Setting Out (3-4-5 & Diagonals)
Square up a layout: the exact diagonal of a rectangle, the error and corner angle from measured diagonals, and a 3-4-5 triangle scaled to your tape.
Diagonal to measure, the difference of two measured diagonals with the corner angle and offset it implies, and a 3-4-5 triple sized to a leg you choose.
Example: A 6 × 8 m slab should measure 10.000 m corner to corner; diagonals of 10.02 and 9.98 mean the corner is 90.24°, out by 4 cm — move one corner 2 cm along the long diagonal.
Two ways to prove
a corner is square.
Diagonals, the 3-4-5 triangle, and what the corner angle tells you.
Diagonals
A rectangle with sides a and b has diagonals √(a² + b²) — both of them. If the two you measure differ, the figure is a parallelogram: moving one corner by half the difference along the longer diagonal squares it. The error of each measured diagonal against the exact value is shown.
3-4-5
Any triangle with sides in the ratio 3 : 4 : 5 has a right angle between the 3 and 4 sides (3² + 4² = 5²). Mark 3 units along one line and 4 along the other; the corner is square when the hypotenuse measures 5. The page scales the triple to side A or to a leg you type, so it fits inside the layout.
Corner angle
With sides a, b and a measured diagonal d, the cosine rule gives the corner angle: cos θ = (a² + b² − d²) / (2ab). The offset at the far end of side b is b × sin(θ − 90°), which is how far that corner sits off the perpendicular. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Pythagoras and the cosine rule (elementary geometry); the 3-4-5 triple as the smallest Pythagorean triple
Last reviewed 20 September 2026. How results are checked: How we verify.