point four units.
Square every time
Work out the diagonal, measure both, and you know your frame, deck or foundation is true.
More size calculators
Each one has its own calculator, worked examples and answers to common questions.