# Why 0.877?

We’ve received many customer calls and visitor questions over the years concerning one seemingly arbitrary number. This number is featured in the important calculation for “THCmax”, or total available THC as we like to call it. The calculation looks something like this:

THCmax = THC + 0.877 * THCA

This number is not at all arbitrary, but where does it come from? In a simple phrase: the structure of cannabinoid molecules.

As you may know, the plant-made versions of the major cannabinoids, sometimes called cannabinoid acids, need to be “decarbed”, or decarboxylated, before they can assume their full active effects. This decarboxylation is why it’s called a decomposition reaction — one molecule becomes two. In our case, one of these molecules is always CO2, (carbon dioxide being the source for decarboxylate). The other molecule is the “active” or “neutral” cannabinoid itself.

The number 0.877 is actually fixed in nature, and it’s based on the ratio of the masses of the cannabinoid molecules. Most major cannabinoids (THC, CBD, CBG, CBC, but not CBN) have the same molecular formula: C21H30O2, for 21 carbons, 30 hydrogens, and 2 oxygens. The equivalent cannabinoid acids (THCA, CBDA, CBGA, and CBCA, respectively) are “neutral” cannabinoids that are “wearing” a CO2 molecule, changing their molecular formula to C22H30O4 with the addition of one carbon and two oxygens.

Each element in a molecule has a measurable weight, and the most common weight of an element is usually the largest number in an element’s box on the periodic table. Carbon has an atomic mass of approximately 12.011, hydrogen about 1.008, and oxygen almost exactly 16.

We can calculate how much each molecule of THC weighs, like this:

THC’s molecular weight = 21 Carbons (12.011) + 30 Hydrogens (1.008) + 2 Oxygens (16.000)

THC’s molecular weight = 314.47

We can calculate the same for THCA:

THCA’s molecular weight = 22 Carbons (12.011) + 30 Hydrogens (1.008) + 4 Oxygens (16.000)

THCA’s molecular weight = 358.48

The molecule released during “decarb”, CO2, has a molecular weight of about 44.01. If we add THC’s 314.47  and CO2’s 44.01, we get the molecular mass of THCA, 358.48. The universe is making sense! So far so good. If we take this a step further, we realize that THCA is, in fact, not entirely THC. It’s only 314.47 / 358.48 = 0.8772 or 87.72%. There’s our 0.877! The remaining 12.28% is CO2, which bubbles away as a gas during decarboxylation – the bubbling of a full melt hash or a dab on a hot nail illustrates this process.

Now, the goal of the available THC calculation is to find, under absolutely ideal conditions, the maximum amount of “active” THC that can be derived from a sample. If THCA is only 87.72% THC, it only makes sense that we account for that fact in our available THC calculation; Multiply the amount of THCA by 0.877 before adding it to the amount of already “activated” THC. Put another way, a gram of 100% pure THCA contains 0.877 grams of THC and 0.123 grams of CO2.

The same exact “activation multiplier” can be used to calculate available CBD, CBG, or any other cannabinoid with a molecular formula of C21H30O2. Some may have noticed that the American Herbal Pharmacopeia blurb about available cannabinoid content features a multiplier of 0.878 for CBGA; this is because CBGA’s molecular structure contains two more hydrogen atoms, for a formula of C22H32O4. When CBGA decarboxylates into CBG, the two hydrogen atoms are retained, and CBG thus has two more hydrogen atoms in its structure than THC or CBD. The same math from above with the molecular weights of CBGA and CBG (360.75 and 316.74 respectively) yield a conversion factor of 0.8780, slightly different than the 0.877 for THCA to THC.

For the -varin class of cannabinoids, THCV being the most well-known (but also including CBDV, CBGV, CBCV, and their respective acids CBDVA, CBGVA… etc.), we need a different activation number because the molecular masses aren’t the same: cannabivarins are missing two carbons and four hydrogens compared to their regular cannabinoid cousins, giving us a molecular formula of C19H26O2 (mass of 286.42), and C20H26O4 (mass of 330.43) for their acids. Our “activation multiplier” for the -varin class is 0.8668 instead of 0.8772. Close, but not the same!

Check out our other blog posts for more curious topics of discussion, and refer to this page for an explanation of all the cannabinoid values we report on our certificates of analysis.

TL;DR: The seemingly arbitrary number 0.877 is a ratio of molecular masses, specifically that of THC divided by that of THCA. If you multiply the amount of THCA by 0.877 and add the amount of already “active” THC, you find the maximum amount of THC remaining after complete decarboxylation. THCA is about 87.7% THC and 12.3% CO2 by mass.

## 19 Comments on “Why 0.877?”

1. Do you know the conversion ratio for determining how much CBN would be produced from THC?

I have some 100 year old Cannabis bottles with the contents in them, which I had tested, and the THC has degraded to CBN but not fully. So after a century, still at least 20% THC in each sample I had tested.

