Study guide
This chapter builds the scientific and mathematical foundation that everything else in pharmacy practice rests on. You will work through the pharmacology, pharmacokinetics, and compounding concepts that explain why drugs behave as they do in the body, and then apply that reasoning to the calculations pharmacists perform every working day. Treat the calculation examples as templates: master the logic behind each one, and you can adapt it to numbers you have never seen before. This material is educational and intended to support exam preparation, not to substitute for clinical judgment or institutional protocols.
Pharmacology, Pharmacokinetics, and Pharmaceutics
Pharmacology describes how drugs produce their effects, usually by binding a receptor, enzyme, or transporter and changing a cell's behavior. Pharmacodynamics is the study of what the drug does to the body, including the relationship between concentration and effect, while pharmacokinetics is the study of what the body does to the drug: absorption, distribution, metabolism, and excretion, often abbreviated ADME. A drug taken orally must dissolve, cross the intestinal lining, survive first-pass metabolism in the liver, and reach the bloodstream before it can act; bioavailability is the fraction of an administered dose that reaches systemic circulation unchanged. Pharmacogenomics adds a layer of individual variation: certain patients carry gene variants, such as CYP2D6 or CYP2C19 polymorphisms, that make them metabolize specific drugs unusually quickly or slowly, which can change both effectiveness and toxicity risk. Pharmaceutics is the science of how a drug is formulated into a usable dosage form, covering topics like dissolution rate, particle size, and how excipients (inactive ingredients that aid manufacturing, stability, or delivery) affect how fast and how completely a drug is absorbed. A helpful way to keep these terms straight: pharmacokinetics answers where the drug goes and how fast, pharmacodynamics answers what happens once it gets there, and pharmaceutics answers how the dosage form was built to make that journey possible. Understanding these relationships lets you reason through unfamiliar drug questions on exam day rather than relying purely on memorized facts.
Nonsterile and Sterile Compounding
Compounding is the preparation of a customized medication for an individual patient when a commercially available product does not meet that patient's needs, such as a child who cannot swallow tablets or an adult who needs a preservative-free formulation. Nonsterile compounding covers preparations like oral suspensions, creams, ointments, and suppositories, and generally follows quality standards addressing ingredient selection, beyond-use dating (the date after which a compounded preparation should not be used, distinct from a manufacturer's expiration date), and documentation. Sterile compounding applies to preparations meant for injection, infusion, or application to the eye, and requires a controlled environment, such as a laminar airflow hood or biological safety cabinet within a cleanroom, along with strict aseptic technique to prevent microbial contamination. A central concept in sterile compounding is intravenous (IV) compatibility: not every two drugs or a drug and a diluent can be mixed safely. Incompatibility can be physical, such as visible precipitation (solid particles forming in solution) or haze, or chemical, such as degradation that is invisible but reduces potency or forms a harmful byproduct. For example, calcium-containing solutions and phosphate-containing solutions can form an insoluble calcium phosphate precipitate if mixed in the wrong concentrations or order, which is one reason total parenteral nutrition formulations follow strict compounding sequences. Pharmacists rely on published compatibility references and visual inspection before, during, and after mixing to catch problems. Risk levels for sterile compounding (low, medium, and high) reflect factors like the number of components combined and the compounding conditions, and they determine how soon after preparation an admixture must be used or discarded.
Calculations: Dosing, Rates, and Compounding Quantities
Pharmacy calculations translate a prescriber's order into a specific, safe, measurable action. A weight-based loading dose delivers a larger initial amount to rapidly reach a therapeutic concentration; for example, a vancomycin loading dose is often calculated at 25 to 30 mg per kilogram of actual body weight for seriously ill patients. For an 80 kg patient at 25 mg/kg, the loading dose is 80 times 25, or 2,000 mg. IV infusion rate problems commonly require converting a weight-and-time-based dose (mcg/kg/min) into a volume-based rate (mL/hr). Suppose dopamine is ordered at 5 mcg/kg/min for a 70 kg patient, supplied as 400 mg in 250 mL of D5W. The concentration is 400,000 mcg divided by 250 mL, or 1,600 mcg/mL. The ordered dose is 5 times 70, or 350 mcg/min, which is 350 times 60, or 21,000 mcg/hr. Dividing 21,000 mcg/hr by 1,600 mcg/mL gives 13.1 mL/hr. Dilution problems use the relationship C1V1 = C2V2, where concentration times volume before dilution equals concentration times volume after. Diluting 5 mL of lidocaine 4% up to a final volume of 20 mL gives (4% times 5) divided by 20, which equals 1%. Compounding-quantity problems combine a dose calculation with a days-supply calculation: if a suspension is 250 mg per 5 mL and a patient needs 375 mg per dose, three times daily for 10 days, each dose requires 375 divided by 50 (the mg per mL), or 7.5 mL; thirty total doses require 7.5 times 30, or 225 mL to dispense.
