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# Lighting variables and formulae #### Luminous flux

Luminous flux defines all of the light that is emitted by a light source in all directions.

Symbol: ϕ
Unit: Lumen
Symbol: lm #### Solid angle

The solid angle is a geometric quantity that describes a space segment inside a sphere. It defines the relationship between the size of an area on the surface of a sphere and the square of the spherical radius.

Symbol:
Symbol: sr

A: Illuminated area (spherical calotte) in m2

r: Distance between the light source and the illuminated area (spherical radius) in m #### Luminous intensity

The luminous intensity conveys the relationship between the luminous flux and a defined solid angle. Luminous intensity is a measure for the light emission from a light source in a certain direction.

Symbol: I
Unit: Candela #### Degree of illuminance

The degree of illuminance is a measure for the light striking a surface. It determines the relationship between the luminous flux that strikes an illuminated surface and the size of this surface.

Symbol: E
Unit: Lux
Symbol: lx #### luminance

Luminance describes a measure for the brightness impression that is created in the human eye of a luminous or illuminated surface. The numerical value of the luminance is obtained by dividing the luminous intensity by the size of the area as seen from the measuring distance.

Symbol: L
Unit: Candela per m2
Symbol: cd/m2 #### Luminous efficiency

The luminous efficiency indicates the efficiency with which the absorbed electrical power P is converted into light, i.e. how much luminous flux per watt of absorbed electrical power is generated by a light source.

Symbol: η
Unit: Lumen per watt
Symbol: lm / W

### Fast rough calculation

The number of luminaires required indoors and outdoors can be determined with a simple approximate calculation.

A standard value of between 3 and 6 m is assumed as the room height for the interior. If the room is higher, the required number of luminaires rises in order to reach the required average degree of illuminance.

Outdoors, we assume mounting heights of 4 to 6 m. As a rule, the degrees of illuminance that must be reached here are so low (about 10 lx) that differences in mounting heights within the defined range are between 1 and 2 lx. This cannot be detected with the naked eye.

The size of the surface and the required degree of illuminance are usually integral components of light planning. The total luminous flux ϕtot must be determined, by means of which the number and type of luminaires required can be defined.

The calculated total luminous flux ϕtot is divided by the luminous flux ϕ of a selected luminaire to give the theoretical number of luminaires.

This result only needs to be divided by the luminaire maintenance factor MF (defined as 0.8).

This gives a rough approximation of the required number of luminaires.  Legend

n: Number of luminaires
E: median degree of illuminance
A: Surface
ϕ: Luminous flux of the luminaire
ϕtot: Total luminous flux
MF: Maintenance factor – defined as 0.8 Outdoors
Mounting height between 4 and 6 m Indoors
Mounting height between 3 and 6 m