Reviewed by the PrepPass team.
Chapter 4 covered getting the prescription right. This chapter covers the math that turns the prescription into a safe, accurate dispense — and the compounding rules that govern what the technician may prepare, how, and for how long it stays good. The NHA outline splits this territory into two domains: 4C (pharmaceutical calculations) and 4D (sterile and non-sterile products, compounding, unit dose, and repackaging)[1]. Calculation questions reward a calm, mechanical process; compounding questions reward knowing the exact numbers — BUDs, competency intervals, and label elements — because the numbers, not general impressions, are what you must know.
4C.1–4C.8 — The calculation mindset
Every calculation on this exam is arithmetic plus unit awareness. Set up each problem the same way: write what the question asks for, write what you know, cancel the units, and only then touch the numbers. Most errors are unit errors — grams versus milligrams, pounds versus kilograms, percent versus ratio strength — not math errors. When a question gives you a formula in words (for example, "days' supply equals doses dispensed divided by doses per day"), translate it to symbols before plugging in numbers[2]. Round only at the end, and round the way the question asks: tablets and capsules round to whole units you can actually dispense, while milliliters and milligrams keep their decimals until the final step.
4C.1, 4C.6 — Measurement systems, conversions, and temperature
Concept. Pharmacy work moves between the metric system and household measurements. The metric prefixes you must know cold: kilo means 1,000, milli means 0.001 (one-thousandth), and micro means 0.000001 (one-millionth)[3]. These prefixes come from the international metric standard maintained with reference to NIST[3]. The conversions to know cold: 1 kilogram equals 2.21 pounds and 1 pound equals 0.45 kilograms[4]; 1 inch equals 2.54 centimeters[4]; 1 fluid ounce equals 29.57 milliliters and 1 cup equals 0.24 liter[4]; 1 gallon equals 3.78 liters[4]. Temperature crosses scales with two formulas: Fahrenheit to Celsius, subtract 32 then multiply by 0.55; Celsius to Fahrenheit, multiply by 1.80 then add 32[4].
Worked example. Convert 25°C to Fahrenheit. Step 1: multiply by 1.80 → 25 × 1.80 = 45. Step 2: add 32 → 45 + 32 = 77°F. Reverse check with 77°F to Celsius: 77 − 32 = 45; 45 × 0.55 = 24.75 ≈ 25°C.
Exam use. The outline lists measurement systems — metric, household, and military time — plus temperature scales as tested knowledge[1]. Practise one-step conversions embedded inside larger problems, such as converting a patient's weight before a weight-based dose.
Military time
Concept. Military time is a 24-hour time system used to eliminate confusion between AM and PM[5]. Instead of restarting the clock after 12, the day runs continuously from 0000 (midnight) to 2359 (11:59 PM)[5]. The conversion rule is one line: morning stays the same, afternoon adds 12[5]. To go back, subtract 12 from any time 1300 or higher to get the PM hour[5]. The two anchors are midnight = 0000 and noon = 1200[5].
Worked example. Convert 2:45 PM to military time, then convert 1645 back. 2 + 12 = 14, so 2:45 PM = 1445. Reverse: 1645 − 12 = 4, so 1645 = 4:45 PM. Interval math across the clock: a dose is due at 0800 and the next dose comes 8 hours later — 8 + 8 = 16, so the next dose is due at 1600, which is 4:00 PM.
Exam use. The NHA outline lists military time under measurement systems[1]. Practise conversion in either direction, and durations computed across noon.
Traps. 1200 is noon, not midnight, and 0000 is midnight[5]. Do not add 12 to a 12:xx PM time: 12:30 PM is 1230, not 2430.
Traps. The temperature formulas are not symmetric — subtracting 32 happens before multiplying when going °F→°C, but adding 32 happens after multiplying when going °C→°F. Household "ounce" is ambiguous: fluid ounces measure volume (29.57 mL), weight ounces measure mass — the question will specify. And 2.2 lb/kg (the rounded value used in dosing examples[6]) versus 2.21 lb/kg (the table value[4]) can shift an answer by a rounding step, so use the value the question gives.
