Setting out
Square a rectangular set-out
- where
- target diagonal (m)
- length (m)
- width (m)
- difference between diagonals (mm)
- measured diagonals (m)
Explain this equation
This gives the diagonal a rectangle should have and compares it with the two diagonals you have measured. Use it to check that a set-out for a building, base or slab is square.
L and W are the planned side lengths in metres. D is the target diagonal. d₁ and d₂ are the two diagonals measured on site. Δ is the difference between them, in mm. Each diagonal's error from D is also shown, plus meaning too long.
The two sides and a diagonal make a right-angled triangle, so by Pythagoras D² = L² + W². In a true rectangle both diagonals are equal; if one is longer, the shape has been pushed out of square. The × 1000 turns metres into millimetres so small errors are easy to read.
A 4 m × 3 m set-out should have 5 m diagonals. Readings of 5.000 and 5.010 m show a 10 mm difference, so the corners need adjusting.
Watch out: equal diagonals alone do not prove the side lengths are right. Check those as well.
Find the target diagonal and compare two measured diagonals.
Enter your values to see the result.
Good to know
Equal diagonals alone do not prove every side or corner is correct. Check side lengths, right angles, datum and position as well.
Sources
- Geometry / arithmetic
Estimates are not design approval or British Standards compliance checks. Structural arch, retaining-wall, wind, foundation, lintel and masonry-capacity design are not performed. Use the project engineer’s specification.