Dose math and calculator literacy

Dimensional analysis is the method of converting between units by multiplying by conversion factors expressed as fractions that equal 1. Every dose calculation involves tracking a set of physical dimensions:

• Mass: mg, µg, ng

• Volume: mL, µL

• Concentration: mg/mL, µg/µL

• Time: hour, day, week

Example (classroom only — non-injectable, fictional)

Consider a fictional oral solution for a fictional condition. The label states: 200 mg/5 mL. A caregiver needs to give 120 mg of the fictional drug.

? mL  =  120 mg  ×  (5 mL / 200 mg)
      =  (120 × 5) / 200 mL
      =  600/200 mL
      =  3 mL

Every term's unit cancels (mg cancels mg), leaving only mL. If the units do not cancel to the desired unit, the calculation setup is wrong.

This example is for dimensional-analysis instruction only. It is not a real product or dose.

A common error is to treat a mass and a volume as interchangeable. They are not; the relationship depends on a verified concentration from the exact product.

Key equivalences for peptide products:

• 1 mg = 1000 µg

• 1 mL = 1000 µL

• A 1% solution (w/v) = 10 mg/mL (1 g/100 mL)

Dose calculations should be rounded only under the product-specific policy used by the responsible pharmacist, clinician, or study protocol. Reporting more digits than a validated measurement system can resolve creates false precision. This repository intentionally does not select a device or give rounding outputs for administration.

The 10× error (decimal misplacement)

A misplaced decimal can turn a documented 0.5 mg quantity into 5 mg. This is a 10-fold error before any route or device is considered.

A 10× error is among the most common medication errors in both inpatient and outpatient settings.

Concentration confusion

When a lyophilized product is reconstituted, the label specifies both the quantity of drug and the volume of diluent. Some products require further dilution. Errors occur when:

• An operator copies a concentration from a different product or presentation

• A calculation assumes a final volume that the validated label does not state

• A non-validated preparation is treated as if its actual peptide content and final concentration were known

Unit mismatch

• Mixing mg and µg (a 1000× error)

• Mixing mL and µL (a 1000× error)

• Treating a product-specific biological “unit” as a universal mass or volume; unit definitions are not interchangeable across products

Ratio and proportion errors

If a pharmacist compounds a dilution and writes "Dilute to 10 mL" when the correct instruction is "Add 10 mL" (or vice versa), the resulting concentration differs by the displacement volume of the solute.

Several websites and mobile applications accept a peptide mass (in mg) and a desired dose (in mg or µg) and return a withdrawal volume. These tools typically:

• Assume a fixed reconstitution volume that may not match a validated product instruction

• Assume complete dissolution and no volume displacement from the lyophilized cake

• Apply a simple proportion while treating all displayed inputs as verified

• Ignore product-specific factors: aggregation losses, overfill, preservative concentration, viscosity, adsorption to container

• Provide no quality or sterility assessment

Why they cannot establish a safe or appropriate dose:

• The reconstitution volume is product-specific and cannot be inferred from peptide mass alone

• The actual peptide content per vial carries labeled overfill that accounts for holdup in the vial and syringe dead space; the calculator may assume a different overfill factor

• The concentration after reconstitution cannot be validated by the user without an assay

• The dose-to-volume relationship assumes that the entire contents are recoverable, which may not be true for viscous or adsorptive formulations

• No calculator can account for individual patient factors (renal function, volume of distribution, concomitant medications, indication) that determine appropriate dose

For an approved product or ethics-approved study, a qualified professional can audit whether the documented prescribed quantity, labeled concentration, unit definitions, route, patient parameters, and product presentation all come from the same current source. Units should cancel correctly, rounding policy should be explicit, and an independent checker should reproduce the result under the applicable institutional procedure. A mathematically consistent result is still unsafe if any input is unverified, the product is unapproved or inauthentic, or the calculation is being used outside the labeled/protocol context.

This atlas therefore does not accept user-entered peptide mass or desired dose, does not calculate an administration volume, and does not recommend a device.

1. Institute for Safe Medication Practices. ISMP's List of High-Alert Medications in Community/Ambulatory Healthcare. 2021. https://www.ismp.org/recommendations/high-alert-medications-community-ambulatory-list

2. USP General Chapter <795> Pharmaceutical Compounding — Nonsterile Preparations. USP–NF. Rockville, MD: United States Pharmacopeia; 2026.

3. USP General Chapter <797> Pharmaceutical Compounding — Sterile Preparations. USP–NF. Rockville, MD: United States Pharmacopeia; 2026.

4. FDA. Guidance for Industry: Safety Considerations for Product Design to Minimize Medication Errors. 2016. https://www.fda.gov/media/98641/download

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6. Lesar TS, Briceland L, Stein DS. Factors related to errors in medication prescribing. JAMA. 1997;277(4):312--317. https://doi.org/10.1001/jama.1997.03540280050033