How to use the calculator
- Measure the distance from the light to the surface you want to light, straight along the beam.
- Enter the beam angle from the lamp’s packaging or datasheet, or switch to “beam angle for a spot size” and enter the diameter you want.
- If the datasheet lists the peak (centre-beam) intensity in candela, enter it to get the illuminance at the centre of the spot.
Formula
The beam is treated as a cone with its tip at the light:
spot diameter D = 2 × d × tan(θ ÷ 2) | beam angle θ = 2 × arctan(D ÷ 2d)
with d the distance and θ the beam angle. Centre illuminance follows the inverse-square law: E = I ÷ d², with I in candela and d in metres giving lux.
What “beam angle” means
Lamp makers usually define the beam angle as the full angle between the two directions where the intensity has fallen to 50% of its peak. So the edge of the calculated spot is where the light is about half as bright as at the centre, and some light still falls outside it. Some datasheets also give a wider “field angle” (often defined at 10% of peak); you can enter that instead to see the outer edge of the light.
Units
Distances in metres or feet, angles in degrees, intensity in candela (cd), illuminance in lux (lx); 1 fc ≈ 10.764 lx.
Source
Plain trigonometry for a cone, and the inverse-square law for a point source. No lamp data is built into the tool; the beam angle and candela come from your lamp’s datasheet.
Limits of this calculator
- It assumes the light points straight at a flat surface. Aimed at an angle, the spot becomes an ellipse and is larger than shown.
- The inverse-square law is accurate when the distance is large compared with the size of the light. Close to large fittings or LED panels it overestimates the illuminance.
- Reflectors and lenses do not produce perfectly even cones, so the real light distribution differs from the simple model.
- For vehicle lights it only shows geometry. Whether a light may be fitted or used on public roads depends on official vehicle lighting rules where you drive, which this tool does not check.