LED Light Beam Angle & Lux Photometrics Calculator
Calculate light beam spread diameter, center illuminance in Lux and Foot-Candles via the Inverse Square Law, and resulting camera aperture f-stop values at any distance.
1. Fixture Output & Beam Angle
2. Photometrics & Exposure Verdict
The Inverse Square Law & Beam Geometry Formulas
Lighting photometrics follow precise geometric equations:
- The Inverse Square Law (E = I / d²): Doubling the distance from your light fixture to the actor cuts the illuminance to one quarter (2 stops loss). Moving from 1 meter to 3 meters cuts light intensity by a factor of 9 (over 3 stops).
- Beam Diameter Formula (D = 2 × d × tan(θ / 2)): The spread diameter of the light cone expands proportionally with distance d and beam angle θ.
- Foot-Candles to Lux: 1 foot-candle = 10.764 lux. In cinema lighting, 100 foot-candles at ISO 800 yields an exposure of approximately f/2.8 at 24 fps (1/48s shutter).
Worked examples: illuminance, exposure and coverage
The tool starts from the lux a fixture gives at one metre, divides it by the square of the distance, and converts to foot-candles by dividing by 10.764. It also turns the lux into an f-stop estimate using 800 and 48 in its formula, which read as an ISO of 800 and a 1/48 second shutter. The first table sets the distance to the tool's default of 3 m, with the standard 55 degree reflector.
| Fixture | Lux at 1 m | Lux at 3 m | Foot-candles | Estimated f-stop |
|---|---|---|---|---|
| 600 W COB | 65,000 lux | 7,222 lux | 671 | f/21.9 |
| 300 W COB | 30,000 lux | 3,333 lux | 310 | f/14.9 |
| 150 W COB | 15,000 lux | 1,667 lux | 155 | f/10.5 |
| 60 W portable | 6,000 lux | 667 lux | 62 | f/6.7 |
Moving the 600 W fixture changes the result in line with the inverse square law. Doubling the distance quarters the lux, which is two stops, and the beam widens in step.
| Distance | Lux | Estimated f-stop | Beam diameter |
|---|---|---|---|
| 1 m | 65,000 lux | f/65.8 | 1.04 m |
| 2 m | 16,250 lux | f/32.9 | 2.08 m |
| 3 m | 7,222 lux | f/21.9 | 3.12 m |
| 4 m | 4,063 lux | f/16.5 | 4.16 m |
| 6 m | 1,806 lux | f/11.0 | 6.25 m |
The beam angle does not change the lux in this tool. It changes only the diameter of the lit circle, and the tool reads that diameter as a coverage label. Over 2.5 m is a full standing subject, over 1.2 m is a medium close-up and anything smaller is a tight spot.
| Beam angle | Beam diameter at 3 m | Coverage label |
|---|---|---|
| 15 degrees, narrow spot | 0.79 m | tight spot |
| 30 degrees, medium reflector | 1.61 m | medium close-up |
| 55 degrees, standard hyper-reflector | 3.12 m | full standing subject |
| 90 degrees, softbox with grid | 6.00 m | full standing subject |
| 120 degrees, bare bulb flood | 10.39 m | full standing subject |
A real fixture concentrates its light when the beam narrows, so the lux at 1 m would rise. This tool does not model that. To compare a narrow beam with a wide one, enter the lux you measured with each as the base value.
Working Vocabulary
Key cinematography and lighting photometrics terms:
- Lux. The SI metric unit of illuminance equal to one lumen per square meter.
- Foot-Candle (fc). The imperial unit of illuminance equal to one lumen per square foot (1 fc ≈ 10.76 lux).
- Beam Angle. The angle between the two opposite points on the beam where intensity drops to 50% of the center maximum (FWHM).
- Field Angle. The angle between the points where light intensity drops to 10% of center maximum.
- Inverse Square Law. The physical law stating that light illuminance is inversely proportional to the square of the distance from the source.