How this calculator works
Electrical input power becomes luminous flux according to the lamp's measured luminous efficacy. One lumen spread uniformly across one square metre gives one lux. The area model assumes all entered lumens reach the area evenly; the sphere model assumes an isotropic point source. LED, incandescent, halogen, fluorescent, metal-halide, mercury and sodium lamps can all be modelled by entering their actual product efficacy rather than a fixed technology guess. Real rooms also involve beam patterns, shadows and reflection losses.
Formula
Phi = P eta; E = Phi/A; for isotropic emission A = 4 pi r². P = EA/eta; r = sqrt(P eta/(4 pi E)).
Worked example
A 10 W lamp at 100 lm/W emits 1000 lm. Distributed evenly over 5 m² this gives 200 lux. A 4 W source at that efficacy gives 31.831 lux at a 1 m spherical radius.
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Frequently asked questions
Can any watt value be converted directly to lux?
No. You also need luminous efficacy and the distribution of light over area.
What efficacy should I use for an LED?
Divide the specific lamp's rated lumens by rated electrical watts. LED products vary substantially.
Will this predict a desk reading in a room?
Only under the stated uniform-light assumption. A fixture photometric file or measurement is better for detailed lighting design.