Feedback Please: The Kodak 18% Grey Card and Metering, a new look.

RobC · Mar 10, 2016

So I thought I would write a little article about Kodak 18% Grey Card and how it relates to photographic metering.
Also might enlighten a few people about light meter calibration in what I hope is as simple and readable and non scientific presentation as possible.

This is draft 1 for proof reading and comments before fixing for 2nd and hopefully last draft:

Please feel free to comment on possible errata, improvments (simple ones and not formulas), grammer, typos, understandable or non understandable etc etc.

Be kind

Mr Bill · Mar 10, 2016

Rob, I have original copies of the ANSI light meter standard (I think early 70s, but I'm not planning to dig it up), and I don't find anything in the standard to directly connect a reflective meter reading to an average scene reflection. (I once went through it carefully in an attempt to do so.) It looks to me like you are trying to do so with the 'K' constant, however it's not really related. In fact, it only seems close because of the units used (if different light units are used, the 'K' value is much different).

As I recall, the only way I saw to correlate to scene reflectance was indirectly - to compare the constants, 'K' (for reflective meter) to 'C' (for incident meter), when the units are the same. (Don't trust my memory on this, though, double check that the formulas support this.) But there is some vagueness in this as the manufacturer may vary either of those constants slightly for various reasons.

I think you need to find a different way to argue the case.

ic-racer · Mar 10, 2016

Nice write up. It might be nice to point out some practical examples of how to use the technique. A typical scene in daylight (your prototypical 9 stop scene) is composed of two light sources. The sun and the sky. They are separated by about 3 stops. Items in the sun can be metered with incident or gray card technique (5 stops from black paint to white paint on the sunny side of a barn for example) and items in the shadow can be metered with incident or gray card technique (5 stops from black paint to white paint in the shadow). It you are exposing the entire barn, sunny side and shadow side, you can safely base negative exposure on the incident or gray card reading in the shadow (shown below) and for transparency, the reading in the sunlight (not shown).

RobC · Mar 10, 2016

Mr Bill said:
Rob, I have original copies of the ANSI light meter standard (I think early 70s, but I'm not planning to dig it up), and I don't find anything in the standard to directly connect a reflective meter reading to an average scene reflection. (I once went through it carefully in an attempt to do so.) It looks to me like you are trying to do so with the 'K' constant, however it's not really related. In fact, it only seems close because of the units used (if different light units are used, the 'K' value is much different).

As I recall, the only way I saw to correlate to scene reflectance was indirectly - to compare the constants, 'K' (for reflective meter) to 'C' (for incident meter), when the units are the same. (Don't trust my memory on this, though, double check that the formulas support this.) But there is some vagueness in this as the manufacturer may vary either of those constants slightly for various reasons.

I think you need to find a different way to argue the case.

ANSI standards are irrelevant today. They are old and not ISO standard. that is why I said old meters usng old standards which used different units are really not covered and if you have an old meter then you need to work that out for yourself. i.e. I'm not doing backwards compatibility. Look to the future.

So how do you derive 18% from todays standards? You can't so you need to know where it sits relative to todays standards and modern meters otherwise it will lead you up the garden path to a contrived point.
FACT: the reflection meter formula clearly adjusts to middle of curve using 8% of reading. I can't alter that because its in the formula and using the K Factor the manufacturer supplies. I didn't make it up myself.
The problem is people have got old standards so ingrained in their minds and don't want to see what is happening today and try and relate everything back to old standards. It won't work or at least is pointless unless yo are using old kit but that isn't what I was writing about.

Mr Bill · Mar 11, 2016

RobC said:
ANSI standards are irrelevant today. They are old and not ISO standard. that is why I said old meters usng old standards which used different units are really not covered and if you have an old meter then you need to work that out for yourself. i.e. I'm not doing backwards compatibility. Look to the future.
. . .
The problem is people have got old standards so ingrained in their minds and don't want to see what is happening today and try and relate everything back to old standards. It won't work or at least is pointless unless yo are using old kit but that isn't what I was writing about.