My goal is to calculate the original contents of THC but don’t know how, thanks for any assistance.

1. Dear Jon. Please keep those bottles a safe place !!

I am a former biomedicine and biochemistry student, now helping to run a danish NGO. I would be very interested in pictures of any kind, gladly the whole thing and close ups of the bottle descriptions etc.
– Happy to read you have some noble intentions, maybe we could somehow connect regarding future work on that intention.

Feel free to contact me/us at:
fflac2017@gmail.com

– I have the manuals for making them btw.

2. Hey Jon,

Very interesting that you have 100-year old cannabis!

The answer to your question is again in stoichiometry. Where THCA has a molecular weight (MWT) of ~358 atomic mass units (AMU), THC has an MWT of ~314 amu (again, 314 / 358 ~ 0.877), CBN as an MWT of ~310 amu. The difference is ~4 amu, from the four hydrogen atoms (each weighing ~1 amu), which is the name difference between THC and CBN (tetrahydro = four hydrogens).

Assuming all THC becomes CBN, and nothing else happens, we can estimate how much THC your century-old cannabis started with. 314 / 310 = 1.013, so THC weighs about 1.3% more per molecule than CBN. This means that 1.000 grams of CBN came from 1.013 grams of THC in this ideal scenario. The reciprocal of this is 0.987, so for every gram of THC you can make at most 0.987 grams of CBN.

What is more likely is that THC degrades into some other things besides CBN, so this more a limiting estimate than anything else. It would be safe to say that *at least* ~1.013 grams of THC was in the plant to make every gram of CBN. We can derive a conversion number between THCA and CBN, too, if we again assume 100% of the THCA eventually becomes CBN: 358 / 310 ~ 1.155, so ~1.155 grams of THCA can degrade to a maximum of one gram of CBN.

This all comes down to ratios of molecular weights, and assuming 100% conversion. The reverse of 0.877 is how much THCA you need to make a given amount of THC; 358 / 314 ~ 1.140, so ~1.14 grams THCA can make up to one gram of THC.

Hope this helps!

I have a handful of bottles and contents actually, the tested ones are from Parke, Davis & Co. One labeled Feb 25, 1919 and the others are similar bottles and label styles, all same time frame.

No. 107 Tablets
CBD 0.0156mg
THC 0.0194mg
CBN 0.0613mg

No. 186 Tablets
CBD 0.0269mg
THC 0.0312mg
CBN 0.0342mg

No. 224 Tablets
CBD 0.00983mg
THC 0.0163mg
CBN 0.0511mg

My goal is to continue to collect these specimens and test them and show the infinite number of ratios being formulated a century ago, to nullify 21st century patents claiming first discovery of using cannabinoids in specific ratios. Appreciate the help!

Jon Marsh

4. Hi I’m curious how to properly calculate thc dosages per gram of decarbed bho/rosin.

For example I’ll say I have bho that is 70% thca content. Now at max decarb without breaking down to much thc from what I’ve found you can activate 70% of your thc before you start breaking it down to fast. Do I need to calculate that as well when making dosage. For example. 1 gram bho with 700 mgs of thca after 70% decarb would be 490 mgs of activated thc left after decarb. Making ruffly 20 dosages of 25 mg capsules. Or do I calculate the .877 % first making 700mg thca 609mgs thc then max 70% decarb making it 426 mgs per 1 gram bho. So far all the scales I have found don’t take the decarb into effect when making a dosage for edibles or capsules after the decarb process. And non have shower this .877 method

1. Hi Bryan

If you are achieving a 70% decarb rate, you’re only decarbing 490 mg of your 700 mg THCA, so you will end up with (490 x 0.877 =) 430 mg of THC + 210 mg THCA in your BHO, and you’ll lose 60 mg of weight as a result of decarb.

However, there is nothing stopping full decarb. If you are relying on the much-circulated graph from the 1990 Journal of Chromatography, I would caution that cannabis science has advanced a LOT since then. All I can find is the graph, with no other supporting articles or research, so I have no idea what the conditions and format of that measurement were. And given that this lab regularly see 90-95% THC distillates and other extractions at well over 70% THC, I’m inclined to disregard that graph and its assumptions until someone shows me more information on it.

I’ve fully decarbed flower in my oven at home with little to no degradation. 250+/- 10 deg F for 75-90 mins. I know this because I tested the flower before and after I decarbed it, there was maybe a per cent or two lost, no more than that. (And anyway, there’s nothing wrong with a bit of CBN, helps you sleep). So don’t let that graph get in your way – decarb it all!

5. Quick and to the point article. Thank you very much for clearing this up, it can be a confusing topic to try to explain to someone why their THCA levels are not directly representative of the total end potency.

