Common LEP Light Source Calculation Formulas
How to calculate candela, LUX, illumination distance and field angle of LEP light engines.
1. Luminous Intensity Calculation
Formula 1
Where:
I = Luminous Intensity (cd)
E = Illuminance (lux)
d = Distance (m)
Example (40 W LEP Module)
Its LUX is 8400 at 15 meters, thus,
I=1.89Mcd
Formula 2
Where:
I = Luminous Intensity (cd)
L = Source Luminance (cd/mm^2)
A = Effective Lens Area (mm^2)
Where:
De = Effective Lens Diameter
This formula is commonly used to calculate source luminance from measured luminous intensity.
Note: Effective lens diameter should be used instead of the maximum mechanical diameter.
Example:
Lens Diameter = 30 mm
Effective Diameter = 28 mm
Calculations should be based on:
De=28mm, rather than 30 mm.
2. Beam Distance Calculation
Three commonly used distance criteria are shown below.
Formula 1 — Searchlight Standard (0.25 lux)
Where:
R = Beam Distance (m)
I = Luminous Intensity (cd)
Example (40 W LEP Module)
Result= 0.25 lux@2,749m
Formula 2 — Emergency Evacuation Lighting Standard (1 lux)
Example (40 W LEP Module)
Result= 1 lux@1,375m
Formula 3 — Office Desk Lighting Standard (minimum 300 lux)
Example (40 W LEP Module)
Result= 300 lux@79m
3. Beam Spot Diameter Calculation
Where:
D = Spot Diameter (m)
d = Distance (m)
α = Half Beam Angle (°)
Dl = Lens Diameter (m)
Example
40 W LEP Module + 55 mm Collimating Lens
Parameters:
d = 10m
α = 2°
Dl = 0.055m
Result:
Spot Diameter=0.75m
4. Beam Angle Definition
Two industry-standard beam angle definitions are commonly used.
Standard 1 — FWHM (50% Beam Angle)
Full Width at Half Maximum (FWHM)
Definition:
The included angle between the two points where the luminous intensity falls to:
50%×Max Intensity
Applications: LED Spotlights, Floodlights, Stage Lighting
Purpose:
- Characterizes the width of the central hotspot.
- Most common beam-angle specification in the lighting industry.
Standard 2 — FWTM (10% Beam Angle)
Full Width at Tenth Maximum (FWTM)
Definition:
The included angle between the two points where the luminous intensity falls to:
10%×Max Intensity
Applications: Outdoor Searchlights, Wall Washers, Roadway Lighting, Long-Range Illumination Systems
Purpose:
- Defines beam spread and spill light.
- Evaluates effective illuminated area.
- Helps determine glare control and beam boundary.
5. LEP Beam Angle Measurement Standard
For LEP beam-diameter calculations, the beam angle is defined according to the FWTM (10%) standard.
Example
For a 40 W LEP module, its center lux is 8400. The beam boundary is defined at 840 lux.
The beam radius is measured from the beam center to the position where illuminance equals 840 lux.
The corresponding beam diameter is: D=2r, where r is the distance from the beam center to the 840 lux contour.