# 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.

Jignesh Parmar has completed M.Tech (Power System Control), B.E(Electrical). He is member of Institution of Engineers (MIE) and CEng,India. Membership No:M-1473586.He has more than 16 years experience in Transmission -Distribution-Electrical Energy theft detection-Electrical Maintenance-Electrical Projects (Planning-Designing-Technical Review-coordination -Execution). He is Presently associate with one of the leading business group as a Deputy Manager at Ahmedabad,India. He has published numbers of Technical Articles in “Electrical Mirror”, “Electrical India”, “Lighting India”,”Smart Energy”, “Industrial Electrix”(Australian Power Publications) Magazines. He is Freelancer Programmer of Advance Excel and design useful Excel base Electrical Programs as per IS, NEC, IEC,IEEE codes. He is Technical Blogger and Familiar with English, Hindi, Gujarati, French languages. He wants to Share his experience & Knowledge and help technical enthusiasts to find suitable solutions and updating themselves on various Engineering Topics.

### 10 Responses to Calculate Lighting Fixture’s Beam Angle and Lumen

1. Vivekanand Pandey says:

Thank you sir

2. It s very useful for me
Thank you sir

3. Md. Mostaq says:

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Dear sir

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sir

5. AJAS ABDUL RASHEED says:

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6. omprakash2063@gmail.com says:

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9. ramya says:

Dear sir, In cable sizing.how will you tell voltage drop of running and staring is limiting between 3 and 6.is these values are fixed.

10. ARULANANDAM M says:

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