6. I see you explained this but I’m having a hard time
My
cbda=18.3%
Cbd =.29%
Thca=.69%
Thc9=.02%
I have 2.47oz of dry flower that I am decarbing at 325 degrees for 45min
And making it into rso.
What is my total percentage per gram of rso Of thc9 and cbd??

7. Hi,

Thanks, just the answers I was looking for.
So, If I understood correctly the THC legal limit in countries where you can buy full spectrum CBD products applies to THCmax or just THC?

Regards,
Andy

8. Enjoyed the article, thx. As the process of conversion/extraction or vise versa is never 100% although we would like that, it isn’t the way it goes in the lab. We do a mass balance to work out where everything expected ends up based on maths and the conversion efficiencies as a result of process and material feedstock variables. The process of kicking out the carboxylic acid group is unlikely to be 100% (some THCa/THC degrades out) and for extraction as a process not smoking, the pull out efficiency is never 100%. In the lab we test a dried down sample (near 0% water) is taken to determine the potential THCA and work out the conversion which usually ranges between 90-97%, then calculate using our standard efficiency number for pull out of 95% to achieve an amount of THC expected from the process when it’s all done, again this didn’t represent when or how the decarboxylation is accomplished. These are all additive and as an example we end up in the range of 74.9%+- of the original content of THCa. If the conversion isn’t good or the extraction process isn’t good we can obtain less and if we mail it we get more. I’m guessing that even with smoking the conversion rates and efficiency will not be 100%, meaning if it says 15% THCa on the label then your intake will be lower. We’ve seen Clients with huge damage to extracts under decarboxylation where a process damages over 50% of the expected amount, so it’s super important to use care and caution when decarboxylating. Cheers!

9. Greetings!

I’m going to be assisting a caregiver in the production of Rick Simpson Oil. My question is regarding optimal time and temperature to decarboxylate it. You had mentioned a chartgraph from the 1990 Journal of Chromatography that has probably been superseded. Is there something more current that you could refer me to? We are probably going to be decarbing only 10 or 20 grams at a time.

Thank you for any guidance you may be able to provide!
SteveO

10. An overlooked comment from my previous post. We plan to use a boiling, saturated brine to heat the flask for decarboxylation. That should yield us a rather stable temperature of approximately 108.7 °C (227.7 °F).

11. Thak you for that interesting article.
Can you please advise on how to calculate the RSO Rick Simpson Oil molecular weight.
as it is combining all the parts of the flower.

I appreciate you kind help
Take care and all the best!

I would LOVE to get your feedback on a govt study that was done in 2016 as well shown below.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5549281/

If you will look at table 1, you will see not only were decarb percentages different for different cannabinoids, but were different for varying temperatures. It totally blew me away and I didn’t know what to think about it and is when I got to googling and found your site.

I’m very happy you have a comment section because I am excited about getting your feedback on it.

Thank you for your time and help ahead of time and have a great week!

https://i.imgur.com/g9Ye0cR.png

1. Yep. Different acidic cannabinoids decarb at different rates, at different temperatures. This has to do with the relative stability of the carboxylic acid functional group on the different structures.

As to why there is a difference in relative molar mass loss during the process, I don’t know. I would guess it has to do with relative differences in loss to degradation products. Again, likely due to the relative stability of the structures themselves.

13. Thank you for taking the time for the reply Nick.

I am not a scientists or chemistry major, so I have to break this down; which the article did a great job of doing btw. I can understand “Different acidic cannabinoids decarb at different rates, at different temperatures.” And if you get the right time and temp, I’m of the understanding that it should be a very predictable loss as shown in the quoted paragraph below. The .877 comes out to a 12.3% loss from decarb with 100% conversion from THCA to THC. With an assumption of no conversion to CBN as it relates to THC with the right time and temp.

The govt study for THC had a smaller loss for 7.94 %, which was impressive and nice. But then very unexpectedly had a swing of 18.05% to 25.2% decarb loss for CBD. And then an astounding 52.67% decarb loss for CBG. With the assumption of the accuracy of the below quote, that I believe we all hold as a constant, I am baffled to their results. We debated this in a fb group and decided it was bad data – thinking contaminants, bad protocols or possible even bad / not properly calibrated test equipment had a play in skewing the results.

“The number 0.877 is actually fixed in nature, and it’s based on the ratio of the masses of the cannabinoid molecules. Most major cannabinoids (THC, CBD, CBG, CBC, but not CBN) have the same molecular formula: C21H30O2, for 21 carbons, 30 hydrogens, and 2 oxygens. The equivalent cannabinoid acids (THCA, CBDA, CBGA, and CBCA, respectively) are “neutral” cannabinoids that are “wearing” a CO2 molecule, changing their molecular formula to C22H30O4 with the addition of one carbon and two oxygens.”

Thoughts on this would be greatly appreciated. What we are looking for in the botanical extraction group is a fairly reliable way of calculating the top cannabinoids your company mentions in the article in the quote above for medicinal purposes.