Dose Arithmetic: Mass Fraction, Volumetric Dosing and What a Scale Can Actually Weigh

Mass fraction: the one calculation everything else rests on human data

Every dose-per-unit question is the same two-step calculation. First, the mass fraction: divide the total mass of active by the total mass of the finished mixture. Second, the dose: multiply that mass fraction by the mass of one serving. Both steps require that the two masses are actually known, which is where most real errors live — not in the arithmetic, but in the confidence placed on the input numbers. The total active mass is known only to the accuracy of the balance that weighed it and the purity of the material, and purity is a number that comes from an assay, not from a supplier claim. The total mixture mass has to include everything: carrier, diluent, sugar, fat, the mass of the solvent only if it stays in the product. And the arithmetic assumes uniformity, which the mixing step has to earn — the mass-fraction calculation gives the batch average, and the batch average is the dose of a given serving only to the extent the batch is homogeneous. Compute the average first, then treat it as an upper bound on your knowledge rather than a property of the serving in your hand.

• Mass fraction = total active mass ÷ total finished mass. Express it as mg per gram, or as a percentage.
• Dose per serving = mass fraction × serving mass.
• Purity matters: 1.00 g of material assayed at 85 % active is 850 mg of active, not 1000 mg.
• The result is the batch mean. Without verified homogeneity it is not the dose of any particular unit.

Sources: United States Pharmacopeia 2023 · Johnson KC 2008

Worked examples: plant material, edible base, tincture, vape base human data

Plant material. 2.0 g of active, assayed at 90 percent, gives 1800 mg of active, distributed over 800 g of carrier. Mass fraction: 1800 mg ÷ 800 g = 2.25 mg/g, which is 0.225 percent by mass. A 0.3 g portion nominally carries 0.3 × 2.25 = 0.675 mg. Edible base. 1.00 g of distillate assayed at 85 percent total cannabinoids gives 850 mg of active, which is taken up into a 500 g gummy mass poured into 100 pieces of 5 g each. Mass fraction: 850 mg ÷ 500 g = 1.7 mg/g; dose per piece: 5 g × 1.7 mg/g = 8.5 mg. Check the arithmetic the other way around, which catches most errors: 100 pieces × 8.5 mg = 850 mg, the mass you started with. Tincture. 1000 mg of active brought to a final volume of 100 mL gives 10 mg/mL. A 1 mL dropper delivers 10 mg; 0.5 mL delivers 5 mg. Do not convert that into drops: drop volume varies by 30 percent or more with dropper tip geometry, viscosity, temperature and how the bulb is squeezed, so a drop is not a unit of volume and a dropper marked only in drops is an unmeasured dose. Vape base. 1.00 g of active at 90 percent, that is 900 mg, brought to 4.0 g total with 3.0 g of diluent, gives 900 mg ÷ 4.0 g = 225 mg/g, or 22.5 percent by mass. A 1 mL cartridge holding about 1.05 g of that liquid contains roughly 236 mg. What it does not tell you is the delivered dose per draw, because the fraction of liquid that is aerosolised and inhaled depends on the coil, the power, the draw duration and the user, and none of those are on the label. Per-cartridge and per-gram figures can be computed honestly; per-puff delivered dose cannot be computed from a formulation sheet.

Sources: Vandrey R 2015 · Meehan-Atrash J 2021 · Huestis MA 2007

Volumetric dosing: the only reliable method at the milligram scale human data

Volumetric dosing means dissolving a weighed mass of the compound in a known final volume of a suitable diluent, then dosing the resulting solution by volume. It is the standard approach in pharmacy compounding and in every analytical laboratory, for one reason: at the milligram and sub-milligram scale, liquid volume can be measured accurately with cheap equipment while solid mass cannot. A 1 mL syringe graduated in hundredths of a millilitre costs almost nothing and is repeatable; a balance that can honestly weigh 5 mg costs orders of magnitude more, needs calibration masses, a draught shield and a stable bench, and is still the weakest link in the chain. Volumetric handling also solves the homogeneity problem at the same time, because a true solution has the same concentration everywhere in it by definition. Worked dilution. Weigh 100 mg of compound — a mass large enough that a modest balance can handle it, which is the whole point — and bring it to a final volume of 100 mL in a diluent in which it fully dissolves at that concentration. The concentration is 100 mg ÷ 100 mL = 1 mg/mL, or 1000 µg/mL. Then 1.0 mL delivers 1 mg, 0.5 mL delivers 500 µg, and 0.1 mL delivers 100 µg. In an insulin syringe, where 100 units correspond to 1 mL, one unit is 0.01 mL and therefore 10 µg, which gives usable resolution two orders of magnitude below anything a consumer balance can resolve. Serial dilution for lower still. Take 1.0 mL of the 1 mg/mL stock — containing 1 mg — and bring it to 10 mL: the new concentration is 0.1 mg/mL, that is 100 µg/mL, and one insulin-syringe unit now delivers 1 µg. Each tenfold step costs one transfer and multiplies your resolution by ten. Two constraints are non-negotiable. The compound has to be genuinely soluble in the diluent at the stock concentration, because exceeding solubility silently produces a suspension that separates and hands back the same non-uniformity you were trying to escape. And the diluent has to be acceptable by the intended route: a solvent that is fine for a laboratory stock solution is not automatically fine to swallow, and one that is tolerable to swallow may be unacceptable to inhale. Those are separate judgements, and the residual-solvent page covers the second.

