Lumens to Lux Calculator
Calculate illuminance in Lux (lx) and Foot-Candles (fc), luminous intensity in Candela (cd), and beam spread coverage with the optical Inverse Square Law.
Light Source & Distance
Step-by-Step Inverse-Square Photometric Derivation Proof
How to Calculate Lux from Lumens
To find Lux from Lumens, distance d, and beam angle θ: 1. Solid Angle: Ω = 2π(1 − cos(θ/2)) sr. 2. Intensity in Candela: I = Lumens / Ω. 3. Illuminance in Lux: E = I / d². 4. Foot-Candles: fc = Lux / 10.764.
Photometric Units: Lumens, Lux, Candela & Foot-Candles
Photometry quantifies optical radiation as perceived by the standardized human visual response curve ($V(\lambda)$):
Total light power emitted
Light per square meter (lm/m²)
Flux per steradian in beam
1 fc = 10.764 Lux
IES Architectural Indoor Lighting Recommendations
| Environment / Task | Target Illuminance (Lux) | Target (Foot-Candles) |
|---|---|---|
| Hallways & Corridors | 100 – 150 Lux | 10 – 14 fc |
| Living Rooms & Dining Areas | 150 – 300 Lux | 14 – 28 fc |
| Commercial Office Desks & Classrooms | 400 – 500 Lux | 37 – 46 fc |
| Precision Assembly & Medical Exam Rooms | 1,000 – 2,000 Lux | 93 – 186 fc |
Real-World Applications of Photometric Analysis
Architectural Lighting Design
Engineers calculate fixture spacing and ceiling heights to ensure uniform lux distribution without dark spots or glare.
Film & Studio Key Lighting
Cinematographers use incident light meters in foot-candles to calibrate key-to-fill light ratios and sensor exposure.
Agricultural Grow Lights
Greenhouses evaluate Photosynthetically Active Radiation (PAR) canopy coverage based on inverse-square light dissipation.
Step-by-Step Worked Numerical Solutions
Problem: Find center lux for a 4,000-lumen ceiling fixture suspended 2.8 meters above a desk with a 90° beam angle.
Common Pitfalls & Mistakes
Assuming Lumens = Brightness on Desk
A 1,000-lumen bulb 5 meters away provides very little desk illuminance (~13 lux), while the same bulb at 1 meter provides 318 lux.
Ignoring Beam Angle Concentration
A narrow 25° spotlight focuses all lumens into a tight intense beam, creating much higher center lux than a wide 120° floodlight.
Linear Distance Falloff Fallacy
Light drops off with distance squared (d²), not linearly. Moving a light from 1m to 2m cuts illuminance to ¼, not ½.
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