Illuminance (Lumen Method)

The lumen (zonal cavity) method for average maintained illuminance and luminaire count.

1. What this check does

Computes the room cavity ratio, the number of luminaires needed for the target average maintained illuminance, a near-square grid that fits the room, and the illuminance that grid delivers. Optionally checks spacing against the luminaire spacing criterion and reports lighting power density.

2. Inputs used

Room length, width and ceiling height; work plane height (default 0.76 m / 30 in) and suspension length.
Target maintained illuminance, chosen by you from IES recommendations or the owner standard.
Luminaire lumens and watts, coefficient of utilization (CU) from the photometric report at the computed RCR, light loss factor (LLF), and optionally the spacing criterion (SC).

3. Formulas and assumptions

Cavity height

h_{rc} = H_{\text{ceiling}} - h_{\text{work plane}} - h_{\text{suspension}}

Room cavity ratio

\mathrm{RCR} = \dfrac{5\,h_{rc}\,(L + W)}{L\,W}

Luminaires

N = \left\lceil \dfrac{E\,A}{\Phi\cdot \mathrm{CU}\cdot \mathrm{LLF}} \right\rceil

Grid

c = \mathrm{round}\sqrt{N\,\dfrac{L}{W}} \qquad r = \left\lceil \dfrac{N}{c} \right\rceil \qquad E_{\text{achieved}} = \dfrac{r\,c\,\Phi\cdot \mathrm{CU}\cdot \mathrm{LLF}}{A}

Columns along the long side.

Spacing check

\max\!\left(\dfrac{L}{c},\ \dfrac{W}{r}\right) \le \mathrm{SC}\cdot h_{rc} \qquad \mathrm{LPD} = \dfrac{\text{count}\cdot \text{watts}}{A}

Symbols

$h_{rc}$	Room cavity height, luminaire plane to work plane	m
$L,\ W,\ A$	Room length, width and floor area	m, m²
$\mathrm{RCR}$	Room cavity ratio
$E$	Target average illuminance	lux
$\Phi$	Rated lumens per luminaire	lm
$\mathrm{CU},\ \mathrm{LLF}$	Coefficient of utilization; light loss factor
$c,\ r$	Luminaire columns and rows
$\mathrm{SC}$	Spacing criterion of the luminaire
$\mathrm{LPD}$	Lighting power density	W/m²

Room section with luminaire plane, work plane, and the room cavity height hrc between them. — **Figure 1.** Room cavities: ceiling cavity, room cavity and floor cavity.

Room plan with a grid of luminaires, spacing along length and width, and the limit SC times hrc. — **Figure 2.** Luminaire grid and maximum spacing.

Rectangular room with luminaires in a regular grid; the result is the average over the work plane.
CU already reflects the room surface reflectances; RokBench does not reproduce CU tables or recommended illuminance values.
LLF combines lamp lumen depreciation, luminaire dirt depreciation and ballast or driver factor as you choose.

4. What is NOT checked

Uniformity and point-by-point illuminance.
Glare and vertical illuminance.
Emergency lighting levels and duration.
Energy-code lighting power density limits.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

IES Lighting Handbook — lumen method and recommended illuminance
ASHRAE/IES Standard 90.1 — lighting power density
NFPA 101 Section 7.9 — emergency lighting
Manufacturer photometric reports (CU tables, spacing criterion)

6. Validation cases

These worked examples run through the engine on every change; the expected values come from the cited source. All cases: Validation.

Lumen method, 20 × 10 m room, 500 lux lighting/lumen · Hand calculation

Pass

Source: Hand calculation from the lumen method equations — hrc = 3 − 0.8 = 2.2 m; RCR = 5·2.2·30/200 = 1.65; N = 500·200/(5000·0.6·0.8) = 41.67 → 42; grid 9 × 5 = 45; E = 45·2400/200 = 540 lux.

Quantity	Expected	RokBench	Error	Result
rcr	1.65	1.65	0%	Pass
requiredCount	42	42	0%	Pass
achievedLux	540	540	0%	Pass

7. Known issues and changes

See the Engineering Notes. Try the tool: Illuminance (Lumen Method).