# Is there a theoretical lower limit to watts needed for lumens?

For example 100 watt incandescent bulb produces 1600 lumens.

Led 23 watt can produce 1600 lumens.

Is there minimum amount of watts needed ?

• Just a note: a 23 W LED bulb often consumes a lot more than 23 W, because of complications they cause in the power network. However, this cost is spread out over all the consumers of electricity, it doesn't show up on your meter - kind of like how you can't say you don't want "green electricity", you just pay extra for it regardless. It's very hard to estimate how much of an impact this has (it depends on how much of the total power consumption comes from LEDs), but it's something the electric companies aren't very happy about, just like solar and wind plants. – Luaan Jul 15 '16 at 13:56
• @Luaan can you elaborate the "complications they cause in the power network" a bit further? – Crowley Jul 15 '16 at 14:05
• @Crowley I suspect that Luaan is referring to the concept of apparent power (reactive load, voltage and current out of phase) and real power (purely resistive load, voltage and current in phase). Compare What is the practical difference between watts and VA (volt-amps)? on Electrical Engineering. – a CVn Jul 15 '16 at 14:28
• @MichaelKjörling "In theory, there is no difference between theory and practice. In practice, there is." - Yogi Berra – user95006 Jul 15 '16 at 17:45
• @nocomprende Pretty much. – a CVn Jul 15 '16 at 19:15

Yes, there is a fundamental limit. It comes down to two factors:

1. How many watts of light energy can the source produce for each watt of electrical energy?
2. How many lumens does each watt of light energy correspond to?

The first question is straightforward - by conservation of energy, 1W of electrical energy can yield at most 1W of light energy.

The second question is not so straightforward, and depends on the spectrum of the light. The lumens is a unit in photometry, the science of measuring light intensity as perceived by the human eye. By the early 20th century, the notion of perceived intensity was quantified in numerous experiments with human subjects, and a standards body called CIE defined the standard luminosity function to summarize all the findings. The luminosity function defines the number of lumens per watt of light energy for different wavelengths, answering our second question. The function has a peak at 555 nm (green), where its value is 683 lm/W.

Thus, a perfectly efficient light source at 555 nm could produce 683 lm/W - this is the theoretical maximum allowed by the laws of physics. If you wanted white light source, then the maximum is lower (depending on the shade of white) - another answer has quoted 250 lm/W from this document.

• Note that the white light figure corresponds to "all the visible light corresponding to a blackbody with temperature like the sun" - so the best possible value for light that appears the same as sunlight to us. That's usually not what LED lights do - those tend to mix a few colours together, rather than using the full spectrum. I wonder if that could mean they would need less W/lm, or if it averages out? In any case, the 683 lm/W figure is probably the absolute maximum. – Luaan Jul 15 '16 at 13:49
• +1 for: "depending on the shade of white." I would like A Whiter Shade of Pale, please. (There must be at least 50 shades of white...) – user95006 Jul 15 '16 at 17:47
• @Luaan: Do modern, high-quality ones still do that? It's really not suitable for users with corrective lenses due to chromatic aberration. – R.. Jul 15 '16 at 19:32
• "1W of electrical energy can yield at most 1W of light energy." - I want that bulb. – John Dvorak Jul 15 '16 at 20:10
• @R.. Not all of them. Some use a phosphor that's excited by the LED's, which offers a broader spectrum, apparently quite similar to incandescent bubls. But I can assure you that I indeed do see the chromatic aberration (among other issues) with some of the bulbs still on market, and not exclusively the cheap ones either. – Luaan Jul 15 '16 at 21:26

Yes there is

the thermodynamic law of Conservation of Energy.

Light is a form of energy, and you can't get more energy out than is put into the system.

This paper http://physics.ucsd.edu/~tmurphy/papers/lumens-per-watt.pdf puts the number at about 250 lm/W for "white" light

I believe the question has been answered (earlier), but not explicitly. The question seems to be if an incandescent bulb requires 100 watts to produce 1690 lumens and an LED 23 watts to produce 1600 lumens, what is the theoretical minimum number of watts required to produce 1600 lumens.

Using Jason and Sergei's answers (and Tom Murphy's paper already linked above), the answer is that an ideal white light source, that is, a 5800 K blackbody truncated to 400 nm - 700 nm range only in emission, would require 3.98 mW minimum per lumen (i.e., at least 3.98 mW to produce 1 lumen of ideal white light as defined). Therefore, the theoretical minimum watts to produce 1600 lumens is 3.98 mW x 1600 = 6.37 watts.

## protected by Qmechanic♦Jul 15 '16 at 22:59

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