Illuminance from a Lamp Calculator (Inverse Square and Cosine Law)
Light level in lux at any point on a floor, desk or wall below a lamp, from its luminous intensity, height and how far to the side the point is.
Results
The dashed line marks the value you entered.
What this tool does
Illuminance falls with the square of the distance and, on a surface the light strikes at an angle, also with the cosine of that angle — so a point on the floor beneath the lamp gets far more than one a couple of metres to the side, as the chart shows. The luminous intensity in candela, in the direction of the point, comes from the lamp's photometric data; a bare bulb emitting the same in all directions gives its lumens ÷ 4π. The formula treats the lamp as a point, which holds once the distance is about five times the size of the light.
Formula
E = I × cos θ ÷ d² · on the floor: E = I × h ÷ d³
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ic | Luminous intensity towards the point | cd |
hm | Height of the lamp above the surface | m |
x | Horizontal distance from below the lamp | m |
EH | Illuminance on the horizontal surface | lx |
EF | Illuminance on a surface facing the lamp | lx |
D | Distance to the lamp | m |
TH | Angle of the light from the vertical | ° |
Worked example
- Luminous intensity towards the point1000 cd
- Height of the lamp above the surface2.5 m
- Horizontal distance from below the lamp1 m
- Illuminance on the horizontal surface128.1 lx
- Illuminance on a surface facing the lamp137.9 lx
- Distance to the lamp2.693 m
- Angle of the light from the vertical21.8 °
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.