(Above) The kelvin rating of sunlight changes throughout the day, depending on cloud cover, seasonality, etc.
K rating is used to describe color temperature of black body radiators
The Kelvin rating that scientists uses refer to specific black body radiation, where the color temperature of the electromagnetic radiation emitted from an ideal black body is defined as its surface temperature in kelvins. For example, a near perfect black body such as the sun burns at a temperature of about 5772 kelvins, emitting a white tone. While the sun burns at a constant temperature; the light that hits the earth's surface is subjected to atmospheric influences and its color tone can range from anywhere from 2000+ Kelvin (dawn/dusk) to 5800k (noon). It can appear more bluish due to scattering of light by cloud cover, or more reddish during dusk/dawn due to the Tyndall effect.
An incandescent lamp approximates an ideal black-body radiator, so its color temperature is essentially the temperature of the filament. Tungsten filaments have to remain below 3600 kelvins to remain solid, and thus they can only produce a warm white glow instead.
For black body generators, we can also infer their spectrum curves (amount of red/blue/green light produced) from the associated K rating, as the ratio of red/blue/green follows predictable curves for black body generators. Interestingly, by definition black body radiators produce a CRI of 100 - so incandescent bulbs produce a CRI of 100, even if their warm tints make for poor color rendition of cool color tones. This would be surprising to folks that think that high CRI lights naturally means attractive color rendering (another common, high level myth), but it is not always the case. This will be covered in another section.
K rating for incandescent bulbs (above) actually hint at the temperatures that their filaments burn at. Not so for non-black body lighting such as Florescent/LEDs. A 6500k T8 florescent light bulb can be cool to the touch - it definitely does not burn at 6500 kevins.
K Rating is used to measure Color co-related temperature (CCT)
The K rating printed on modern commercial lights (applies for non-incandescent lights such as LEDs, fluorescent lighting etc) is different from the Kelvin rating used on black body generators. In this application, the K rating indicates the average visual color hue of the light (as perceived by human color vision) as approximate to a black body generator of the same Kelvin. This K rating is known as CCT (color correlated temperature).
For example, a florescent bulb may be labeled 5800k because it has the same visual hue as sunlight (meaning that its color tone looks like sunlight). However, unlike a true black body radiator (i.e. the sun), a fluorescent bulb does not burn at 5800 kelvins. Its K rating label is given purely by how visually similar it is to a true black body radiator of the same kelvin rating. Neither does the fluorescent lamp have the same spectrum distribution (amounts of red/blue/green light) as the sun. In fact, most non-specialty bulbs have spectrum curves that are nothing like sunlight despite the 6500k rating label - so it is pure rubbish so say that they produce light similar to sunlight. The only similarity is in the visual color hue.
In the graphs above, we see the spectra distribution chart comparing sunlight vs standard 6500k LEDs. The difference is spectrum distribution is vast, despite the 6500k rating label. Modern lights have their K rating calculated using CCT *(color correlated temperature), it was designed to give the lighting industry a way to describe the overall color hue of a light. Lower K rating lights had warmer tones, while higher K rating lights tend towards being more bluish. Interior designers would use the K rating system to match lights when designing interiors. The calculation of CCT is thus based on human color vision's sensitives to different color spectrum.
The CIE diagram below represents all of the chromaticities visible to the average person. These are shown in color and this region is called the gamut of human vision. The CCT (kelvin rating) of a light bulb, can simply be understood as the color tone that best matches a point on the chart. However, because the calculation is an approximation, in reality bulbs of the same CCT can still produce very different color renditions.
It is the spectrum distribution of light that affects plant growth and photomorphogenesis, not it's visual color hue. Hence, the idea that a light is great for plant growth just because it is of a certain K rating is a spurious claim. What spectrum of light is used by plants for growth is covered in this section. Many lighting salesman make the mistake of thinking that their lights produce the same spectrum as sunlight just because their lights share the same color hue (CCT rating) as sunlight.
Due to the approximate nature of CCT, lights with the same K rating can have quite different color hues. A 6000k light can appear whitish (point B above), Greenish (point A) or reddish (point C).
Bulbs that have the same K rating label can have very different spectrum distribution. Here we compare a 6500k BML RGB LED unit on the left vs a plain white 6500K LED on the right. The BML unit on the left has much larger spikes in red due to the mix of red LEDs used.
Here is a comparison of two 6500k T5 tubes; Giesemann on the left and Wavepoint tropical wave 6500k at center. A spectra distribution chart for sunlight is on the right.
6500k indicates the rough color hue of a light, but has no direct bearing on whether it is a good bulb for plant growth or not. As mentioned above, It is the spectrum distribution of light that affects plant growth and photomorphogenesis, and you cannot tell the exact spectrum distribution of a light just by its K rating value. Every website out there that claims 6500K is better for plants is purely a marketing gimmick.
For aquarist purposes, K rating is useful when buying household lighting and re-purposing it for aquarium use. For most commercial household lights, it follows convention that buying a light in the 5000k - 8000k range produces a neutral white color tone, anything below 3000k will be warm white and anything above 10000k will be bluish. Again, this only indicates the visual hue of the light and give no hints as to the actual light's strength (you need to read it's PAR values for this) or spectrum curves (need to read it's spectrum charts as above).
However, when buying lights from specialty dealers or aquarium specific fixtures, then the label on K rating may not even be a good indication of the light's general color tone. A T5 tube can be labeled 6500k but produce a pinkish light for example, and a 10000k light may not be bluish white but actually be blue.
My own BML LED light fixture is rated at 3600K. It is a red heavy fixture with a mix of blues (from blue diodes and from white LEDs, which contribute quite a lot of blue spectrum by themselves). Despite the lowish K rating, and lowish CRI rating (78), the light renders colors well.
6500k is a neutral white bulb in most cases, which produce neutral color rendering tones in a tank. I use a wide range of lights myself; much to the chagrin of sites that want to claim that low K rating bulbs won't work... take a look for yourself on my tanks below, grown with fixtures rated at very different K ratings.
Grown with 4200K:
Grown with 12000K:
Grown with 12000K:
Head here to learn more about reading PAR Values.
Head here to learn about spectrum curves.
Head here to learn more about aquarium lighting for planted tanks