Luminous Flux Converter

Luminous flux measures the total amount of visible light emitted by a source.

Key units:

• Lumen (lm): total light output from a source
• Candela (cd): light intensity in a specific direction
• Lux (lx): lumens per square meter (illuminance)
• Foot-candle (fc): lumens per square foot (used in the US)

Relationships:

• 1 lux = 1 lumen per m²
• 1 foot-candle = 1 lumen per ft² = 10.764 lux
• 1 candela (uniform sphere) = 4π lumens ≈ 12.566 lumens

Lux to Foot-candle conversion:

• lux = foot-candles × 10.764
• foot-candles = lux × 0.0929

Typical illuminance levels:

The three units here describe genuinely different things, and a spotlight makes it click. Lumens measure the total light a source pumps out in every direction. Candela measure how concentrated that light is in one direction. Take a bare bulb and a spotlight of the same lumen output: the spotlight has a far higher candela rating because it focuses those lumens into a narrow beam, while the bare bulb spreads them everywhere and reads low in candela despite emitting just as much total light. Lux is the third piece, what actually lands on a surface once distance and spread are accounted for.

This is why bulbs are now sold by lumens rather than watts. Watts only ever measured power drawn, and it tracked brightness only because old incandescent bulbs were all similarly inefficient. LEDs broke that link: a 9-watt LED and a 60-watt incandescent both put out about 800 lumens, so lumens are the honest brightness number. The figure worth comparing on the box is lumens per watt, the efficacy, where a good LED reaches 80 to 100-plus lumens per watt against an incandescent’s dismal 15 or so.

Point source to surface: the formula that ties candela to lux

E = I / d²

Illuminance in lux equals intensity in candela divided by the square of the distance in metres. A 1,000-candela spotlight puts 1,000 lux on a surface one metre away, 250 lux at two metres, and 40 lux at five. That is the inverse-square law, and it is the single most useful equation in practical lighting because it is what actually decides whether a room is bright enough.

Two caveats before you lean on it. First, it assumes the light arrives head-on; if the surface is tilted, multiply by the cosine of the angle from perpendicular, which is why the same fitting lights a floor well and a wall poorly. Second, it treats the lamp as a point, which is a fair approximation once you are five or so source-diameters away and a poor one right up close, so it overestimates for a big softbox at arm’s length.

Beam angle is the missing third number. A source’s candela figure and its lumen figure are related through how tightly the beam is packed, and a narrow spot with a modest lumen rating can out-punch a floodlight with three times the output. For a symmetric cone, candela is roughly lumens divided by the solid angle in steradians, which is 2π(1 - cos(half-angle)). A 40-degree flood therefore spreads the same lumens over about seven times the solid angle of a 15-degree spot, and reads about seven times lower in candela while emitting exactly as much light.