## Calculate Lighting Fixture’s Beam Angle and Lumen

May 1, 2018 Leave a comment

**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:__

__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:__

__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:__

__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.**

## Recent Comments