Enter the luminous flux and distance into the calculator to determine the illuminance, or enter the illuminance and distance to determine the luminous flux. You can also enter the illuminance and luminous flux to determine the distance. This calculator assumes a point light source with uniform emission (inverse-square law), so E = Φ / (4πr²) with distance measured from the source to the point of interest.
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Lumens to Lux Formula
The following formula is used to estimate the illuminance (lux) at a distance from a light source when the source is treated as an ideal point source with uniform emission (inverse-square law).
E = F / (4πd²)
Variables:
- E is the illuminance in lux
- F is the luminous flux in lumens
- d is the distance from the light source to the point of measurement in meters
To calculate the illuminance for an isotropic point source, divide the luminous flux by 4π times the square of the distance. (More generally, illuminance is defined as E = F / A, where A is the illuminated area in m².)
| Lumens (lm) | Distance (m) | Illuminance (lux) |
|---|---|---|
| 100 | 0.5 | 31.831 |
| 100 | 1 | 7.958 |
| 100 | 2 | 1.989 |
| 100 | 3 | 0.884 |
| 300 | 0.5 | 95.493 |
| 300 | 1 | 23.873 |
| 300 | 2 | 5.968 |
| 300 | 3 | 2.653 |
| 800 | 0.5 | 254.648 |
| 800 | 1 | 63.662 |
| 800 | 2 | 15.915 |
| 800 | 3 | 7.074 |
| 1500 | 0.5 | 477.465 |
| 1500 | 1 | 119.366 |
| 1500 | 2 | 29.842 |
| 1500 | 3 | 13.263 |
| 3000 | 0.5 | 954.930 |
| 3000 | 1 | 238.732 |
| 3000 | 2 | 59.683 |
| 3000 | 3 | 26.526 |
| Assumes a point source with uniform emission (inverse-square law). Formula: E (lux) = Φ (lumens) / (4πr²), r in meters. For reference: 1 foot-candle = 10.764 lux. | ||
What is Illuminance?
Illuminance is a measure of how much luminous flux is spread over a given area. It is commonly measured in lux (lx), where one lux is equal to one lumen per square meter. Illuminance is an important concept in lighting design, as it helps in understanding how well a space will be lit and how evenly the light will be distributed. Higher illuminance levels indicate brighter lighting, while lower levels indicate dimmer lighting.
How to Calculate Illuminance?
The following steps outline how to calculate the illuminance.
- First, determine the luminous flux (F) in lumens.
- Next, measure the distance (d) from the light source to the surface in meters.
- Finally, calculate the illuminance (E) using the point-source inverse-square approximation: E = F / (4πd²).
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Luminous Flux (F) = 800 lumens
Distance (d) = 2 meters