Conceptual boundary: This page teaches arithmetic literacy. It does not provide a dose, accept user inputs, calculate an administration volume, or choose a device. Approved-product calculations belong to qualified professionals using the current label; A clinical-stage candidate with scientific or public relevance. Investigation is not approval, and a studied exposure is not a recommendation. Source de la définition: Scope and selection methodology · Glossaire work belongs to an ethics-approved protocol.
Dose calculation concept visual
Dimensional analysis: the foundation
Dimensional analysis converts between units by multiplying by conversion factors that equal one. Units should cancel to the intended output, making mismatches visible.
Classroom example — non-injectable
A fictional oral solution for a fictional condition is labeled 200 mg/5 mL. A fictional written quantity is 120 mg.
? mL = 120 mg × (5 mL / 200 mg)
= 3 mLThe milligram units cancel, leaving millilitres. This arithmetic result is part of a fictional classroom example only; it is not a real product, dose, or recommendation.
Known quantity: 120 mg. Conversion factor: 5 mL per 200 mg. The mg units cancel, leaving 3 mL as an arithmetic result only, not a recommendation.
Concentration versus dose
| Term | Definition | Units |
|---|---|---|
| Amount | Quantity of substance stated in an order, label, or protocol | Mass units such as mg or µg |
| Concentration | Amount per unit volume | Compound units such as mg/mL |
| Volume | Quantity of solution | Volume units such as mL |
| Mass per administration | An amount derived only when the governing source supplies a valid relationship | Mass units |
In the fictional oral classroom example, 120 mg is the known amount and 200 mg/5 mL is the labeled concentration. A mass and a volume are not interchangeable; their relationship depends on a verified concentration from the exact product.
Unit prefixes and conversion
| Prefix | Symbol | Factor | Pure unit equivalence |
|---|---|---|---|
| milli- | m | 10⁻³ | 1 mg = 0.001 g |
| micro- | µ | 10⁻⁶ | 1 µg = 0.001 mg |
| nano- | n | 10⁻⁹ | 1 ng = 0.001 µg |
These equivalences define units only. They provide no product identity, concentration, clinical amount, or administration output.
Significant figures and rounding
Repeated or early rounding can compound error across conversions. Reporting more digits than a validated measurement system can resolve creates false precision. Any applied rounding policy belongs to the governing product label, study protocol, pharmacy policy, and validated measurement system; this atlas supplies none.
Common error modes
| Error | Detection question | Consequence |
|---|---|---|
| Unverified source | Do all inputs come from the same validated record? | Correct arithmetic can preserve a false premise |
| Decimal displacement | Does the written value preserve place value? | A tenfold discrepancy can result |
| Concentration / amount confusion | Is an amount being treated as a volume or concentration? | The equation represents the wrong quantity |
| Unit mismatch | Do mass and volume prefixes cancel explicitly? | Thousandfold discrepancies can be hidden |
| Product-specific unit treated as universal | Is a biological unit being converted without its product definition? | Non-equivalent units are falsely equated |
| Ratio wording ambiguity | Does the source distinguish a final total from an added quantity? | The assumed final concentration can change |
| Early rounding | Was full precision retained until the governing policy applies? | Repeated rounding can compound error |
- Do all inputs come from a validated source? If no, stop: arithmetic cannot repair the source.
- Do units cancel?
- Is concentration confused with amount?
- Was rounding deferred?
- An internally consistent calculation still does not establish appropriateness.
What online “peptide calculators” do
Some websites accept a displayed peptide mass and desired amount, assume a liquid volume, and return a withdrawal volume. The proportion may be internally consistent while the identity, actual content, concentration, formulation, sterility, overfill, adsorption, container losses, and patient context remain unknown.
Arithmetic cannot validate an unapproved or inauthentic product. A calculator also cannot supply indication, population, renal or hepatic context, concomitant medicines, or current approved labeling. It therefore cannot establish a safe or appropriate amount.
Auditing arithmetic without turning it into an administration tool
An arithmetic audit can ask whether every input comes from one current validated source, units cancel, amount is distinct from concentration, and rounding is deferred. It cannot determine whether a product is authentic, approved, indicated, suitable, or appropriate for a person.
See Dose language and safety boundaries, the approved-product label index, routes and absorption, and evidence grading for the separate evidence questions. For what was actually administered or labeled per compound — presented as documented evidence, never as a calculator input or recommendation — see the studied and labeled exposures index.
Sources
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
USP General Chapter
<795>Pharmaceutical Compounding — Nonsterile Preparations. USP–NF. Rockville, MD: United States Pharmacopeia; 2026.USP General Chapter
<797>Pharmaceutical Compounding — Sterile Preparations. USP–NF. Rockville, MD: United States Pharmacopeia; 2026.FDA. Guidance for Industry: Safety Considerations for Product Design to Minimize Medication Errors. 2016. https://www.fda.gov/media/98641/download
Cohen MR, ed. Medication Errors. 2nd ed. American Pharmacists Association; 2007. ISBN 978-1582120625.
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