 # 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
Abbreviation: 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: Ω
Abbreviation: sr

A: Illuminated surface (spherical calotte) in m2
r: Distance between the light source and the illuminated surface (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:
CandelaAbbreviation: cd

• 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
Abbreviation: 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 luminance is obtained by dividing the luminous intensity by the size of the surface as seen from the measuring distance.

Symbol: L
Unit: Candela per m2
Abbreviation: cd/m2

• Luminous efficiency Luminous efficiency specifies how efficiently the consumed electrical power P is converted into light, that is, how much luminous flux per watt of consumed electrical power is generated by a light source.

Symbol: η
Unit: Lumen per watt
Abbreviation: 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 for the room height indoors. 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. It is important to determine the total luminous flux φtot, by means of which the required luminaires and their number can be defined.

The total luminous flux φtot is divided by the luminous flux φ of a selected luminaire, the result being 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.

The formula:

n = Number of luminaires
E = Average degree of illuminance
A = Surface
φ = Luminous flux of the luminaire
φtot = Total luminous flux
MF = Maintenance factor – defined as 0.8

Outdoors
Indoors