TLDR: Color temperature (or CCT: Correlated Color Temperature) is commonly used to describe the color of white light in illumination (lighting) applications. It's measured in Kelvin -- the same way we measure how hot really hot stuff is. White light with a higher Kelvin is more bluish, white light with a lower Kelvin is more yellowish.
Describing Light as "Warm" or "Cool"
Things gets confusing when people talk about "warm" or "cool" colors because the hotter the Kelvin measurement, the bluer the white light. In normal conversation, "cool" tones typically mean something bluer and "warm" tones mean more yellow/orangey/reddish. I've heard LED and lighting pros use the terms "warm" and "cool" to describe both bluish whites and yellowish whites! It's OK to ask someone using these terms to clarify if they mean "warm" or "cool" in terms of degrees Kelvin or in terms of warm meaning yellowish and cool meaning bluish.
If you're not able to ask the source which one they mean, go with "warm" meaning more orangey-yellow and "cool" meaning more bluish. That's which way it's meant most of the time.
27K, 3K, 35K, 4K
"When I buy a light bulb or a lighting fixture or an LED -- what do these friggin' numbers mean?"
27K or 2700 K or 2700 Kelvin - "warmest" or most orangey-yellow standard lighting color. Think Grandma's old school incandescent lighting, on the side of candle light (although not quite that warm).
3K or 3000 K or 3000 Kelvin - still on the warm side, but a bit of a brighter-feeling, bluer white than 27K.
35K or 3500 K or 3500 Kelvin - a common color of indoor white lighting -- bluer than 3K, but not as grating on the nerves as 4K.
4K or 4000 K or 4000 Kelvin - the "bluest" or "coolest" typical white lighting color. You might find this in clinical settings or where retail stores want to make shiny baubles look extra sparkly.
Why Is Color Measured in Kelvin?!
It's weird, right?
It is. It's OK to think it's weird.
There is a reason behind the madness, though!
The color of light described in Kelvin is the color of a thing called a "black body radiator". As its burning temperature changes, its color changes. The hotter it burns, the bluer the light. Just like your parents may have told you if they loved you: blue and white flames are hotter and more dangerous to little kid fingers than orange and yellow flames.
A black body radiator is not a real, physical thing, however. It's a theoretical construct. There aren't real black body radiators that we know of in real life (yet?). The idea is of a material/object that doesn't reflect any light whatsoever. No light can bounce off it. The only light we see from this object are the wavelengths it radiates or burns.
So, it's similar to a lump of coal. If I asked you what color the coal was it would depend on if it was on fire or not! If it were not on fire, you might say it was black. If the coal was burning, you might say orange. If you were to measure the temperature of the orange bits of burning coal, you could describe that specific color orange with the temperature you measured.
"This color orange is the hue of char-your-flesh-hotness Kelvin."
This visualization works OK except for when that coal turns to ash as it's burning. At that point, it's got some white and gray ash in there that will reflect outside light that hits it. Then what color is it? It's all sorts of colors at that point! Which is why to describe these colors, scientists made up a pretend thing - the black body radiator - that reflects no light at all ever. Not before it's "lit", not as it burns -- it never reflects any light. That way, there is a consistent understanding of how to describe "red hot" and "white hot" colors of light and everything in between.
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