Renal Function, Alligation, and Pediatric Dosing
Many drug doses must be adjusted for kidney function, most often estimated with the Cockcroft-Gault equation: creatinine clearance (CrCl) equals (140 minus age in years) times weight in kilograms, divided by 72 times serum creatinine in mg/dL, multiplied by 0.85 for female patients. For a 68-year-old woman weighing 60 kg with a serum creatinine of 1.1 mg/dL: 140 minus 68 is 72; 72 times 60 is 4,320; 72 times 1.1 is 79.2; 4,320 divided by 79.2 is approximately 54.5; multiplied by 0.85 gives approximately 46.4 mL/min. Alligation is used when a pharmacist must blend two stock concentrations to reach a target strength that is not commercially available. To prepare 120 g of 2.5% hydrocortisone cream from 1% and 5% stock, arrange the differences diagonally: the distance from 5% to 2.5% (2.5) becomes the parts of 1% cream needed, and the distance from 2.5% to 1% (1.5) becomes the parts of 5% cream needed, for 4 total parts. Each part equals 120 divided by 4, or 30 g; so 75 g of the 1% cream (2.5 parts) and 45 g of the 5% cream (1.5 parts) combine to give the target strength. Pediatric dosing is typically calculated in mg/kg/day and then checked against an adult maximum dose ceiling, because a child's calculated dose should never exceed what would be given to an adult. For an 18 kg child ordered amoxicillin 40 mg/kg/day divided every 12 hours, the daily dose is 40 times 18, or 720 mg, divided into two doses of 360 mg each; this is compared against the applicable adult maximum before dispensing.
Heparin Rate Conversion and Pharmacokinetic Parameters
Heparin infusions are ordered in units per hour but supplied as a labeled concentration in units per milliliter, so the pharmacist converts between the two. If a bag contains 25,000 units in 250 mL of fluid, the concentration is 25,000 divided by 250, or 100 units/mL. An order for 1,200 units/hr requires 1,200 divided by 100, or 12 mL/hr on the infusion pump. Weight-based heparin protocols may express the order directly in units/kg/hr, requiring an extra multiplication step by the patient's weight before this same division is applied. Beyond single calculations, pharmacokinetic parameters describe a drug's behavior over time: half-life is the time required for a drug's concentration to fall by half, and after roughly four to five half-lives a drug is considered essentially eliminated or, when starting a fixed dosing regimen, to have reached steady state (the point where the amount going in per dosing interval equals the amount being eliminated, so peak and trough concentrations stop changing meaningfully from dose to dose). Volume of distribution is a calculated value relating the amount of drug in the body to its measured plasma concentration; a high volume of distribution suggests a drug distributes extensively into tissues rather than remaining in the bloodstream. These parameters underlie why loading doses, maintenance doses, and dosing intervals are chosen the way they are, and they connect directly to the drug-development and literature-evaluation skills covered later in this domain, since clinical trials are the source of the pharmacokinetic data pharmacists apply at the bedside.
Key terms
- Bioavailability
- — The fraction of an administered drug dose that reaches systemic circulation unchanged and is available to produce an effect.
- Pharmacogenomics
- — The study of how a person's genetic makeup affects their response to a drug, including metabolism speed and effect intensity.
- Beyond-use date
- — The date after which a compounded preparation should not be used, based on stability and sterility considerations rather than manufacturer testing.
- Precipitation (IV incompatibility)
- — Formation of visible solid particles when two incompatible substances are combined in an intravenous admixture, signaling the mixture is unsafe to administer.
- Loading dose
- — An initial, often larger dose given to rapidly achieve a therapeutic drug concentration before regular maintenance dosing begins.
- Alligation
- — A calculation method for determining the proportions of two different-strength stock preparations needed to create a desired intermediate strength.
- Creatinine clearance (CrCl)
- — An estimate of kidney filtration function, commonly calculated with the Cockcroft-Gault equation, used to guide renally adjusted dosing.
- Steady state
- — The point during a fixed dosing regimen at which drug elimination per interval equals drug intake per interval, so concentrations stabilize between doses.
- Volume of distribution
- — A calculated pharmacokinetic value relating the total amount of drug in the body to its plasma concentration, reflecting how extensively a drug distributes into tissue.
- Osmolarity
- — A measure of solute concentration in a solution, expressed as osmoles per liter, relevant to determining whether an IV solution is safe for peripheral versus central administration.
- Ratio strength
- — A way of expressing concentration as a ratio of drug to total preparation, such as 1:1000, commonly used for very dilute preparations.
- Beyond-use risk level
- — A sterile-compounding classification (low, medium, or high) based on preparation complexity and conditions that determines allowable storage time before use.
Exam tips
- When a calculation problem gives you extra information (like a patient's height when only weight is needed), pause and identify exactly which values the formula requires before plugging in numbers.
- Always recheck the units at each step of an IV rate conversion; mismatched units (mcg vs. mg, minutes vs. hours) are the most common source of calculation errors.
- For alligation problems, sketch the tic-tac-toe grid on scratch paper; doing the subtraction visually reduces arithmetic mistakes under time pressure.
- Memorize the Cockcroft-Gault formula structure rather than a single worked example, since exam problems will vary age, weight, sex, and creatinine values.
- For pediatric dosing questions, always complete the max-dose comparison step, even if the question seems to end at the mg/kg calculation; omitting the safety check is a common missed point.