Different from the rest of the electromagnetic vocabulary, the most important thing to remember about the terminology around visible light is that it is a complete human construct related to our own perceptions. In other words, the notion of visible light and associated color only exist because we have eyes, i.e. antennas that tune into these frequencies of the electromagnetic spectrum. Now, once we accept this, the notion of all these units starts to make sense.
First, we need to start with the unit called the candela. You probably notice the similarity between “candela” and “candle.” Effectively one candela is the amount of visible light emitted by one candle in a given direction. As you might expect, this was really important in the days before electricity when rooms were lit by candle light. It is often referred to as luminous intensity. You can see that would be a very useful measure if you were planning a dinner party during medieval times and you wanted to estimate how much light you needed to light the banquet hall and to subsequently tell your local candle maker how many candles to make. In addition, there is a precise definition of light frequency spread around the color green that goes with it - for now I won’t attempt to confuse with that aspect so just think of it as good old fashioned visible light. Unfortunately, you don’t see the unit candela used much anymore. Instead, if you go buy a light bulb, you will no doubt find the number of lumens listed on the package next to the number of watts.
The candela is a unit that describes light in a given direction, but doesn’t necessarily take into account the spread factor or anything else. The lumen was created as the measure of total luminous power (i.e. visible light power) as defined by our set of ideal human eyes. Somewhere along the way the switch was made to use the unit lumen, presumably because it maps nicely to that other unit of raw power that we know so well, the watt. However, I must admit, since they are just units related by a unit-less constant, it really doesn’t matter. One lumen is defined as one candela-steradian, or the amount of light power needed to send 1 candela of light in all directions (isotropically). For those of you that don’t remember your geometry, steradians are used to describe the surface area of the unit sphere (4 π) much like radians are used to in describing the circumference of a unit circle (2 π). So to translate between lumens and candelas, just multiply by 4 π. Hence 1 candela = 12.6 or 4 π lumens. The lumen is nice because it is relatively easy to quantify in the same way that we described RF transmissions by equivalent isotropic radiation, otherwise, it really doesn’t matter. With this type of measure we can decide how much total visible light, as we humans think of it, is output per unit of time.
Now, in order to determine how much light we need for a given area, however, we need to be able to calculate the light density. For this we us the unit lux. A lux describes a density of 1 lumen per square meter (lm/m2). So it I wanted to illuminate 2 square meters of wall at 1 lux, I would need 2 lumens of light.
Finally we return to our friend the watt. We know that the watt describes total power, no matter what form it emerges. So take our traditional 60 watt incandescent light bulb. We all know from experience that theses get really hot, too hot to touch by the human hand when turned on. The web site able2know.org states that the surface temperature of a 60 watt light bulb at room temperature to be 260 degrees F (127 degrees C). So we know that a lot of energy is wasted on heat instead of visible light. This same 60 watt bulb emits about 520 lumens. Hence we introduce the final term of the day, “luminous efficacy.” This is defines how good the light bulb is at putting out visible light versus wasted heat. Using the numbers above, the luminous efficacy of the 60 watt incandescent bulb is about 8.67 lumens per watt - not very good and certainly not very green.