๐ก Lumens to Lux Calculator
Assumes an idealized point source radiating light equally in all directions.
Enter a light source's total luminous flux (lumens) and its distance (m) to calculate the illuminance (lux) at that point, based on the inverse-square law (illuminance is inversely proportional to the square of the distance from the source). Assumes an isotropic point source emitting light equally in all directions.
How to use
- Enter the light source's total luminous flux (lumens).
- Enter the distance (m) from the light source.
- The illuminance (lux) at that distance is calculated automatically.
How the calculation works
This tool calculates the illuminance (lux) at a given distance from a light source's total output (luminous flux, in lumens), assuming a point source that emits light equally in all directions. First, the flux is divided by 4ฯ, the solid angle of a full sphere in steradians, to get the luminous intensity in each direction (candela). Then the inverse-square law gives the illuminance: intensity divided by the distance squared. Intensity (cd) = flux (lm) รท 4ฯ Illuminance (lx) = intensity (cd) รท distance (m)ยฒ Because illuminance falls with the square of the distance, doubling the distance gives one quarter of the illuminance, and tripling it gives one ninth.
Worked example
1000 lm bulb at 1 m Intensity: 1000 รท 4ฯ โ 79.6 cd Illuminance: 79.6 รท 1ยฒ โ 79.6 lx Same bulb at 2 m Illuminance: 79.6 รท 2ยฒ โ 19.9 lx (a quarter of the value at 1 m) Recommended illuminance (JIS Z 9110) Offices: 750 lx; reading in a living room: around 500 lx
Things to be aware of
- Fixtures that direct light downwards, such as ceiling lights, downlights and spotlights, give more light directly below than this calculation. Use the fixture's light distribution data if you have it.
- Light reflected from ceilings and walls is not included, so real rooms are usually brighter than the calculation.
- The point-source approximation works well when the distance is large compared with the size of the light source.
FAQ
What is the inverse-square law?
A physics law stating that the intensity of light from a point source is inversely proportional to the square of the distance from it โ doubling the distance reduces illuminance to one-quarter.
What formula is used?
First, luminous intensity (candela) = total flux (lumens) รท 4ฯ, then illuminance (lux) = luminous intensity (candela) รท distance (m) squared.
Does this exactly match real light fixtures?
This calculation assumes an idealized point source radiating light equally in all directions. Directional fixtures (like spotlights) or those with reflectors and lenses will produce different actual illuminance than this calculation.