Maximum spacing
S = min(ratio x MH, sqrt(Phi x UF x MF / E))
The tighter of the distribution rule and the illuminance rule wins, because both have to be satisfied.
Guide
Turning a fixture count into positions that respect the ceiling grid, the structure, and the way people actually use the room.
Decide the maximum spacing from the mounting height and the distribution ratio, then check it against the illuminance target. When the illuminance rule demands closer spacing than the distribution allows, the answer is more output per fixture rather than more fixtures, or an accepted lower light level with the client informed in writing.
Recessed fixtures need the plenum depth, lay-in fixtures need the grid module, and everything needs a support point. A perfect photometric grid shifts by a few hundred millimetres as soon as the joists, ducts, and sprinkler heads are drawn in. Set the grid from the photometry, then adjust the whole array rather than individual fixtures, so the spacing stays close to even.
Wall and end-of-row offsets are normally half the spacing, which puts light on the perimeter where the room would otherwise go dark and keeps the wall from being washed unevenly. Corners usually need one more fixture, not a tighter overall spacing, and racks and tall furniture change the offset again.
Rows and columns make circuiting easy, but the occupant needs zones: perimeter daylight, presentation or whiteboard rows, task areas, and circulation. Draw the zones first and let the electrician follow, otherwise the switching ends up being whatever was convenient to wire and the controls credits in the drawings are never realised.
Fixtures over fixed equipment, behind racking, or above a clean-room ceiling cannot be serviced. Group the long-life sources over the inaccessible positions and the easily replaced ones where access exists, and record the driver and lamp types on an equipment schedule that survives the handover.
S = min(ratio x MH, sqrt(Phi x UF x MF / E))
The tighter of the distribution rule and the illuminance rule wins, because both have to be satisfied.
offset = S / 2
The standard half-spacing offset from the wall or the end of the row, adjusted for tall furniture or racking.
E = N_grid x Phi x UF x MF / A
Always recompute after adjusting positions, because a shifted grid delivers a different average than the ideal one.
Inputs: Standard troffers at 4,000 delivered lumens, utilization factor 0.7, maintenance factor 0.8, target 300 lux, nine foot ceiling.
The ratio rule allows about nine feet between fixtures, while the illuminance rule allows sqrt(2,240 / 300) = 2.7 metres, or 9.0 feet. They agree, so a nine foot grid works, with a four and a half foot offset from the walls.
Inputs: High bay fixtures at 24,000 delivered lumens, utilization factor 0.75, maintenance factor 0.7, target 300 lux, twelve foot mounting height, wide distribution.
The illuminance rule allows sqrt(12,600 / 300) = 6.5 metres, or 21 feet, which exceeds the ratio rule of 1.3 x 12 = 15.6 feet. The distribution governs here, so the fixtures go at 15.6 feet and the room ends up brighter than the target.
Align the array with the room and the work plane first, then shift the whole array if a ceiling module demands it. Individual fixtures should never be moved off the array, because uneven spacing is more visible than a small overall offset.
Treat the racking as part of the room geometry: it changes the utilization factor and it decides whether rows run above the aisle or above the rack. Run the count with a realistic utilization factor rather than adjusting the spacing afterwards.
Enough to match the way the room is used: perimeter daylight, presentation, task, and circulation covers most commercial spaces. More than about six zones in a single room tends to be under-used, and the wiring cost exceeds the energy it saves.