Diagonal calculator in feet and inches
Find the diagonal of a rectangle, a missing side of a right triangle, or how far a corner is out of square. Every measurement goes in and comes out in feet, inches and fractions.
Your corner
20' 0"
In the app, any two of rise, run and diagonal solve the third, straight from the keypad.
diagonal = √(length² + width²)
3-4-5 multiples
| Side | Side | Diagonal |
|---|---|---|
| 3 ft | 4 ft | 5 ft |
| 6 ft | 8 ft | 10 ft |
| 9 ft | 12 ft | 15 ft |
| 12 ft | 16 ft | 20 ft |
| 15 ft | 20 ft | 25 ft |
| 18 ft | 24 ft | 30 ft |
Every row is exact, so any of them squares a corner with no fractions to read. The same ratio works in millimetres: 600, 800 and 1000.
A rectangle's diagonal is the long side of a right triangle, so the diagonal of a room, slab or deck is the square root of length squared plus width squared. This diagonal calculator does that in feet and inches, finds a missing side when you have the diagonal, and takes all three measurements from a corner you have already built to tell you how far it is out of square. Adding or dividing lengths instead? Use the feet and inches calculator.
Squaring a corner with the 3-4-5 rule
Mark 3 ft along one line and 4 ft along the other. The distance between the two marks is exactly 5 ft only when the corner between them is 90°. On a larger layout, use a multiple, because a longer triangle shows a small error more clearly: 12-16-20 turns a 1/16 in misreading into a smaller angle than 3-4-5 does. The table on this page lists the multiples that come out in whole feet.
Checking a slab, deck or foundation
For a whole rectangle, measure both diagonals. If they are equal, the rectangle is square. If they differ, the corners are not 90°. For a single corner, choose CHECK SQUARE and enter the length, the width and the diagonal you measured. The calculator gives the diagonal a square corner would have, the difference, and the actual corner angle.
Diagonals of common rooms and slabs
The diagonal each layout should measure when every corner is square, to the nearest sixteenth.
| Size | Square diagonal |
|---|---|
| 4 × 8 ft | 8' 11-5/16" |
| 8 × 10 ft | 12' 9-11/16" |
| 10 × 12 ft | 15' 7-7/16" |
| 12 × 16 ft | 20' 0" |
| 20 × 30 ft | 36' 11/16" |
| 24 × 36 ft | 43' 3-3/16" |
Which way to move a corner
A diagonal that measures long means the corner is open, wider than 90°. One that measures short means it is closed. With form boards or batter boards, move the far end of one side toward the other to close the corner, or away to open it, then measure again. On a 12 by 16 layout, moving the end of the 12 ft side 1/2 in changes the diagonal by about 0.4 in, so move in small steps and check each one.
Finding a missing side
If you know the diagonal and one side, choose A SIDE. The other side is the square root of the diagonal squared minus the known side squared. A 20 ft diagonal with a 12 ft side leaves 16 ft, because 400 − 144 = 256.
In millimetres
Choose MM and type plain numbers, or type 600mm with any setting. The 3-4-5 ratio holds in any unit, so 600, 800 and 1000 mm square a corner exactly, and 1.2 m, 1.6 m and 2 m do the same over a longer run.
Questions about right triangles and squaring
What is the 3-4-5 rule?
A triangle with sides of 3, 4 and 5 always has a 90° corner between the 3 and the 4. Measure 3 ft along one line and 4 ft along the other, and if the distance between those two marks is exactly 5 ft, the corner is square. Any multiple works the same way: 6-8-10, 9-12-15 or 12-16-20.
How do you square a foundation?
Measure both diagonals. A rectangle is square only when its two diagonals are equal. For a single corner, use this calculator's CHECK SQUARE mode: enter the length, the width and the diagonal you measured, and it says whether the corner is open or closed and by how much.
What is the diagonal of a 12 by 16 room?
Exactly 20 ft. It is the 3-4-5 triangle four times over, which is why 12 by 16 is a common layout for checking a corner.
What is the diagonal of a 4 by 8 sheet of plywood?
8 ft 11-5/16 in to the nearest sixteenth, or 107.33 in. Measuring both diagonals of a sheet is also the quick way to check that it was cut square: on a square sheet they are equal.
What is the diagonal of a 10 by 12 room?
15 ft 7-7/16 in to the nearest sixteenth. 10 squared plus 12 squared is 244, and the square root of 244 is 15.62 ft.
What does it mean if the diagonal is too long?
The corner is open, wider than 90°. If the diagonal is too short, the corner is closed, tighter than 90°. Move the far end of one side toward the other to close an open corner, or away from it to open a closed one, then measure again.
How do you find a missing side of a right triangle?
Square the diagonal, subtract the square of the side you know, and take the square root. With a 20 ft diagonal and a 12 ft side, 400 − 144 = 256, and the square root of 256 is 16 ft. Use SIDE mode to do it in feet and inches.
