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

What is the Relation between  Lux, Lumen, and Illumination?

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

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

The Lux value of any light source is not a static value so cannot be part of a standard specification. Only the 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 miter.

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 the light; it can also mean glory or 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 lumens/watt because in that light everything is just different intensity of green.

Let's 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 meter, lights up that square meter with an illuminance of 1000 lux. The same 1000 lumens, spread out over ten square meters, produce 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.

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

Required illumination at the surface is 1390 Lux
The distance from Lighting Fixture to the illumination surface is 3 Meters.
The Fixture Beam Angle is 10 Degrees.

Calculation:
Required Lux at Surface (E2) =1390 Lux.
Distance between Lighting Fixture and Surface (D) = 3 Meters.
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 the lighting fixture’s lumen and diameter of illumination at the surface when known the following values:.
Required illumination at the surface is 22 Lux
The lighting Fixture Lumen is 1547 Lumen.
The distance from Lighting Fixture to the illumination surface is 4 Meters.

Calculation:
Required Lux at Surface (E2) =22 Lux.
Distance between Lighting Fixture and Surface (D) = 4 Meters.
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 Meters.

Lux Meter

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A lux meter is a device that uses for measuring brightness. A lux meter works by using a photocell 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 Greatist 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