How Calculate Lux and Lumen of Light Illumination in a Surface?

What is the Relation between  Lux, Lumen and Illumination?


Lux is luminous intensity what is also said as candela per meter squared. It is the amount of light fallen on a surface .

Basically lux means daylight, brightness, illumination. For ‘light of the world’ the Vulgate has lux mundi. ‘At first light’ is prima luce.


Lux value of any light source is not a static value so cannot be part of a standard specification. Only manufacturer can determine and specify the total lumen output.


Lux is a measure of the perceived brightness level per unit area. 1 lux = 1 lumen / sq metre.



What Is Lumen?

Lumen is the measure of visible light emitted by a light source.  It is also referred to as "luminous flux" or sometimes as "luminous power".

Lumen means a source of light, a lamp, an opening in the wall that lets in light; it can also mean glory, excellence. In the plural lumina can mean ‘eyes’. But there is also a certain amount of overlap between the two words.


A typical incandescent bulb provides about 860 lumen output for 60 W input so about 14 lumens/watt.


An LED will give about 800 lumens for 10 Watts so about 80 lumens/watt.


No practical light source will achieve 683 lumen/watt because in that light everything is just different intensity of green.


Let consider the mathematical example below to understand the relation between lux and lumen of light:



A flux of 1000 lumens, concentrated into an area of one square metre, lights up that square metre with an illuminance of 1000 lux. The same 1000 lumens, spread out over ten square metres, produces a dimmer illuminance of only 100 lux. Mathematically, 1 lx = 1 lm/m2. or, lux = lumens / (solid_angle * distance^2)
For graphical understanding look at the following single graph to find the relationship between Lux and Lumen.


Lux and Lumen Relationship

Case Study-01: 
The calculation of lighting fixture’s lumen and diameter of illumination at surface when known the following values:

Required illumination at surface is 1390 Lux
The distance from Lighting Fixture to illumination surface is 3 Meter.
The Fixture Beam Angle is 10 Degree.

Lux and Lumen Calculation

Calculation:

Required Lux at Surface (E2) =1390 Lux.
Distance between Lighting Fixture and Surface (D) = 3 Meter.
Fixture Beam Angle (ϕ)= 10°
Irradiance at 1.0 meter (E1)= DxDxE2
Irradiance at 1.0 meter (E1)=1390x3x3 =12510 Lumen / M2
Irradiance at 1.0 meter (E1)= 12510 Lumen / M2
Solid Angle of The Lamp (Ω) =2xπx(1-COS(ϕ/2))
Solid Angle of The Lamp (Ω) =2×3.14x(1-COS(10/2)) =6.28x(1-0.996)
Solid Angle of the Lamp (Ω) =0.0239 Steradian.
Required Lumen of Lighting Fixtures= E1x Ω
Required Lumen of Lighting Fixtures=12510×0.0239
Required Lumen of Lighting Fixtures=299 Lumen.
Illumination Diameter at surface =0.018xDx ϕ
Illumination Diameter at surface =0.018x3x10
Illumination Diameter at surface =0.54 Meter.


Case Study-2: 

The calculation of lighting fixture’s lumen and diameter of illumination at surface when known the following values:.
Required illumination at surface is 22 Lux
Lighting Fixture Lumen is 1547 Lumen.
The distance from Lighting Fixture to illumination surface is 4 Meter.

Calculation:
Required Lux at Surface (E2) =22 Lux.
Distance between Lighting Fixture and Surface (D) = 4 Meter.
Irradiance at 1.0 meter (E1)= DxDxE2
Irradiance at 1.0 meter (E1)=4x4x22 =352 Lumen / M2
Irradiance at 1.0 meter (E1)= 352 Lumen / M2
Solid Angle of The Lamp (Ω) = Lumen of Lighting Fixtures / E1
Solid Angle of the Lamp (Ω) =1547 / 352
Solid Angle of the Lamp (Ω) =4.394 Steradian.
Solid Angle of The Lamp (Ω) =2xπx(1-COS(ϕ/2))
39 =2×3.14x(1-COS(ϕ/2))
Fixture Beam Angle (ϕ)=145°
Illumination Diameter at surface =0.018xDx ϕ
Illumination Diameter at surface =0.018x4x145
Illumination Diameter at surface =10.44 Meter.



Lux Meter

Sponsored:
A lux meter is a device that uses  for measuring brightness. A lux meter works by using a photo cell to capture light. The meter then converts this light to an electrical current.  It specifically measures the intensity with which the brightness appears to the human eye.


Common Digital Lux Meter Available at Local Market :
  1. The Dr. Meter Digital Illuminance Meter
  2. The Geartist Digital LCD Lux Meter
  3. The Tondaj Digital Luxmeter Light Meter
  4. The Maximum Horticulture LX-1010B Digital Luxmeter Light Meter
  5. The CEM DT-1309 Professional Digital Lux Meter

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