Setting out and cutting
Diagonal (45°) tile layout: pitch and cuts
- where
- diagonal repeat along the wall (mm)
- tile edge length (mm)
- grout joint width (mm)
- corner-to-corner length of one tile (mm)
- number of tile repeats along the run
- length of the wall or run (m)
Explain this equation
For square tiles laid at 45°, gives how often the pattern repeats along a wall, the tile diagonal and how many repeats fit. Use it to centre a diagonal layout and plan the edge cuts.
a is the tile edge and j the joint, so a + j is the straight pitch. Turned through 45°, each tile spans its diagonal along the wall. c is the corner-to-corner length, which is the long side of a half-tile triangle.
A square’s diagonal is its side times √2, from Pythagoras. The 1000 turns the run from metres into millimetres, and dividing by the pitch gives the number of repeats, including the fraction left for cuts.
Sense check: a 300 mm tile with a 3 mm joint repeats every 428.5 mm, so about seven repeats fit a 3 m wall. The pitch is about 1.41 times the straight pitch.
Watch out: split the leftover fraction between both ends so you do not finish with a sliver. Rectangular tiles at 45° behave differently.
For square tiles laid at 45°, gives the repeat distance along a wall, the tile diagonal (the long edge of a half-tile triangle) and how many repeats fit the run.
Enter your values to see the result.
Good to know
Diagonal tiles repeat along a wall at (tile + joint) × √2, about 1.41 times the straight pitch. Each edge piece is cut along or parallel to the tile diagonal; half-tile triangles have a long edge of a × √2 (less the joint allowance). Use the fractional repeat count to centre the pattern so the cuts at each end are equal and not slivers. Tiles per m² are the same as for a straight lay; waste is higher (allow roughly 15% rather than 10%, or work it out from the cuts).
Common mistake
Setting out diagonal tiles from one wall and ending with a thin sliver at the other. Centre the layout using the repeat count first.
Limits
Square tiles in a true 45° pattern. Rectangular tiles at 45° have different repeats in each direction.
Sources
Results are calculations from the published methods and manufacturer figures shown, and depend on the data you enter. Always follow the tile, adhesive and grout manufacturers’ instructions, BS 5385 and the Tile Association guidance. Coverage rates vary by product and substrate. Check prices and VAT rules with your own records and HMRC.