Rob please. Gimme a break. After you say, "Be kind," you completely dismiss my response like that. Okay, where, pray tell, are you getting YOUR information from. I hope you're not gonna tell me it's from the ISO 2720 standard. If so, check the date and see if it's not from 1974 (if it is, I guess you have to reconsider your position on "old" standards and meters, etc.).
http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=7690

Fundamentally, the metering standards - ANSI and ISO - are pretty similar. My point about the K constant is that it is NOT a "dimensionless" number - it changes when the units are different. If it were truly a factor for scene reflectivity then it should not change just because the light units did.

If there is IS a relationship between the reflectivity of the scene and the 'K' value as used in the metering standard, you ought to be able to find it in your copy of the standard and explain it concisely. I certainly don't see it.

RobC · Mar 11, 2016

Why would I want to change units from cd/m^2 when that is what my meter uses?

Convert your formula to SI units then it will make sense to you. Lux is SI unit and so are Candelas. Foot lamberts and Foot Candles aren't. Its not surprising you can't see a relationship (well maybe it is if you have thought about it but are still stuck in non SI units).

2^Ev = (B*S)/K

plugin some sensible SI units and we get

2^12 = (( 512*100)/12.5) = 4096

this gives my 8% when using SI units (Candelas/m^2)

now lets use NON SI units using FL and we get

2^12 = (( 149.434*100)/3.6) = 4096

yes K = 3.6 in non SI units and equates to a percentage of 27.8 but the conversion ratio between FL to Cd/m^2 is 3.43 and when you divide the %age value of 27.8 by the conversion ratio of 3.43 you get 8.1. So the %age of 8% in SI units equates to the %age of 27.8 in FL when you apply the conversion to the percentage or to the K Factor by multiplying 3.6*3.43 = 12.3

Si units link the film speed which uses Si units of Lux to the meter reading in cd/m^2 which is also in SI units. You must do the conversion. You can't expect SI units for film speed and non SI units with your meter to equate and expect them to give a meaningful relationship without proper conversion. Thats how I see it.

Oh what a surprise! 8% is the middle of a 7 1/3 stop range and my meter adjusts by 8% to get to the middle of the film curve.

And note that EV values cover a spread of Candela values between readings and Minolta quote 570 for EV 12 and not 512 so the numbers are ballpark but fit within the spread between readings.
I worked out NON SI values working back from 2^Ev and converting 512 cd/m^2 to FL so my non SI K factor of 3.6 is a bit off but close enough for the purposes of my explanation as I see it.

Stephen Benskin · Mar 11, 2016

I don't want to take notes, so I'll do quick posts. In the paragraph that starts with "This effectively means that 18% reflectance is the middle of a 5 stop range," you use the term "subject brightness range." This is an outdated term. It has been replaced with subject Luminance range or log subject Luminance range. Brightness is a psychological term and Luminance is psychophysical.

Also, you might wish to elaborate on the sentence, "This is important to know because different films are designed to capture different SBRs according to their ISO speed test criteria." As it is written, it is an incorrect statement.

And just an FYI on Munsell values:
The Optical Society of America's chair for The Committee of Colorimetry was Loyd Jones.

RobC · Mar 11, 2016

so they are not linear and don't equate to the exponential photographic scale either.
When did Munsell publish his scale and who was the author of the Book of Colour?

Thanks, I'm collecting comments and will address them in a few days.

Stephen Benskin · Mar 11, 2016

RobC said:
so they are not linear and don't equate to the exponential photographic scale either.
When did Munsell publish his scale and who was the author of the Book of Colour?

Thanks, I'm collecting comments and will address them in a few days.

The Book of Color is Munsell. The Committee on Colorimetry later published their report in book form as Science of Color.

Munsell and OSA dealt with psychophysical values. 18% and later 19.77% are perceived "middles" and were determined under precise conditions as influences such as simultaneous contrast, local inhibition and adaption have a major influence to how a particular tone is perceived.

