About

Lighting specification requires a distinct separation between the intensity of light falling on a surface and the total output of the source. This tool bridges that gap by converting Illuminance (measured in Lux) into Luminous Flux (measured in Lumens). Accurate calculation is critical for architects and safety engineers who must ensure specific brightness levels on work surfaces (workplanes) without over-specifying energy consumption.

The relationship involves the geometry of the light spread. A simple multiplication of area and illuminance suffices for uniform distribution. However, real-world applications often involve directed beams or spherical radiation, where distance and beam angle dictate the surface area covered. Miscalculating this geometry can lead to dark spots in safety-critical areas like stairwells or surgical theaters.

Formulas

The fundamental conversion relies on the definition that Illuminance is Luminous Flux per unit Area. To find the total Flux, we integrate over the surface area.

Φ_V = E_v × A

Where Φ_V is Luminous Flux (lumens), E_v is Illuminance (lux), and A is the surface area (m²).

For a specific distance r, the area depends on the light geometry:

{

Spherical Source: A = 4πr²Directed Beam: A = 2πr²(1 − cos(θ2))

In the directed beam case, θ represents the apex angle (beam angle) of the cone. This formula calculates the area of the spherical cap illuminated by the source at distance r.

Reference Data

Environment / Activity	Target Illuminance (lx)	Typical Source (lm)	Note
Public Areas (Corridors)	50 − 100	450 − 800	Safety orientation
Warehousing (Loading)	150	1500 +	Large area coverage
General Office Work	500	2000 − 3000	Desktop level
Mechanical Workshop	750	5000 +	Detailed machining
Drawing / Drafting	1000	1000 (Spot)	High contrast required
Precision Assembly	1500	2000 (Spot)	Electronics/Watches
Medical Surgery	10000 − 100000	20000 +	Focused cavity
Direct Sunlight	32000 − 100000	∞	Natural reference
Full Moon	0.1 − 0.3	N/A	Night vision
TV Studio Lighting	1000 − 2000	10000	Camera sensor req

Frequently Asked Questions

A standard light bulb emits light in almost all directions (spherical). However, a spotlight or LED downlight focuses that same energy into a tight cone. If you measure 500 Lux on a table, a focused beam requires significantly fewer total Lumens to achieve that brightness compared to a bare bulb, because the light is not wasted on the walls and ceiling. Ignoring the angle will result in a gross overestimation of the required bulb power.

Technically, Lumens are a property of the light source itself and do not change with distance. However, this calculator determines the Lumens *required* to maintain a specific Lux level at a specific distance. As you move the surface further away (increase r), the light spreads out over a larger area (following the inverse square law), requiring a more powerful source (more Lumens) to maintain the same brightness.

Think of Lumens as the "flow" of water coming out of a hose (total output). Think of Lux as how wet a specific patch of ground gets (density). If you spray the water over a large area (wide angle or far distance), the ground gets less wet (low Lux) even though the flow (Lumens) remains constant.

This tool assumes a point source geometry (bulbs, spots, downlights). LED strips are linear sources. While the general principle (Lux = Lumens / Area) holds, the geometry for the surface area calculation differs. For strips, you typically calculate Lumens per meter, and the falloff is linear rather than quadratic.

In lighting design, the "working plane" is typically assumed to be 0.76 meters (30 inches) above the floor (standard desk height), unless measuring for corridors where the floor itself is the reference plane.