## Calculate Lighting Fixture’s Beam Angle and Lumen

#### Example 1: Calculate Lighting Fixture’s Lumen and Diameter of Illumination at surface having following details.

• 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. ### 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.

#### Example 2: Calculate Lighting Fixture’s Beam Angle and Illumination Diameter at surface having following details.

• 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.

#### Example 3: Calculate Lux Level and Illumination Diameter at surface having following details.

• Lighting Fixture Lumen is 299 Lumen.
• The distance from Lighting Fixture to illumination surface is 3 Meter.
• The Fixture Beam Angle is 10 Degree.

### Calculation:

• Required Lux at Surface (E2) =1390 Lux.
• Distance between Lighting Fixture and Surface (D) = 3 Meter.
• Fixture Beam Angle (ϕ)= 10°
• 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.
• Lumen of Lighting Fixtures= E1x Ω
• 299= E1x0.0239
• Irradiance at 1.0 meter (E1)= Lumen of Lighting Fixtures / Ω
• Irradiance at 1.0 meter (E1)=299 / 0.0239
• Irradiance at 1.0 meter (E1)= 12506 Lumen / M2
• Lux at Surface (E2) = E1 / (DxD)
• Lux at Surface (E2) =12506 / (3×3)
• Lux at Surface (E2) =1389.5 Lux
• Illumination Diameter at surface =0.018xDx ϕ
• Illumination Diameter at surface =0.018x3x10
• Illumination Diameter at surface =0.54 Meter.