Two more notes:

"The ISO standard for Negative Film Speed shows that the required Subject Brightness Range for a negative developed using manufacturers recommended developer, temp and time would require a 7 stop range ( 2.1 log in red above) to achieve a negative density of 1.3Log above fb+fog which I have determined to be required for a full scale negative to print from black to white at grade 2."

The standard doesn’t say this. ISO contrast parameter is not a recommendation for normal development. It relates to the concept of the Delta-X Criterion.

"So the middle of a 7 stop range is what %age reflection?"

Typo?

Mr Bill · Mar 11, 2016

Mr Bill said:
If there is IS a relationship between the reflectivity of the scene and the 'K' value as used in the metering standard, you ought to be able to find it in your copy of the standard and explain it concisely.

Rob, this is the real issue to me. Are you working from the actual standard? If so, I expect that it has the full derivation of the 'K' constant, as does the ANSI standard. If it does, you should be able to discover any explicit relationship to scene reflectance. (I see no such relationship in the ANSI standard.)

Given the close interaction between the two organizations at the time ("The American National Standards Institute, representing the United States, holds the secretariat for ISO/TC 42."), I expect that both take care of the loose ends in similar manner.

Note: I presume that we are past all that business about "old standards," and that your current ISO standard did originate in the same general time frame (1974) as my ANSI standard.

RobC · Mar 11, 2016

I'm not looking at standards. I'm making a reasoned attempt to explain the Kodak 18% Grey card and how it relates to photographic exposure (or not) as well as explaining the basics of light metering related to it. But you can't do that without talking about exposure ranges and how light meters actually work. And that drags you and me down the standards path where I'd rather not go because it results in discusions like the one we're having which puts people off.
The problem is there is so much ingrained thinking about an 18% card and so much of what seems to me to be wrong information, that its damn near impossible to break through that and take a fresh look at it and how exposure works, which IS incredibly simple, but not if its mostly based on false truths and you have to explain elementary maths to get past it.

The fact something isn't in a standard doesn't mean it doesn't exist or isn't implied. Work it out for yourself. The standard meter formulas tells you its there if its using units which work together and not if its using units which don't, but it is implied. You can't multiply Meters by Feet and expect to get a sensible answer without converting to same units so why would you think you can multiply Foot Lamberts by Lux and get a sensible answer. You won't unless you use same units on both sides. SI units being the preffered choice.
So in short, the standards are contrived and create confusion if they are based on mixing up units without applying meaningful conversion to same units.

I'm still waiting for someone to show me my failed reasoning of what a reflection meter actually does. The formula is not mine, the numbers are not mine. The maths says the meter is calbrated to 8% of reading being in middle of curve. I'm not interested in being told the standards don't say that when the metering formula and very simple maths shows it is.

Stephen Benskin · Mar 11, 2016

RobC said:
I'm still waiting for someone to show me my failed reasoning of what a reflection meter actually does. The formula is not mine, the numbers are not mine. The maths says the meter is calbrated to 8% of reading being in middle of curve. I'm not interested in being told the standards don't say that when the metering formula and very simple maths shows it is.

Sorry Rob but you are misinterpreting the information. You need to understand what the standards are saying. I don't have time to go into detail but you are wrong about K (review the relationship between the constants K, q, and P), you are also making an assumption about the importance of average reflectance that really doesn't exist, and you might want to think about exposure or in other words, the addition of flare.

Mr Bill · Mar 11, 2016

RobC said:
I'm not looking at standards. I'm making a reasoned attempt to explain the Kodak 18% Grey card and how it relates to photographic exposure (or not) as well as explaining the basics of light metering related to it. But you can't do that without talking about exposure ranges and how light meters actually work.

Rob, I get it. But the place to make the connection, IMO, is with the relationship between a film speed standard and the light meter standard. (I'm not exactly certain how to do this, but I think Stephen is.) Either that or make it more of an opinion or experience piece, or possibly just quote from technical papers or a qualified manufacturer's official documentation.

