Converting millicandelas to lumens!

Converting / comparing lumens, candelas, millicandelas Many people ask what are lumens, lumens/watt, candelas, and millicandelas and how to convert among these units. A lumen is defined as the "luminous flux" of 1/683 of a watt of monochromatic light that has a frequency of 540 terahertz, or a wavelength of approx. 555.5 nm. One thing worth noting is that a lumen is defined secondarily, in terms of the candela (which is 1 lumen per steradian), and the candela is defined primarily (it's the "beam candlepower" of 1/683 watt per steradian of 540 THz monochromatic light.) Light of wavelengths other than 555.5 nm have a different amount of lumens per watt of radiation. The number of lumens in a watt of wavelength other than 555.5 nm is 683 times the photopic function of the wavelength in question, divided by the photopic function of 555.5 nm (which I believe is very close to but not exactly 1). A "USA-usual" 100 watt, 120 volt, 750 hour "regular" (A19) lightbulb usually produces 1710 lumens. Lumens per watt is a measure of efficiency in converting electrical energy to light. Multiply this by the watts dissipated in the LED to get lumens. A typical red, orange, or yellow or yellow-green LED has a voltage drop around 2 volts and is getting around .04 watt at the typical "standard" current of 20 milliamps. A blue, white, or non-yellowish-green one typically has a voltage drop of 3.5 volts at 20 mA and gets .07 watt at 20 mA. A candela is a lumen per steradian, or "beam candlepower". (Actualy, as mentioned above, the candela is a primarily defined metric unit, while the lumen is defined in terms of the candela.) So lumens are candelas times the beam coverage in steradians. Candelas are lumens divided by the beam coverage in steradians. Ideally, that is - assuming that all light is within the beam and the "candlepower" is constant within this beam. So you may now be wondering what a steradian is. It is 1 / (4 * pi) of a whole sphere or 1 / (2 * pi) of a hemisphere or about 3283 "square degrees", to the extent there is such a thing as a "square degree". To get steradians from the beam angle: Steradians = 2 * pi * (1 - cos (.5 * (beam angle))) (NOTE: There are a few other expressions equal to this. Proving that is homework for 12th graders taking trig / "elementary functions".) So if you determine the steradian beam coverage and multiply that by the candela figure (or 1/1000 of the millicandela figure), you get the lumen light output - very roughly! The beam is not uniform and it does not contain all of the light. Obtaining lumens from beam angle and candela can easily be in the +100 / - 50 percent range. Actual lumens are generally higher than predicted by this formula with smaller beam angles of 8 degrees or less since the nominal beam does not include a secondary "ring-shaped" "beam" that usually surrounds the main one. Also note that some beam angle figures are optimistic and could lead one to expect a lot more lumen light output than actually occurs.