Tile Layout: Centering and Balanced Cuts
Where to start the first tile along a run so the cuts at the walls are not slivers.
Example
You enter
- Run, wall to wall (in) 132
- Tile size along the run (in) 12
- Grout joint width (in) 0.125
- Smallest acceptable cut (in; 0 = half a tile) 0
You get
- Start full cut-in 10.75
- Tile centered cut-in 11.375
- Joint centered cut-in 5.3125
- First full edge (in) 11.5
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeEvery layout holds the same number of tiles give or take one; what changes is where the leftover goes. Starting with a full tile at one wall puts it all in one cut at the far wall; centering splits it into two equal cuts, and centering on a tile or on a grout joint moves each cut by half a tile, so when one centered layout leaves a sliver the other does not. A 132 in run of 12 in tile at a 1/8 in joint gives ten full and a 10.75 in cut starting full, nine full and two 11.375 in cuts centered on a tile, and ten full and two 5.31 in cuts centered on a joint, under half a tile. It recommends the layout with no cut under the minimum (half a tile by default), preferring a centered one, and says how far from the wall the first full tile's edge goes. Run it once per room dimension; the count and waste are the tile count calculator's.
Formula or tablepitch P = tile + joint; start full: n = floor((run + joint) / P), cut = run - n x tile - n x joint (0 when it fits exactly); centered: the largest k of the right parity (odd on a tile, even on a joint) with cuts = (run - k x tile - (k - 1) x joint) / 2 - joint >= 0; a sliver is a cut under the minimum (default half a tile).
Source and editionFirst-principles layout arithmetic by name; joints run between tiles and between a full tile and its cut, not against the wall. Avoiding cuts under half a tile is common tile-setting practice, not a numbered standard requirement.
Free accessFirst-principles arithmetic on the reader's own room and tile.
What governsEstimate. AHJ and licensed professional govern.
API field namesrun_in, tile_in, joint_in, min_cut_in, start_full_cut_in, tile_centered_cut_in, joint_centered_cut_in, first_full_edge_in
- Square room, one axis run it again for the other dimensionstated scope
- Minimum cut half a tile by default, or the reader's entrysetting practice