### Daylight Factors

Defining the daylight factor

The daylight factor (DF) is a very common and easy to use measure for the subjective daylight quality in a room. It describes the ratio of outside illuminance over inside illuminance, expressed in per cent. The higher the DF, the more natural light is available in the room. It is expressed as such:

DF = 100 * Ein / Eext
Ein
inside illuminance at a fixed point
Eext
outside horizontal illuminance under an overcast (CIE sky) or uniform sky.

The Ein illuminance can be considered as the sum of three different illuminances:

• the direct iluminance if the sky is visible from the considered point (ED)
• the illuminance due to the reflexions on the outside environment (EER)
• the illuminance due to the reflexions on the inside surfaces (EIR)

Hence, the daylight factor can be expressed as the sum of three component:

DF = DC + ERC + IRC
DC
direct component
ERC
externally reflected component
IRC
internally reflected component

A daylight factor can be measured for a specific point or expressed as an average. The latter is the arithmetic mean of the sum of point measurements taken at a height of 0.85 m in a grid covering the whole floor area of the room. Different countries have different regulations and may require the use of point or average measurements.

A daylight factor can also be expressed as an average using experimental formulas. Several formulas for estimating the averageDF in a room are in use today. Depending on the country and its legislation, one or the other might be more common:

IES formula
DFm, IES = ( Awindow ε U * 100 ) / ( Afloor )
BRE formula
DFm, BRE = ( Awindow α M t ) / ( Atotal ( 1 - ρm² ) )
Sumpner formula
DFm, Sumpner = ( Awindow α M t ) / ( 2 Atotal ( 1 - ρm ) )
Italian legislation
DFm, Italy = ( Awindow ε ψ t ) / ( Atotal ( 1 - ρm ) )
Awindow
Surface area of the window, excluding frame, bars and other obstructions [m²]
Afloor
Floor area of the room [m²]
Atotal
Total internal surface area of the room [m²]
ε
Factor to account for external obstructions
U
Utilisation factor
α
Angle of visible sky from the mid-point of the window [°]
M
Maintenance factor of the window
t
Transmission factor of the glazing
ρm
Average reflection factor of all internal surfaces
ψ
Factor to account for thickness of the window wall

Rooms with an average DF of 2% are considered daylit. However, a room is only perceived as well daylit when the DF is above 5%. Daylight factors are always measured under an overcast sky or in an artificial sky which simulates a standard CIE overcast sky.

Average DF Appearance Energy implications
< 2% room looks gloomy Electric lighting needed most of the day
2% to 5% Predominantly daylit appearance, but supplementary artificial lighting is needed. Good balance between lighting and thermal aspects
> 5% Room appears stongly daylit Daytime electric lightin rarely needed, but potential for thermal problems due to overheating in summer and heat losses in winter
DF and appearance, thermal performance

In addition to the DF formulas for side-lit rooms shown above, more specific ones canbe derived such as daylight factors for atrium spaces.