• Weigh a mass your balance can actually handle, then dilute down to the dose — never try to weigh the dose.
• 100 mg into 100 mL = 1 mg/mL. 1 mL = 1 mg; 0.1 mL = 100 µg; one insulin-syringe unit (0.01 mL) = 10 µg.
• Serial dilution: 1 mL of stock into 10 mL final = one tenfold step. Two steps takes 1 mg/mL to 10 µg/mL.
• Label every container with compound, concentration and date. An unlabelled stock solution is an unknown.
• Verify solubility at the stock concentration. A cloudy or settling stock is a suspension, not a solution.
• Diluent acceptability is route-specific and is a separate question from solubility.

Sources: United States Pharmacopeia 2023 · United States Pharmacopeia 2023 · United States Pharmacopeia 2023

Scales: resolution, accuracy, linearity — and where people get hurt contested human data

This is the part that does the damage, because a digital display invites a confidence the instrument does not support. Three different properties get conflated. Resolution, or readability, is the size of the smallest increment the display can show — the last digit. Accuracy is how close the reading is to the true mass, and it is always worse than the readability, sometimes by several counts. Linearity is whether the error is constant across the range: a balance may be within a count at half of its capacity and several counts off near zero or near full load, which is exactly the region where small masses live. Repeatability is a fourth property: place the same mass five times and see the spread. Run the numbers on the instruments people actually own. A kitchen scale reading in 0.1 g steps has a readability of 100 mg. Its last digit alone is 20 times a 5 mg dose, so a 5 mg target cannot even be displayed, let alone measured; the reading for 5 mg is 0.0 g, and the difference between 0 mg and 49 mg of compound is invisible to it. A jeweller-style scale reading in 0.01 g steps has a readability of 10 mg, twice a 5 mg dose, and typical specified accuracy of a few counts, so its honest uncertainty around a 5 mg target spans zero to several doses. A consumer milligram scale reading in 0.001 g steps displays single milligrams, which is why people trust them, but the specified accuracy of inexpensive units is commonly a few milligrams and their linearity near the bottom of the range is poor — a display of 5 mg may correspond to anything from 2 to 8 mg, and the user has no way to know which. An analytical balance with 0.1 mg readability, sited properly and calibrated with certified masses, is a different class of instrument, and even that one has a minimum mass below which its own repeatability dominates the result. The formal version of this constraint is the minimum weighable quantity: the smallest mass for which the balance repeatability, multiplied by a coverage factor, stays inside the accuracy you require. The classical pharmacy form of the same calculation divides the balance sensitivity requirement by the acceptable percentage error — a sensitivity requirement of 6 mg with a 5 percent acceptable error gives a minimum weighable quantity of 120 mg, which is why compounding pharmacists dilute rather than weigh small doses. A serviceable rule of thumb that falls out of the same arithmetic: do not weigh below roughly 50 to 100 times the readability of the balance if the number has to mean anything. On a 1 mg-readability scale that puts the floor around 50 to 100 mg. Then there is the environment, which routinely dwarfs the instrument specification. Calibrate with certified masses at a mass near the working range, not with a coin. Re-zero often, because drift with temperature is real. Watch tare error: taring a container and then adding material means the container mass is inside the measurement chain, and a large tare on a small net mass eats resolution. Static electricity on a plastic scoop or weighing boat will move a powder and shift a reading by milligrams. Draughts, a leaning bench, vibration from a refrigerator compressor, and off-centre loading all produce errors larger than the last digit. None of this is fussiness; it is the difference between a number and a guess wearing a decimal point.

Contested — caveat. The accuracy columns are typical figures for these instrument classes rather than a specification for any particular model, and consumer-scale performance varies widely between units and over their life. Determine the minimum weighable quantity for the balance in hand from its own repeatability, as USP <1251> describes, rather than relying on a class generalisation. The 50-100× readability figure is a practical rule of thumb, not a compendial requirement.

Sources: United States Pharmacopeia 2023 · United States Pharmacopeia 2023

The honest conclusion human data

If you cannot weigh it, you must dilute it and dose by volume. That sentence is the operational content of this page. A compound whose dose is measured in single milligrams, handled with a kitchen scale or a pocket scale, is not being dosed — it is being guessed at, and the guess has an error distribution several times wider than the dose itself. The guess does not become better because the display shows three decimal places, because the material looks fine, or because it worked last time. The remedy is cheap and available: weigh a mass the instrument can handle, dissolve it to a known concentration, label the container, and measure the dose with a syringe. That single change converts an unmeasurable solid-handling problem into a measurable liquid-handling one, removes the mixing-uniformity failure mode at the same time, and leaves a documented concentration behind, which is also the only thing that lets a clinician help if something goes wrong.

• A milligram-scale dose off a 0.1 g or 0.01 g scale is a guess, not a measurement.
• Dilution moves the weighing step to a mass the instrument can actually resolve.
• A labelled stock solution is also a record: it tells a clinician what was taken and at what concentration.
• No arithmetic on this page substitutes for knowing what the compound is; an unidentified substance has no dose.

Sources: United States Pharmacopeia 2023 · United States Pharmacopeia 2023 · Castaneto MS 2015