Foot-Candles Vs. Lumens

Without the sun, Earth would have no source of energy to keep biochemical processes going, and life would not exist. One feature of the sun's enormous energy is the amount and quality of light it puts out.

Visible light makes up only a small fraction of electromagnetic radiation, which also includes radio waves, microwaves, x-rays and other "invisible" waves. Because "visible" is as much a physiological and concern as one of physics per se – after all, the sun existed well before eyes did – some units in physics concerning light account for this, while others deal only with light energy itself.

The foot-candle (or footcandle) is an example of a unit tailored to the power of the human eye, whereas a related unit, the lumen, is more fundamental to physics. If you're curious how to work between these units, read on.

The lumen is a measure of luminous flux, or the "flow" of light through a specified geometric space. All modern measurements of light are based on the lumen, but the lumen itself is derived from the candela.

The candela (cd) was chosen long ago when candles were the main form of household illumination. It is the amount of visible light emitted in a given direction, from a source that emits radiation with a fixed frequency and intensity, that corresponds to one "typical" candle from back in the day.

The lumen in turn is the "light flow" of 1 candela through 1 square radian (sr) of space. A radian is equal to 360/2π (about 57) degrees.

The footcandle represents the amount of visible light emitted from a 1-cd source striking a surface 1 foot away: 1 footcandle = 1 lumen/ft². Note that this is a "quantity" of light rather than a flow of light, inasmuch as light can be treated as something that be quantified in such a way. Light, by definition, is always moving.

The original footcandle meaning seems quaint today, in an era when the amount of light generated by a single candle is trivial compared to the output of modern human lighting equipment. Still, the candela, the lumen and the footcandle remain handy and are popular base and derived units in electromagnetic physics.

The lux is a unit similar to the footcandle, but using metric (SI) units. While 1 footcandle is the amount of light 1 foot from a 1-cd source, 1 lux is the amount of light from the same source at a distance of 1 m. Because 1 m = 3.28 ft, 1 m² = (3.28)² ft². This in turn makes 1 cd equal to 10.76 lux, reflecting the expected result that light is "diluted" as it travels outward from its source.

You might wonder if the power of a light bulb affects the amount of light it emits. The answer is yes, although not in a consistent way across equipment. Certain bulbs are more efficient than others and can convert more of their electromagnetic energy to visible light.

At maximum efficiency, 683 lumens can be "harvested" from 1 watt (W) of power. However, a typical 100-W incandescent light bulb is good for only about 17 lumens per watt. This gives an efficiency of only (17/683) = 0.0249 = 2.49 percent. Newer light-emitting diode (LED) bulbs are far more efficient, but also more expensive.

You can see that no direct conversion is possible for translating footcandles to lumens because these are not quite the same type of data. But if you remember that the only thing distinguishing them is whether it is a unit of flow in square feet or a strict amount, you can become adept at these conversions.

See the Resources for a list of other helpful light-related conversions.