How this instrument works
Luminous flux, Φ, is the total quantity of visible light a source emits in every direction, measured in lumens. Illuminance, E, is a density — how much of that flux lands on each square metre of a surface, measured in lux, where one lux is defined as one lumen per square metre. Multiply a density by the area it covers and you recover the total: Φ = E × A. The formula is nothing more than undoing the division baked into the definition of lux.
The shape of the equation is why a bulb's lumen rating alone never tells you how bright a room will feel. Five thousand lumens spread across a 10 m² study reads as a crisp 500 lux — a typical office reading level — but the same fixture dropped into a 20 m² open-plan room only manages 250 lux, because identical total output is now divided across double the floor. Electricians and lighting designers run this multiplication in reverse constantly: pick the illuminance a space needs from a lighting standard, multiply by the room's area, and that is the flux the installation has to supply before fixture losses.
The formula assumes E is uniform across the whole area A, which real installations only approximate. A single ceiling fixture leaves corners dimmer than the centre directly beneath it, so this result is a design target — the average a well-distributed layout should hit — not a guarantee that a light meter will read the same figure everywhere on the floor. It also has a distinct cousin: illuminance from a point source at a known distance follows the inverse-square law and involves candela, luminous intensity in a direction, rather than this flat area relationship.
- Enter the target level in "Illuminance, lux" — 500 lux suits general office and reading tasks; lighting standards list lower figures for corridors and higher ones for detailed work.
- Enter "Illuminated area" in square metres, or switch the unit menu to square feet if that is how the space was measured.
- Read "Luminous flux, lumens" — the total light output the fixture or fixtures must supply, combined, to reach that illuminance evenly.
- To check a bulb you already own instead, divide its printed lumen rating by the room's area to see what illuminance it actually delivers.
Worked example — sizing a fixture for a 500 lux home office
Take a 10 m² home office, roughly 3.2 m by 3.2 m, and the common target of 500 lux for reading and screen work. The formula runs directly: Φ = E × A = 500 lux × 10 m² = 5,000 lumens. That is the total luminous flux every fixture in the room must deliver, combined, before fixture and ceiling losses, to hit 500 lux evenly across the floor.
The same figure explains why a lumen rating on a box is meaningless without a room to put it in. That 5,000-lumen installation hits 500 lux in this 10 m² office; move it into a 20 m² open-plan room and it only manages 250 lux — half as bright — because the identical total output is now spread across twice the floor area. Illuminance is what the eye actually experiences, and it always depends on both numbers together.
Questions
What is the difference between lumens and lux?
Lumens measure total light output — everything a source emits, summed across all directions. Lux measures density: lumens landing on each square metre of a surface, since 1 lux is defined as 1 lumen per square metre. A 5,000-lumen fixture reads as 500 lux across a 10 m² room but only 250 lux once the same output is spread over 20 m², because the total light did not change, only the area it covers.
Why does the formula use area instead of distance?
Because this calculation finds the flux needed for a target illuminance averaged over a whole surface, not the intensity a point source produces at one distance. That second case uses candela and the inverse-square law, E = I ⁄ r², an entirely different relationship from Φ = E × A. If the problem gives a point source and a distance rather than a room and its floor area, that inverse-square formula is the one to reach for instead.
How much luminous flux does a typical room actually need?
It depends entirely on the target illuminance and the floor area, which is exactly what this calculation supplies. Lighting standards suggest roughly 300 to 500 lux for general office and reading tasks, 100 to 150 lux for corridors and storage, and 750 lux or more for detailed inspection work; multiply whichever figure fits by the room's area in square metres to get the required lumens.
Does this formula assume the light lands perfectly evenly?
Yes. Φ = E × A gives the average illuminance across the whole area if that flux is spread uniformly, which real fixtures only approximate — a single ceiling light leaves corners noticeably dimmer than the spot directly beneath it. Lighting designers treat this result as a starting target and add a uniformity allowance before specifying the actual fixture count and placement.
Can I use this to check whether a bulb I own is bright enough?
Yes — rearrange the formula to E = Φ ⁄ A. Divide the lumen rating printed on the packaging by the room's floor area in square metres to see the illuminance it actually delivers. A 3,000-lumen bulb in a 15 m² room gives 200 lux, comfortable for a living room but noticeably dim for close reading or detailed handwork.
What is candela, and why isn't it part of this calculation?
Candela measures luminous intensity — how concentrated a source's output is in one particular direction — and connects to illuminance through the inverse-square law rather than simple multiplication by area. This instrument answers a more common design question: given a target lux level and a room's floor area, how many total lumens must the installation supply? Candela belongs to a separate, point-source calculation built around distance.