I spent years as the Quality Control mgr in a large processing lab, part of a studio chain. We kept probably 50 to 100 current ANSI standards, and I'm a bit anal what they say or don't say. I believe that you have to take them very literally. From my limited experience, the people on the committees are taking a great wealth of knowledge and experience, then distilling it down to a few carefully worded pages. More than once, when one of our vendors couldn't help us solve a problem, their best expert might say, I'm on an ANSI committee with so and so, and that's who you need to be talking to. So I know that, at least some of the time, these committees have had very qualified members. Anyway, I think it's a mistake to try to second guess what the wording MIGHT mean or imply.

wiltw · Mar 11, 2016

Stephen Benskin said:
And just an FYI on Munsell values:
The Optical Society of America's chair for The Committee of Colorimetry was Loyd Jones.View attachment 152289

And to quote Munsell, " The scale of value ranges from 0 for pure black to 10 for pure white. Black, white and the grays (as shown in figure 2) between them are called “neutral colors”. They have no hue. Colors that have a hue are called “chromatic colors.” The value scale applies to chromatic as well as neutral colors. The value scale is illustrated for all neutral colors on the chart labeled Munsell’s Nearly Neutral, included in this book of color." IOW, scale value 5 is merely the middle of the range of brightnesses between 'white' and 'black' without reference to exposure per se (or metering). Nor does the Munsell scale have reference to a dynamic range of f/stops (which itself varies widely, depending upon B&W neg vs. color transparency vs. which digital camera you might have in hand!)

The world has wrongly used the 18% grey card as a target for metering, when it really should be "If I expose and print correctly, the midtone target will be reproduced as a midtone in my slide or print."
A separate question is "What is the suitable reflected brightness target for metering, which will result in a midtone subject being reproduced as a midtone in my slide or print?"
And there we run into a number of variables...

sometimes my incident meter reading matches exactly my reflected meter pointed at an 18% grey target
sometimes my incident meter readinig differs by about 1/3 EV from my reflected meter pointed at an 18% grey target

...why is that? I dunno precisely, but I do not bother to buy a 12% grey target for reflected metering because of the above inconsistency which prevents me from adhering to a single principle on the topic!

markbarendt · Mar 11, 2016

RobC said:
But you can't do that without talking about exposure ranges and how light meters actually work.

Actually I think you can.

RobC said:
I'm not looking at standards. I'm making a reasoned attempt to explain the Kodak 18% Grey card and how it relates to photographic exposure (or not) as well as explaining the basics of light metering related to it.

First with regard to your "or not" thought.

The grey card ins't part of the ISO standard, that means to me that it has no direct relationship to photography or metering.

With that said IMO it is a really handy tool. It is more standardized as a reference point than the palm of a hand (because your palms and mine differ but the cards don't). The card and the palm though can both fulfill the same roll in finding exposure.

Any target in the scene that we know what to expect from can fill the same roll as the grey card. Your camera bag, your palm, your car, the clear northern sky, ... The offset/math will be different for each of these reference points but the value the reference point brings is always the same; we can understand how to set exposure to avoid underexposure.

That relationship is typically very specific, it is IMO a real value with a +/- 1/3-stop accuracy even where plus or minus development are employed.

The gray card does not necessarily define a specific zone in the scene.

DREW WILEY · Mar 11, 2016

And there is no guarantee the gray card you are using has the specific reflectance value it claims. The quality control on these things can be awful.

craigclu · Mar 11, 2016

DREW WILEY said:
And there is no guarantee the gray card you are using has the specific reflectance value it claims. The quality control on these things can be awful.

Yes my card differs quite a bit from a friend's. Mine tends to agree with 2 incident meters that I use so my trust level is better because of the nature of my gear (mostly by coincidence)! I believe mine was the back side of a reflector panel as an accessory for a 283 Vivitar flash from the late 1970's and was described as an 18% card. It is quite matte in surface finish but it's still sensitive to light angles.

markbarendt · Mar 11, 2016

markbarendt said:
The gray card does not necessarily define a specific zone in the scene.

