Calculate illuminance, lumens, or distance from any two values with this lumens to lux calculator for meters, feet, inches, lux, and fc.
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Lumens To Lux Distance Formula
The calculator assumes a point light source that emits light uniformly in all directions. Under that assumption, the light spreads over the surface area of a sphere, so illuminance decreases with the square of the distance.
E = Φ / (4*pi*d^2)
Φ = E*4*pi*d^2
d = sqrt(Φ / (4*pi*E))
- E = illuminance in lux (lx)
- Φ = luminous flux in lumens (lm)
- d = distance from the light source in meters (m)
- pi = 3.14159…
The calculator can solve for any one missing value when you enter the other two:
- Illuminance: enter lumens and distance to estimate lux at that distance.
- Luminous flux: enter lux and distance to estimate the lumens needed from an ideal point source.
- Distance: enter lumens and target lux to estimate how far away the light source can be.
Unit options are converted internally before the formula is applied. Lux is the base illuminance unit, lumens is the base luminous flux unit, and meters is the base distance unit.
Common Light Level References
Use these values as rough references when interpreting a lux result. Actual lighting requirements depend on the task, room layout, beam angle, surface reflectance, and safety standards.
| Situation | Typical illuminance | Notes |
|---|---|---|
| Moonlit outdoor area | 0.1 to 1 lx | Very low visibility |
| Hallway or storage area | 50 to 150 lx | Basic movement and orientation |
| General room lighting | 100 to 300 lx | Living rooms, bedrooms, casual areas |
| Office desk or classroom | 300 to 500 lx | Reading, writing, computer work |
| Detailed task work | 750 to 1500 lx | Inspection, fine assembly, precision work |
Unit Conversion Values Used
| Unit | Conversion |
|---|---|
| 1 foot-candle | 10.764 lux |
| 1 kilolumen | 1000 lumens |
| 1 foot | 0.3048 meters |
| 1 inch | 0.0254 meters |
Example Calculations
Example 1: Find lux from lumens and distance
You have a 1000 lm point source and want the illuminance at 2 m.
E = 1000 / (4*pi*2^2)
E = 19.8944 lx
The estimated illuminance is 19.8944 lux.
Example 2: Find distance from lumens and target lux
You have a 1500 lm point source and want to know the distance where illuminance is 100 lx.
d = sqrt(1500 / (4*pi*100))
d = 1.0925 m
The estimated distance is 1.0925 meters.
FAQ
Why does the formula include 4*pi*d^2?
The term 4*pi*d^2 is the surface area of a sphere with radius d. For an ideal point source emitting equally in every direction, the same total lumens spread across a larger spherical area as distance increases. That is why lux drops quickly as distance increases.
Is this accurate for LED bulbs, flashlights, or spotlights?
It is only an approximation for those lights. Many real lights do not emit uniformly in all directions. A spotlight or flashlight concentrates light into a beam, so the lux inside the beam can be much higher than this point-source estimate. For directional lights, beam angle, candela, and the beam pattern are often needed for a better estimate.
What is the difference between lumens and lux?
Lumens measure total light output from a source. Lux measures how much light lands on a surface area. A high-lumen light can produce low lux if it is far away or spread over a wide area, and a lower-lumen light can produce high lux if it is close or tightly focused.