4C.2 — Individual dose, total daily dose, and weight-based dosing
Concept. The individual dose is what the patient takes at one time; the total daily dose is the individual dose multiplied by the number of doses per day. Weight-based dosing expresses the daily amount per unit of body weight, typically mg/kg/day[1]. To find one dose from a daily amount, divide by the frequency; to find the quantity to dispense, multiply one dose by doses per day by days.
Worked example. An order reads 10 mg/kg/day for a 20 kg child, divided twice daily, tablets are 100 mg. Step 1: total daily dose = 10 × 20 = 200 mg/day. Step 2: one dose = 200 ÷ 2 = 100 mg. Step 3: tablets per dose = 100 ÷ 100 = 1 tablet. For a 30-day supply: 1 tablet × 2 × 30 = 60 tablets.
Exam use. Calculating individual and total daily dosages and medication quantities from dosage are explicit 4C tasks[1]. These calculations chain together — miss the daily dose and every downstream number is wrong.
Traps. "Divided twice daily" means split the daily total; "10 mg/kg/dose" is a different order from "10 mg/kg/day" — read the denominator. Convert pounds to kilograms before multiplying by a mg/kg factor, never after.
4C.3–4C.4 — Days' supply and medication quantities
Concept. Days' supply is the estimate of how many days a prescription is intended to last, calculated as the number of doses dispensed divided by the number of doses taken per day[2]. Package-size math is the same idea for liquids and injectables: total units on hand divided by units used per day[1]. Package-size conversions also include drops per mL and milligrams per package[1]: if a dropper is given as delivering 20 drops per mL, then 2 mL is 40 drops — once the drops-per-mL factor is stated, it is a straight unit conversion.
Worked example. An insulin prescription dispenses two 10 mL vials of 100 units/mL, used as 30 units before each meal, three times daily. Step 1: units per vial = 100 × 10 = 1,000. Step 2: total units = 2 × 1,000 = 2,000. Step 3: units per day = 30 × 3 = 90. Step 4: days' supply = 2,000 ÷ 90 = 22.2, recorded as a 22-day supply[2].
Exam use. Days'-supply calculation is its own 4C task, and accuracy matters beyond the exam: days' supply drives insurance audits, accurate billing, and fraud/waste/abuse controls[1, 2].
Traps. For inhalers, convert to doses per day first — 2 puffs every 4 hours is 2 × 6 = 12 doses/day, so 200 puffs ÷ 12 = a 17-day supply, not 100 days[2]. Do not round up a days' supply past what is actually dispensed. Combination products and "as directed" sigs cannot be calculated — flag them, don't guess.
4C.5, 4C.7 — Percent strength, ratio strength, and dilution
Concept. Percent strength is grams of drug per 100 units: for liquids, % w/v means grams per 100 mL (5% = 5 g/100 mL); for solids, % w/w means grams of active drug per 100 g of total preparation (1% hydrocortisone cream = 1 g per 100 g)[7]. The w/v, w/w, and v/v expressions each name what is in the numerator and denominator: weight per volume, weight per total weight, volume per total volume[7]. Ratio strength writes the same idea as 1 part drug to a stated number of parts total — 1:1000 epinephrine is 1 g of solute per 1000 mL ("one in one thousand")[7]. Dilution conserves drug mass: starting strength × starting volume = final strength × final volume.
Worked example. How many grams of drug are in 250 mL of a 5% (w/v) solution? Step 1: 5% = 5 g per 100 mL. Step 2: 250 ÷ 100 = 2.5. Step 3: 5 × 2.5 = 12.5 g. Dilution check: to make 500 mL of 10% from 70% stock, starting volume = (10 × 500) ÷ 70 = 71.4 mL of stock, then add diluent to 500 mL.
Exam use. Percent concentration, ratio strength, and dilution/concentration are all listed 4C knowledge[1]. Ratio-strength work almost always resolves to "convert to mg/mL first": 1:1000 = 1 g/1000 mL = 1 mg/mL. A v/v worked example: 4 mL of liquid drug brought to 100 mL total volume is 4% v/v[7].
Traps. % w/v versus % w/w differ in the denominator (100 mL vs. 100 g) — creams and ointments are w/w. A 1:100 ratio is stronger than a 1:1000 ratio; the bigger the second number, the more dilute. In dilution math, the unknown goes on the side you are solving for, and volumes must be in the same units on both sides.