I wanted to stretch this thought out a bit.

While the grey card can help define a workable exposure setting in relation to the films speed, say for the placement of the shadows to avoid underexposure with negatives, an exposure is a place and fall activity, we only get to peg one point on the film curve to the scene, the reality is that that is to the shadows.

The mid-tones and highlights are variables, the gray card tone might be developed to fall at a density of .5. .6, .7, or ..., and that number isn't all that important because the paper grade can skew film development adjustments either way from there.

If one uses a fixed film development regime and a fixed grade paper then one may be able to have the gray card tone carry through in a planned manner but that's not necessarily the norm.

Stephen Benskin · Mar 12, 2016

As Jack Dunn states, Lg “is not, as is sometimes mistakenly assumed, located precisely at the luminance level corresponding to the arithmetic average of a hypothetical scene containing evenly distributed tonal areas.

From Jack Holm's paper, Exposure Speed Relations and Tone Reproduction:

"Two significant assumptions which are often neglected in exposure determination concern the scene range and mean 'reflectance. They are as follows:

That the luminance range of a statistically average scene is 160:1 (log range 2.2), and the resulting exposure range on the image capture medium is 80:1 (log range 1.9), corresponding to a camera flare factor of 2.

That the mean log luminance of a statistically average scene is approximately 0.95 log units below the highlight log luminance (edge of detail in white) and 1.25 log units above the shadow log luminance (edge of detail in black), and that this mean luminance is assumed to be the luminance metered, directly or indirectly, for exposure determination. These values result in the mean luminance correlating with a Lambertian scene reflectance of 12% for 100% highlight reflectance."

I agree for a statistically average scene, the mean reflectance is 8%. Jack Dunn uses 9% reflectance in his book Exposure Manual, most probably because he rounded the luminance range down to 7 stops. Eight percent reflectance can be considered the real world average reflectance. If this sounds fairly low for photography, it is, for contrary to what most people believe, the average reflectance for photography isn’t the mean of the values of the real world subject, but the mean of the values of the real world subject measured within the camera. From a photographic perspective, the mean of the camera image is the value that really matters, and the fundamental difference between the real world luminance range and the camera’s illuminance range is the camera image includes flare (Graph 1).

Take another look at Holm's mean log luminance of a statistically average scene. It falls 0.95 log units below the highlight log luminance and 1.25 above the shadow log luminance. Add one stop flare and that makes the shadow log luminance fall only 0.95 below the mean. 0.95 above and 0.95 below.

Bill Burk · Mar 12, 2016

Hi RobC,

I always enjoy articles that prompt discussions, and you bring up some important points.

I found something you can sink your teeth into regarding the 18% gray card. Advice to open up one stop is an approximation. You're really supposed to open up 2/3 stop (but who could work with that, so they just say "open up one stop").

The Wikipedia article for light meter has a link to a Kodak page that shows how to relate an 18% gray card to illuminance.

http://www.kodak.com/cluster/global/en/consumer/products/techInfo/am105/am105kic.shtml

Relate the table to Sunny 16. Sunny 16 is commonly considered to be 81920 lux.

The chart doesn't go to 81920 lux, it stops at 64300 lux. What would be Sunny 16 from there?

Convert 64300 to log: 4.808
Add 1/3 stop, or 0.1: 4.908
Convert from log back to arithmetic: 80909 lux
2/3 stop more than 64300 would be 101908 lux and that overshoots by a significant amount.

Looking at the chart and working up to the shutter speed recommended for a reading of an 18% gray card in Sunny 16 conditions would be 4 1/3 stop faster than 1/30

By following the dial on my exposure meter from 1/30 second up 4 1/3 stops, I find a shutter speed of 1/600 second. This is what would be recommended by an exposure meter looking at a gray card in Sunny 16 conditions for ISO 400 film.

This is 2/3 stop higher shutter speed than the Sunny 16 rule. So you should open up 2/3 stop from a gray card reading, because it is 2/3 stop lighter than the calibration point.

