Generally I see efficiency related to the lumens per watt, but what is the actual typical efficiency of LEDs in terms of electrical energy in to optical energy out? What sort of conversions apply?
To make things clear let's define what we are talking about.
There are two terms which are mixed up pretty often:
- Luminous efficiency:
The luminous efficiency is a dimensionless quantity which is derived from the luminous efficacy. It is simply the quotient of luminous efficacy of the source and maximum possible luminous efficacy of radiation.
- Luminous efficacy:
This is the value you see more often. It usually has the unit of lumen per watt. And gives the luminous flux per power, which is a useful quantity to see how much light we will get with a given power.
With this we have to be a bit careful as well. Because the power can be the radiant flux of the source or the electrical power. So the former can be called luminous efficacy of radiation, and the latter luminous efficacy of a source or overall luminous efficacy.
Now the problem arises, that we cannot see all colors equally well. And lumens are actually weighted based on the response of our eye:
Public Domain, Link
So with this, you can create some values of upper bounds (based on the redefinition of the unit candela). This would be the luminous efficacy of radiation.
- Green light at 555 nm: 683 lm/W
- Maximum for CRI=95 at 5800K: 310 lm/W (based on truncated black body radiators)
- Maximum for CRI=95 at 2800 K: 370 lm/W
For more see here.
If you lower the color rendering index (CRI), you can achieve higher values. But not higher than 683 lm/W.
So how efficient are LEDs?
Here we have values of luminous efficacy of a source.
Well there is a race of efficiency. Cree posted a press release with a laboratory LED of 303 lm/W at 5150K. The CRI was not mentioned, I guess it is lower than 95, but based on the data above that seems like it would have a luminous efficiency of something like 80% to 90%.
Of course your average available LED has less. 100 lm/W would be around 25% to 30% and the new 200 lm/W chips announced recently (as of August 2017) reach 50% to 60%.
Note that the above is for photopic vision (day-vision), things change with scotopic vision, but that's usually not so interesting.
If you really want to get into the guts of it, you'd have to take the spectrum of the LED and find out what the highest theoretical maximum for that spectrum is (based on the weighting curve) and then you can calculate the value.
As each and every LED has a different spectrum it is hard to get this data easily.
I hope I haven't made a mistake here, because I always find the topic a bit confusing no matter how many times I revisit it.
As noted in the comments, it depends.
Older LEDs often have a lower efficiency than newer types.
Some bulbs have more efficient electronics to convert the mains voltage to the DC voltage needed for the LEDs.
But for a given LED light bulb you could make an estimate as often the amount of power needed by an incandescent light (with a similar amount of light output) is printed on the box. According to Wikipedia the average efficiency of an incandescent light bulb is 2.2 %.
Lets take the Ikea "LEDARE" E-27 600 lumen light bulb as an example:
Equivalent power for incandescent bulb: 48 W Actual power used: 8.6 W
So that means this bulb claims to be 48 / 8.6 = 5.6
times more efficient than an incandescent bulb so that would result in:
5.6 * 2.2 % = 12.3 % efficiency.
For this Ikea Ledare lamp.
Note that this is the total efficiency so the efficiency of the electronics times the efficiency of the LEDs themselves.
Proper LED driver electronics should have an efficiency of 85 - 99 % (that is my personal guess !) So the actual efficiency of the LEDs will be slightly higher than the 12.3 % I just calculated.
That's assuming all numbers given by Ikea are true of course.
You need 1/683W of power to generate 1 lumen of light. It means that efficiency is somewhere around 12%. This is how it goes:
Firstly, let's assume that we have a light that radiates equally to all directions. By definition, 1 candela is 1/683W (550nm monochromatic light). 1 candela radiates to 1 steradian angle, which is 1/4π (8%) of the full sphere surface area. So, you need 4π/683W to produce 1 candela to all directions and the total luminous flux is 4π = 12,6 lm.
Which power is equal to 1 lm? You get it by dividing 4π/683W by 4π and the end result is (4π/683W) / 4π = 1/683W. Essentially, you need 1/683W of power to create 1 lumen luminous flux (1/4π = 0,08 candela to all 1 steradian angles).
Using above figure you need 900 times 1/683W = 1,32W to produce 900 lumen luminous flux.
My real light bulb, procured from a local store, state 900 lm and 11W of electric power. I assume that it radiates light equally to all directions. Using previous figures, electrical efficiency of the bulb is 1,32 W / 11 W = 0,12 which is equivalent to 12% efficiency.
The question was not about a "luminous" quantity, but instead, about a "radiant" quantity, stating specifically "in terms of electrical energy in to optical energy out".
For those who seem to misunderstand, a "luminous" quantity is determined by applying a weighting function to a "radiant" quantity. Wikipedia has a page describing the "luminous efficiency function"/"luminosity function".
The radiant efficiency of a light emitting diode is dependent upon the fraction of carriers injected into the active region, the fraction of the spontaneous recombinations that are radiative, and the extraction efficiency of the photons generated. The extraction efficiency may be particularly dependent upon internal reflections at the surface of the LED. In addition to this, Phosphor-based LEDs will also have a "Stokes shift" loss, referring to the difference between the band maxima of the absorption and emission spectra, typically from blue to yellow.
Surprisingly, a web search turned-up almost nothing in the nature of research reporting the radiant efficiency of LEDs. There is a very general statement here, though - https://www.dial.de/en-GB/projects/efficiency-of-leds-the-highest-luminous-efficacy-of-a-white-led - claiming that "very efficient LEDs at present achieve values between 40% and 50%." There is also a chart there comparing the spectra of incandescent, florescent, and LED lighting.
It may also be useful to read here - "Safe LED Operating Current" https://electronics.stackexchange.com/q/380033 - where user "Misunderstood" suggests that "At least 20% of the wattage is radiant watts".
So, to answer specifically, but only as a rough guess, the radiant efficiency of an LED is likely between 20% and 40%. And then, 60% to 80% of the input power will be generating heat. Those numbers should allow for at least rough operating temperature and heat sink calculations.