Lighting Calculator: Lumens, Lux and Number of Luminaires

How lumens and lux relate

The lumen (lm) measures the total light a source emits. Lux (lx) measures how densely light falls on a surface: one lumen on one square metre is one lux. So lux = lumens / square metres. Not all the light leaving a luminaire reaches the working plane, though. Some is lost on walls and ceiling. The lumen method allows for that with two factors.

The lumen method

n = E × A / (Φ × UF × MF)

• E: required average illuminance (lx)
• A: room area (m²)
• Φ: luminous flux of one luminaire (lm)
• UF: utilisation factor, the share of light reaching the working plane
• MF: maintenance factor, for dirt and light loss over time

Read the other way round, the formula gives the illuminance from a known number of luminaires: E = n × Φ × UF × MF / A.

Example

An 8 m × 6 m office needs 500 lx. Take 3600 lm luminaires with UF 0.5 and MF 0.8. Each luminaire delivers 3600 × 0.5 × 0.8 = 1440 lm to the working plane. The number needed is 500 × 48 / 1440 = 16.7, so 17 luminaires. With 17 the average illuminance is 510 lx.

Utilisation factor and room index

The utilisation factor is read from the manufacturer's table, which is entered with the room index: K = a × b / (h × (a + b)). Here h is the height of the luminaire above the working plane. Wide, low rooms have a high index and narrow, tall rooms a low one. The utilisation factor rises with the index.

Point source method

The illuminance one source produces at a given point follows from its luminous intensity: E = I × cos θ / d². With the source 3 m up and the point 4 m to the side, the distance is 5 m and cos θ = 0.6. For 2400 cd the illuminance is 2400 × 0.6 / 25 = 57.6 lx.

Limits

The lumen method gives an average. Uniformity, glare, colour rendering and emergency lighting are assessed separately. Required illuminance levels are not built into the tool and must come from the applicable standard. For a final design use lighting software and the manufacturer's photometric data.