Now what's 2/3 stop less than 18%? Find that and you will find a calibrated reflectance equivalent.

Following a reference I like to turn to to visualize percent reflection in terms of logarithmic density:

https://www.xrite.com/product_overview.aspx?ID=763&Action=support&SupportID=3730

18% equates to 0.74 reflection density
Add 2/3 stop (0.2) to make it denser (darker) = 0.94 reflection density
Which equates to 11%

So by this exercise it can be demonstrated that a meter is calibrated to 11%, because with a card of that reflectance in Sunny 16 light conditions your meter would indicate 1/400 second at f/16 for ISO 400 film speed.

Your thought that it is 8% would require a card with density of 1.10

Which would be to say an 18% gray card reads 0.36 density difference from what it should, and you would be recommending users to open up almost 1 1/3 stop.

So I don't agree with 8% and this is one demonstration towards the discussion. 8% is nearly 2/3 stop too dark for the job.

Another fun calculation you can work off that Kodak chart is the hypothetical... What would K have to be if the meters were calibrated to 18%.

Taking the formula N squared / t = ( L times S ) / K and substituting...

32 squared / 1/30 second = ((16,000 lux times 0.18 ) times 400) / K

30,720 = 1,152,000 / K

30,720 K = 1,152,000

K = 37.5

So K would have to be 37.5 if the meter were to be calibrated to 18%

RalphLambrecht · Mar 12, 2016

RobC said:
So I thought I would write a little article about Kodak 18% Grey Card and how it relates to photographic metering.
Also might enlighten a few people about light meter calibration in what I hope is as simple and readable and non scientific presentation as possible.

This is draft 1 for proof reading and comments before fixing for 2nd and hopefully last draft:

Please feel free to comment on possible errata, improvments (simple ones and not formulas), grammer, typos, understandable or non understandable etc etc.

Be kind

interesting stuff but it is my understanding that the 18% reflection value is based on a Kodakfield study,conducted by Condit in the 1940s,where he took readings of over 100 scenes around Rochester,determining an 18% reflection average and a 7 1/3 avg SBR;a copy of hthis study can be ordered from any local library;that's how I got mine.

RobC · Mar 12, 2016

I thought that was it but it wasn't clear to me. Its neither here nor there really becasue I'm more interested in relating it to what a reflection meter actually does and we know what the figures for those are. We know the film speed, we know the K Factor and from the EV number produced we know the Candelas or Foot Lamberts value it read so we can relate it very precisely to an 18% reflectance without speculating about how film speed and/or K were derived. And importantly we can see very easily how far it is from the center of the film curve that the meter aims for.

RalphLambrecht · Mar 12, 2016

RobC said:
I'm not looking at standards. I'm making a reasoned attempt to explain the Kodak 18% Grey card and how it relates to photographic exposure (or not) as well as explaining the basics of light metering related to it. But you can't do that without talking about exposure ranges and how light meters actually work. And that drags you and me down the standards path where I'd rather not go because it results in discusions like the one we're having which puts people off.
The problem is there is so much ingrained thinking about an 18% card and so much of what seems to me to be wrong information, that its damn near impossible to break through that and take a fresh look at it and how exposure works, which IS incredibly simple, but not if its mostly based on false truths and you have to explain elementary maths to get past it.

The fact something isn't in a standard doesn't mean it doesn't exist or isn't implied. Work it out for yourself. The standard meter formulas tells you its there if its using units which work together and not if its using units which don't, but it is implied. You can't multiply Meters by Feet and expect to get a sensible answer without converting to same units so why would you think you can multiply Foot Lamberts by Lux and get a sensible answer. You won't unless you use same units on both sides. SI units being the preffered choice.
So in short, the standards are contrived and create confusion if they are based on mixing up units without applying meaningful conversion to same units.
just to complicate things:I don't think there is such a thing as false truths! and to the discussion at hand:metering method aside:just expose for the shadows,develop for the highlights and ignore the rest.
I'm still waiting for someone to show me my failed reasoning of what a reflection meter actually does. The formula is not mine, the numbers are not mine. The maths says the meter is calbrated to 8% of reading being in middle of curve. I'm not interested in being told the standards don't say that when the metering formula and very simple maths shows it is.

