# Why do the brightness, luminous efficacy and power of this lightbulb not agree?

A particular LED lightbulb has luminous flux (brightness) $\Phi_{\rm v}=820\ \rm lm$, consumes electrical energy at a rate of $P=9\ \rm W$, and has a luminous efficacy of $\eta=83\ \rm lm/W$.

The mathematical implication is that the bulb dissipates $$\frac{\Phi_{\rm v}}\eta = \frac{820\ \rm lm}{83\ \rm lm/W} = 9.9\ \rm W$$ in illuminating the ambient environment; however, this is already greater than the power consumption, and the rate at which the bulb dissipates heat hasn’t even been considered yet.

What gives?

Addendum: It actually isn’t clear whether the luminous efficacy cited gives the ratio of luminous flux to total radiant flux or whether it gives the ratio of luminous flux to the radiant flux associated with just luminous radiation.

• "however, this is already greater than the power consumption" - it's within 10% - close enough for consumer specs. "and the rate at which the bulb dissipates heat hasn’t even been considered yet" - why should it? efficacy <> efficiency. – Bruce Abbott Apr 2 '18 at 12:51
• @BruceAbbott You make an excellent point. I brought up the dissipation of heat, because that might bring the total radiated power to be greater than the power consumption by even more than ten percent (i.e., $\Phi_{\rm e}>1.1P$). – gen-z ready to perish Apr 2 '18 at 12:54
• You can't get more radiated power out than electrical power in. But lumens are not a measure of light power, and infrared light is not counted - "luminous flux accounts for the sensitivity of the eye by weighting the power at each wavelength... Light outside the visible band does not contribute." en.wikipedia.org/wiki/Luminous_flux – Bruce Abbott Apr 2 '18 at 13:01
• @BruceAbbott Yes, I am aware that this violates the principle of conservation of energy, which is why the whole issue confused me. I never indicated that ‘lumens’ were a “measure of of light power.” – gen-z ready to perish Apr 2 '18 at 13:18
• The lumen is based on the candela, which is the perceived brightness of a common wax candle - a completely arbitrary standard. 1 lumen = ~0.0015 Watts of 'green' light at 555nm, so a bulb that converted 1W into 83lm of green light would have a power efficiency of ~12%. However the eye's response to blue and red light is less, so a 'white' bulb has to put out more light to produce the same lumens and therefore its efficiency is higher! (if you were confused before...) – Bruce Abbott Apr 2 '18 at 14:20

## Unreliable data

• from a traditionally non-technical supplier and constantly changing supplier specs ( lumens is never capitalized unless beginning word in a sentence , as it is not named postumously after someone) so it is an error but not sure why. ( to err is human)

Here a similar bulb from same brand in a different country (Canada) is 8.5W 800 Lumens https://www.homedepot.ca/en/home/p.60w-equivalent-daylight-5000k-a19-dimmable-led-light-bulb-6-pack.1000835489.html Note they dropped the efficacy spec., possibly correct ! who knows. only your Test Engineer knows for sure.

If they started with emitters that were regulated to 7.5W with 106 lumens/Watt sources and had a design with 0.5W loss (14%) then it would use 8W with 100 lumens/Watt. The same bulb at 5000'K but with warm white might absorb 10% more energy to convert the blue source to warmer phosphor emissions and get only 95 lumens/Watt. Yet so many suppliers say they have the same efficacy for any CCT temperature from warm to cool. (Warning fake data)

Go to a reputable source like Philips, Cree, etc for better data,.

• luminous flux is the correct measurement for luminaires and LED components.
It is a weighted average of the Radiant Flux in the visible spectrum.

## Anecdotal

For what it's worth I have bought both warm and neutral white 5000'K in this brand from this suppier and the latter are awful white balance (poor CRI) and hideous so my wife insisted I change them in the hallway to warm white.

My preference is tri-phosphor 4500k 4ft T8 tubes or 4000~4500'K custom LEDs. But this range is also the hardest to control in phosphor thickness and std deviation or consistency vs cool and warm.

• I agree that their labeling is atrocious. How am I supposed to know what “Lumens per Watt” refers to specifically‽ (+1 by the way) – gen-z ready to perish Apr 2 '18 at 5:09
• better suppliers give CCT,CRI, and lumens/Watt with beam pattern but must give cost per year based on std consumption – Tony Stewart Sunnyskyguy EE75 Apr 2 '18 at 5:13
• I suspect someone in Canada challenged them on their data and it was corrected on the Home Depot site in Canada or the supplier changed their specs and it has a different part number.. These will change every year – Tony Stewart Sunnyskyguy EE75 Apr 2 '18 at 5:15
• I also suspect that our US laws are geared towards letting manufacturers selling here to package specifications nearly without regulation. They probably can "round down" the power rating. I'll bet it is more than 9 W as well as mis-stating the lumens. In many states here, it's "legal" to write "New Crop" on apples sold in grocery stores so long as there is at least 1 apple in 10 that is actually from the current crop being harvested that year. The other 9 can be from a prior year and it's legal. Almost no protection in the US, anymore. – jonk Apr 2 '18 at 7:35
• Yes the rules bend when it favorited profits of the seller more than quality to the consumer. Buyer beware that low cost must come with highest quality specs and the traceability, ethics and reputation to stand behind them. – Tony Stewart Sunnyskyguy EE75 Apr 2 '18 at 12:28