Diagonal
Square-up calculator · v1.0
Inputs
Diagonal
0mm
Methods
04 ways to find a diagonal
01 Pythagoras +
Formulaa² + b² = c²
Example600 × 800 → √(360000 + 640000) = 1000 mm
Use whenYou have both side lengths. The default for any rectangle.
02 √2 Shortcut +
Formuladiagonal = side × 1.4142
Example600 mm square → 600 × 1.4142 = 848.5 mm
Use whenIt's a perfect square (A = B). Fast mental maths on site.
03 3 : 4 : 5 Rule +
Formulaany triangle 3 : 4 : 5 = 90°
ExampleMark 3 m one side, 4 m the other → diagonal must read 5 m. Scales to 600/800/1000.
Use whenSquaring up a frame, deck, or slab on site without a calculator.
04 SOH CAH TOA +
Formuladiagonal = side ÷ cos(angle)
Example600 mm side at 45° → 600 ÷ cos(45°) = 848.5 mm
Use whenYou know one side + one angle. Rafters, stair stringers, hip cuts.
05 Tolerance Reference +
| Work | Tolerance |
|---|---|
| Rough framing / wall studs | ±5–6 mm |
| Floor joists / decks | ±3–5 mm |
| Door & window openings | ±2–3 mm |
| Cabinet carcasses | ±1–2 mm |
| Tile layout / benchtops | ±1 mm |
| Drawer boxes / fine joinery | ±0.5–1 mm |
Tip
Pull both diagonals across the frame — they should match this number. If they don't, it's racked. Refer to 05 above for the tolerance that suits your work.
JACK / CALCULATORS
v1.0 · 2026