Square up footings, decks, slabs and walls: the exact diagonal, a 3-4-5 check triangle sized to your layout, and the correction when your diagonals don't match.
Tip
Stand at one width side facing the layout. Diagonal 1 runs from your near-left corner to the far-right corner; diagonal 2 runs from near-right to far-left. Enter both to get the correction.
Diagonal when square
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3-4-5 check triangle
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Diagonal to width / to length
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Diagonal difference
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Slide far side by
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Corner error
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Every rectangle is two right triangles back to back, and the diagonal is their shared hypotenuse. That makes the Pythagorean theorem the fastest squareness check on a job site: set the side lengths, then pull a tape corner to corner both ways. When both diagonals match the calculated number, every corner is 90°.
diagonal = √(width² + length²)
correction = (d₁² − d₂²) ÷ (4 × width)
Diagonal = √(12² + 16²) = √400 = 20 ft. This is a 3-4-5 triangle scaled by 4 (12-16-20), so it comes out exact. Suppose the tape reads 20' 3-9/16" one way and 19' 8-3/8" the other (20.298 ft and 19.698 ft). The correction is (20.298² − 19.698²) ÷ (4 × 12) = (412.0 − 388.0) ÷ 48 = 0.5 ft = 6 in. Slide the far ledger 6 in toward the short diagonal and both will read 20 ft.
Slide the far side sideways by x and the rectangle becomes a parallelogram. Its diagonals are d₁² = w² + l² + 2wx and d₂² = w² + l² − 2wx. Subtract and everything cancels except 4wx, which gives x = (d₁² − d₂²) ÷ 4w with no approximation. The same parallelogram appears in the law of cosines, which is where those ± 2wx terms come from.
| Layout | Diagonal (ft) | Diagonal (ft-in) |
|---|---|---|
| 8 × 10 ft | 12.806 | 12' 9 11/16" |
| 10 × 12 ft | 15.620 | 15' 7 7/16" |
| 12 × 16 ft | 20.000 | 20' 0" |
| 12 × 20 ft | 23.324 | 23' 3 7/8" |
| 16 × 20 ft | 25.612 | 25' 7 3/8" |
| 20 × 24 ft | 31.241 | 31' 2 7/8" |
| 24 × 24 ft | 33.941 | 33' 11 5/16" |
| 24 × 30 ft | 38.419 | 38' 5" |
| 24 × 36 ft | 43.267 | 43' 3 3/16" |
| 30 × 40 ft | 50.000 | 50' 0" |
Rounded to the nearest 1/16 in.
When you only have one corner to set, such as a wall plate meeting another or the first corner of a footing, use a 3-4-5 triangle instead of full diagonals. The calculator sizes it to your layout: for 12 × 16 ft it gives 12 – 16 – 20, the biggest multiple that fits. Large triangles are more accurate, because a 1/8 in tape error is a smaller fraction of 20 ft than of 5 ft. For the full field method, see how to square the footings for a house.
Use the Pythagorean theorem: diagonal = √(width² + length²). A 12 ft × 16 ft deck has a diagonal of √(144 + 256) = √400 = 20 ft exactly. When both diagonals of your layout measure that number, all four corners are 90°.
A four-sided shape with equal opposite sides is a parallelogram, and a parallelogram's diagonals are equal only when its corners are right angles. If one diagonal is longer, the corners at its ends are less than 90° and the shape is leaning toward that diagonal.
Any triangle with sides in the ratio 3:4:5 has a right angle between the 3 and 4 sides, because 3² + 4² = 5². Measure 3 units along one string line, 4 units along the other, and adjust until the distance between the marks is exactly 5 units. Use the largest multiple that fits (6-8-10, 9-12-15, 12-16-20): bigger triangles make small measuring errors matter less.
Slide the far side sideways by (d1² − d2²) ÷ (4 × width), where d1 and d2 are the two measured diagonals and width is the side you are sliding. For a 12 ft wide layout with diagonals of 20 ft 3-9/16 in and 19 ft 8-3/8 in, that is 6 inches. The ratio between the shift and the diagonal difference changes with the shape of the layout, so the exact formula saves a second trip around it.
It depends on the work. For concrete footings and foundations, within 1/4 in over a typical house footprint is a common target. Deck and wall framing is usually held to 1/8 in, and cabinet or tile layout to 1/16 in. The tighter the finish that follows, the tighter the layout needs to be.
Yes. The math is unit-free, so choose millimetres or metres and enter all measurements in that unit. Imperial results are shown in feet, inches and sixteenths; metric results are shown as decimals.
Deepen your understanding of triangles and trigonometry with our guides and tutorials:
Square, plumb and straight: what each term means, how to check it with a level, string line or the 3-4-5 method, worked numbers and typical tolerances.
How to square building footings with the 3-4-5 method and a diagonal check: the math, a worked 24 × 36 ft garage layout, tolerances, and layout tools.
How to square a ground-mounted solar array pier layout: diagonal targets from the Pythagorean theorem, a worked 8-pier example, and grid checks.
The Pythagorean theorem a² + b² = c² explained: what it says, why it holds only with a right angle, its history from Babylon to Euclid, and three proofs.
Triangles are the strongest shape in engineering: three fixed sides lock the angles. The geometry, a worked force example, and how trusses use it.
How to calculate stair stringers: riser count, unit rise and run, stringer length and stair angle, with IRC limits and a worked 48-inch deck stair.
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