4C.1 — Milliequivalents
Concept. Milliequivalents express the chemical combining power of ions: 1 mEq equals the molecular weight in milligrams divided by the valence[7]. They are used for cations such as sodium, potassium, calcium, and magnesium and anions such as chloride, acetate, and bicarbonate[7]. The atomic weights you need: Na 22.990, K 39.098, Cl 35.453, Ca 40.078, Mg 24.305[8].
Worked example. How many milligrams are in 20 mEq of potassium chloride (KCl)? Step 1: molecular weight = 39 (K) + 35.5 (Cl) = 74.5 mg per mEq, since KCl has valence 1[7]. Step 2: 20 × 74.5 = 1,490 mg. For a divalent ion such as calcium: 40.078 ÷ 2 ≈ 20 mg per mEq.
Exam use. mEq calculations are named 4C knowledge[1]. Also learn that 0.9% saline carries 154 mEq of sodium per liter[7].
Traps. Valence is the trap: Ca²⁺ and Mg²⁺ divide the atomic weight by 2. Do not confuse mEq with mg — convert before comparing. For salts, use the molecular weight of the whole salt (KCl = 74.5), not just the ion.
4C.2 — Pediatric dosing: Young's, Clark's, Fried's, and BSA
Concept. Pediatric doses scale the adult dose by age or size. Young's rule = age in years ÷ (age + 12) × adult dose[6]. Clark's rule = weight in pounds ÷ 150 × adult dose[6]. Fried's rule = age in months ÷ 150 × adult dose, used for children under 1 year of age[6]. The body-surface-area method = child's BSA (m²) ÷ 1.73 m² × adult dose, where the Mosteller formula gives BSA as the square root of (height in cm × weight in kg ÷ 3600)[6, 9].
Worked example. Adult dose 100 mg; child is 7 years old. Young's rule: Step 1: 7 ÷ (7 + 12) = 7 ÷ 19 = 0.368. Step 2: 0.368 × 100 = 36.8 ≈ 37 mg[6]. BSA check for a child with BSA 0.6 m² and adult dose 75 mg: 0.6 ÷ 1.73 = 0.347; 0.347 × 75 = 26 mg.
Exam use. Pediatric dosage calculations (Young's, Clark's, Fried's) and BSA are explicit 4C knowledge[1]. The outline names the rule — you supply the formula.
Traps. Fried's uses months, Young's uses years — a 4-year-old is 48 months under Fried's. Clark's divides by 150 (pounds), Fried's divides by 150 (months); same number, different units. BSA's 1.73 m² is the standard adult surface area, not the child's.
4C.4 — Intravenous flow rate
Concept. IV infusion rate is measured in milliliters per hour: rate = total volume ÷ time in hours. The mL/hr unit is listed 4C knowledge[1]; the rate itself is plain division once the units line up.
Worked example. Run 1 liter of D5W over 4 hours. Step 1: convert liters to milliliters → 1,000 mL. Step 2: 1,000 ÷ 4 = 250 mL/hr.
Exam use. IV flow rate (mL/hr) is listed 4C knowledge[1]. It is one step once the volume is in milliliters.
Traps. Convert liters to milliliters before dividing. If the order gives minutes, convert to hours first. The rate answers "how fast," not "how much" — don't confuse it with total volume.
Sources cited in this excerpt
- nha-plan-full. https://knowledge.nhanow.com/hubfs/Test%20Plans/2023%20ExCPT%20Test%20Plan.pdf
- ihs-days-supply. https://www.ihs.gov/rpms/training/course-materials/
- ucsd-metric-prefixes. https://casswww.ucsd.edu/archive/physics/ph7/Units.html
- nist-conversions-census. https://www2.census.gov/library/publications/2002/compendia/statab/121ed/tables/app4.pdf
- military-time-24h. https://lifeisaspecialoperation.com/military-time-converter/
- medcrave-pediatric-dosage-formulas. https://medcraveonline.com/JPNC/JPNC-12-00463.pdf
- uw-pharm309-lesson2-drug-amounts. http://courses.washington.edu/pharm309/calculations/Lesson2.pdf
- iupac-atomic-weights. http://media.iupac.org/publications/analytical_compendium/Cha01sec8.pdf
- metabolism-mosteller-bsa. https://www.metabolismjournal.com/article/S0026-0495(05)00437-3/abstract