Why 0.877?

Ball-and-stick model of the Δ9-tetrahydrocannabinol molecule.

A lot of customers ask about “Δ9-THC Potential” on lab reports and why we use 0.877 to calculate it. This post from Confidence Analytics explains the chemistry and the math in straightforward terms.

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.

[THC Potential = THC + (0.877 * THCA)]

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!

We hope this answers some of your questions about our favorite herbal product, or perhaps piques your interest to learn more about chemistry.

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.

Thanks Confidence Analytics!

Let’s talk about how The Good Lab might help you. Give us a call at 720-245-8323.

Testing for THC in hemp


We folks at The Good Lab were concerned about SB17-090, a bill regarding how THC is calculated in hemp, and how it might negatively impact hemp producers if certain adjustments in the calculations weren’t considered.

So we wrote this email to the bill’s sponsors:

After reading SB17-090 regarding how THC is measured in hemp, we’re concerned that there is a calculation error that could negatively and unfairly impact hemp farmers. Simply adding THC-A and delta-9-THC together will not give an accurate or fair result. Considering that Amendment 64 specifies delta-9-THC, factoring in a correction value to account for decarboxylation is important.

Decarboxylation is a chemical reaction that removes a carboxyl group and releases carbon dioxide (CO2). When THC-A is decarboxylated and converted to delta-9-THC, there is a reduction in the molecular weight that will affect the final percentage calculation. The molecular weight of THC is less than that of THC-A due to the loss of the carboxyl group.

At our lab, we calculate the delta-9 potential in hemp or cannabis using a factor of 0.877. I’ve attached a sample potency report so you can see how we make our calculations.

This article from High Times further explains the error in the current bill’s calculation and why you can’t simply add THC-A and delta-9-THC together to get the accurate number you’re looking for..

We respectfully recommend an amendment to SB17-090 correcting this calculation error.

Apparently, the sponsors passed our concerns onto the Colorado Department of Agriculture. We were excited to get the following response from Mitch Yergert, Director, Division of Plant Industry:

This bill (SB17-090) only affects the testing being conducted by CDA at our lab. We have no desire to affect how the private labs conduct testing for hemp producers. We know most (if not all) of you use HPLC and will continue to do so. We were very specific in the bill to not require a certain piece of equipment or methodology to accommodate this and additionally our approach could change in future years to HPLC or even something else if a better type of machine comes along. We don’t believe the bill language would prevent this in the future.

Currently we use a GC for our analysis as it is more cost effective for the program and the hemp producers. Because of this we don’t have the issue with needing to calculate the THC-A conversion. We would recommend you use the 0.877 molecular weight value as the most conservative approach. We have seen some reports that actual yield from decarboxylation will be less than the exact .877 and that makes scientific sense. We have seen numbers as low as 0.700 in one study. But we don’t have sufficient data to select a specific number less than 0.877 that we would stand behind.

As your testing is not regulatory and we don’t base our regulatory decision on those numbers, by using the .877 number you are providing a conservative estimate to the grower which provides the highest potential THC for the crop. That seems to be the best number for the grower to consider. They can make the decision how to move forward with their crop based upon that. It is conceivable if they are minimally over in your testing using HPLC and the 0.877 conversion and we run a GC analysis, that the value could come in at 0.3 or slightly under, but that is good for everyone.

I believe the variability in sampling conducted by the grower versus CDA is probably a much bigger variable in the process than whether the private labs use HPLC and we use GC. So comparing the two numbers just based on the lab values may not be that productive.

What was really exciting was the validation we got from the CDA about the importance of private labs like ours.

The private labs perform a very valuable function for the hemp producers as the industry tries to get established. We appreciate you efforts to work with them and us on this issue.

We’re excited to work with the CDA, hemp farmers as well as other private cultivators to produce and develop high-quality hemp and cannabis products.

For more information on how The Good Lab might help you, please give us a call at (303) 455-3801.