Stephen Benskin · Mar 12, 2016

RalphLambrecht said:
interesting stuff but it is my understanding that the 18% reflection value is based on a Kodakfield study,conducted by Condit in the 1940s,where he took readings of over 100 scenes around Rochester,determining an 18% reflection average and a 7 1/3 avg SBR;a copy of hthis study can be ordered from any local library;that's how I got mine.

Ralph, if you are referring to "The Brightness Scale of Exterior Scenes and the Computation of Correct Photographic Exposure," I don't remember anything about 18% reflectance in that paper (although it's been more than a few years since I've thoroughly read the paper). In fact, I remember finding it interesting that it's not mentioned in any of Jones' seminal papers. I believe the perceived importance of 18% gray is primarily promoted from popular photographic writings.

The 18% gray card is more of a visual reference than an exposure device; however, it should be noted that the instructions that comes with the Kodak Neutral Gray Card says that if the card is used for metering an exterior scene, the exposure should be increased by 1/2 stop. This would indicate an effective 12% reflectance (to be clear, exposure meters are NOT calibrated to reflectance).

Rob, I've written rather extensively about K. There's a 20 plus page document available at http://64.165.113.140/content/benskin/. It's titled "Defining K." One of the problems of deriving information from the standards is that the purpose of the standard isn't about theory. All the research and supporting arguments for what's in a particular standard comes from scientific papers. The one exception to this is in the appendixes in the standard for general purpose photographic exposure meters (ANSI PH3.49 - 1971). The standard makes it clear that the appendixes are not part of the standard. The various sections that explain K are almost verbatim from the previously published paper Re-evaluation of Factors Affecting Manual or Automatic Control of Camera Exposure by James F. Scudder, C.N. Nelson, and Allen Stimson (also available at the above link). Here is an excerpt from the paper's abstract:

"The film exposure level maintained by an automatic control in a camera depends primarily on the film speed but several other variables can manifest substantial influence. The effects of field-luminance distribution and spectral sensitivity, as well as sensitometric, optical and photometric relations are expressed analytically and the equations for camera exposure are derived. The resulting constant relates the ASA standard film speed to the preferred exposure for an area in an average scene having the average luminance indicated by the meter. This constant, when combined with nine variables which are a function of camera design, meter design, and scene structure, provides an equation that is simplified by substituting empirical values for all but three parameters. The exposure constant is expressed as a function of the lens transmission, spectral characteristics of the detector and the discrimination of the field luminance measurement."

I'm still waiting for someone to show me my failed reasoning of what a reflection meter actually does. The formula is not mine, the numbers are not mine. The maths says the meter is calibrated to 8% of reading being in middle of curve. I'm not interested in being told the standards don't say that when the metering formula and very simple maths shows it is.

I've attempted to explain this to you a number of times in the past. By evaluating the variables in the equation for K, it's purpose can be better understood. I did a breakdown of the variables in Defining K that might be useful. Rob, I hope to adequately explain that while you got the math correct, your interpretation and application of K is in error. There is a lot to unpack and I'm still trying to determine an approach and how much effort I want to put into it. But something to think about for starters, you determined correctly that the ratio of C and K produces the effective average reflectance of the reflective meter (12%), but then mistakenly conclude meter's are calibrated to 8%. And yes, the 8% correlation is just a coincidence.

RalphLambrecht · Mar 12, 2016

DREW WILEY said:
And there is no guarantee the gray card you are using has the specific reflectance value it claims. The quality control on these things can be awful.

Well, you can measure its reflection density with a densitometer;It should be 0.75.The one from Kodak I have ,does and that calculates to 18% BTW

Feedback Please: The Kodak 18% Grey Card and Metering, a new look.

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