Generally you would as a starting point be looking at a spacing of about 3ft apart for standard downlights.
This is a possible method of calculation that I obtained somewhere on an earlier web trawl:
Lighting Calculations
How Many Fittings are Required for a Room
The utilisation factor table and a few simple formulas allow us to calculate the number of fittings required for any room.
Utilisation factor table that is available on most fittings.
e.g. UTILISATION FACTOR TABLE (for 2x36 bare batten)
LOR: 88.1% SHR NOM 1.75: 1.0 Disregard SHR MAX.
Reflectance Room Index (K)
Ceiling Wall Floor 0.75 1.00 1.25 1.5 2.0 2.50 3.00 4.00 5.00
0.50 0.30 0.20 0.30 0.37 0.42 0.46 0.52 0.56 0.59 0.63 0.66
Across the Top of the Table
Name Description
LOR Light output ratio for this fitting. Not required in a simple calculation.
SHR NOM Nominal Spacing to Height ratio. For a given mounting height we can see the nominal spacing between fittings. E.g. 1.75 to 1 means that for every 1 metre of mounting height (above work plane) we should have a maximum 1.75 metres between fittings.
SHR MAX Used by lighting design software and not needed for manual calculations.
Reflectance Select a horizontal line for the reflectance values that best describe the room.
Typical Reflectance Values are:
Ceiling Walls Floor
Air Conditioned Office 0.7 0.5 0.2
Industrial 0.5 0.3 0.2
Utilisation Factor (body of the table)
This is a value between 0 and 1 that represents the percentage of total lamp lumens in the room that fall on the work plane. It takes into account the room reflectances, room shape, polar distribution and light output ratio of the fitting.
Step 2: Calculate Room Index (K)
Room Index:
The room index is a number that describes the ratios of the rooms length, width and height.
Formula: K = (L x W)/ (Hm (L+W))
Where: L = Room Length, W = Room Width, Hm = Mounting Height of Fitting (from working plane), Work Plane = Desk or Bench Height
The result of this calculation will be a number usually between 0.75 and 5.
Note: This formula for K is only valid when room length is less than 4 times the width or when the K value is greater than 0.75.
Step 3: Using the room index and reflectance values in the utilisation factor table
For the horizontal row select the reflectance that best describes the room.
For the vertical column select the room index value K as calculated above.
The utilisation factor for this fitting in this room is where the row and column intersect.
Step 4: To calculate the number of fittings required use the following formula:
Formula: N = (E x A)/(F x uF x LLF)
Where:
N = Number of Fittings, E = Lux Level Required on Working Plane , A = Area of Room (L x W), F = Total Flux (Lumens) from all the Lamps in one Fitting, UF = Utilisation Factor from the Table for the Fitting to be Used, LLF = Light Loss Factor. This takes account of the depreciation over time of lamp output and dirt accumulation on the fitting and walls of the building.
Typical LLF Values
Air Conditioned Office 0.8
Clean Industrial 0.7
Dirty Industrial 0.6
Step 5: Space the number of fittings uniformly around the room drawing and check the SHR nominal for the fitting has not been exceeded. If it has been exceeded re space the fittings to get back to SHR nom.
Step 6: Work out the number of fittings required in each axis of the room:
Number in Length = Root (Total * L/W)
Number in Width = Root (Total * W/L)
