Every formula behind every problem on this site, with what it is for and one worked example each.
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Knowing a formula and knowing when it applies are different skills, and exams test the second one. Each entry below gives the formula, the situation it belongs to, and a single worked example, then links to practice on that topic.
Percentage strength and ratio strength are two ways of saying how much drug is in a preparation.
% w/v = grams of drug per 100 mL • 1:X ratio = 1 g in X mL • mg/mL ÷ 10 = % w/vExpress 1:2,500 as a percentage. 1:2,500 means 1 g in 2,500 mL, so (1 ÷ 2,500) × 100 = 0.04% w/v.
Practice percentage & ratio strength →When you dilute a concentrated stock solution, the amount of drug stays constant while the volume increases, so the concentration falls.
C₁ × V₁ = C₂ × V₂ → V₁ = (C₂ × V₂) ÷ C₁How many mL of a 20% stock are needed to make 120 mL of a 2% solution? V₁ = (2% × 120) ÷ 20% = 12 mL (then QS to 120 mL with diluent).
Practice dilution →Alligation mixes two preparations of different strengths to get an intermediate strength.
parts of high = target − low • parts of low = high − target • volume of each = (its parts ÷ total parts) × final volumeMake 250 mL of 25% dextrose from 70% and 10% stock. Parts of 70% = 25 − 10 = 15; parts of 10% = 70 − 25 = 45; total = 60. Volume of 70% = (15 ÷ 60) × 250 = 62.5 mL (and 187.5 mL of the 10%).
Practice alligation →These three units describe amounts of electrolytes.
mmol = mg ÷ molecular weight • mEq = mmol × valencemOsm/L = (grams per liter ÷ MW) × number of particles × 1,000How many mEq are in 1 g of KCl (MW 74.5, valence 1)? mmol = 1,000 ÷ 74.5 = 13.4; mEq = 13.4 × 1 = 13.4 mEq. Osmolarity of 0.9% NaCl = 9 g/L ÷ 58.5 × 2 × 1,000 = 308 mOsm/L.
Practice milliequivalent (meq), millimole & milliosmole →IV rate problems come in two flavors: gravity drip rates in drops per minute, and pump rates in mL/hr for weight-based infusions.
drops/min = (volume × drops per mL) ÷ time in minutesmL/hr: bag concentration (mcg/mL) → dose (mcg/min) → × 60 → ÷ concentrationInfuse 1,000 mL over 8 hours with a set that gives 15 drops/mL. (1,000 × 15) ÷ (8 × 60) = 15,000 ÷ 480 = 31.25 → 31 drops/min.
Practice iv infusion & drip rate →Many chemotherapy and some pediatric drugs are dosed per square meter of body surface area (BSA).
BSA (m²) = √(height[cm] × weight[kg] ÷ 3600) • dose = mg/m² × BSAA patient is 170 cm and 70 kg. BSA = √(170 × 70 ÷ 3,600) = √3.306 = 1.82 m². A 175 mg/m² order → 175 × 1.82 = 318.5 mg.
Practice body surface area (bsa) & chemo dosing →Total parenteral nutrition problems total the calories from dextrose, amino acids, and lipids.
IV: dextrose 3.4 kcal/g • protein 4 kcal/g • 20% lipid = 2 kcal/mLOral/enteral: carbohydrate 4 kcal/g • protein 4 kcal/g • fat 9 kcal/ggrams of nitrogen = grams of protein ÷ 6.25Calories from 1,000 mL of dextrose 20%? Grams = 1,000 × 20% = 200 g; 200 × 3.4 = 680 kcal.
Practice tpn & nutrition calculation →Solutions placed in the eye, nose, or bloodstream should be isotonic with body fluids (equivalent to 0.9% NaCl).
(1) drug in formulation = %×vol ÷ 100 (2) NaCl equivalent = drug g × E (3) NaCl for volume = 0.009 × vol (4) NaCl to add = step 3 − step 2Make 30 mL of 1% pilocarpine HCl (E = 0.24) isotonic. (1) drug = 0.3 g; (2) 0.3 × 0.24 = 0.072 g; (3) 0.009 × 30 = 0.27 g; (4) 0.27 − 0.072 = 0.198 g.
Practice isotonicity & e-value →Creatinine clearance estimates kidney function to guide renal dose adjustments.
CrCl = [(140 − age) × weight] ÷ (72 × SCr) × 0.85 if female • use SCr as given unless the question says to round itIBW (Devine) = 50 kg male or 45.5 kg female + 2.3 kg per inch over 5 feetIBW first → actual < IBW use actual; actual > 125% of IBW use AdjBW = IBW + 0.4(actual − IBW); otherwise IBW • some references use 120% or 130%, so follow the cutoff the question gives70-yr-old male, 5'10" (IBW = 73 kg), weighs 82 kg, SCr 1.2. Since 82 kg is between IBW and 125% of IBW (91.3 kg), use IBW. CrCl = (140 − 70) × 73 ÷ (72 × 1.2) = 59.1 mL/min.
Practice creatinine clearance (cockcroft-gault) →Core PK calculations connect dose, concentration, and the body's handling of a drug.
t½ = 0.693 ÷ k • Vd = Dose ÷ C₀ • CL = k × VdLoading dose = C_target × Vd • k = ln(C₁ ÷ C₂) ÷ (t₂ − t₁)Two levels: 40 mg/L at hour 0, 10 mg/L at hour 8. k = ln(40 ÷ 10) ÷ 8 = 1.386 ÷ 8 = 0.173 hr⁻¹, so t½ = 0.693 ÷ 0.173 ≈ 4 hr.
Practice pharmacokinetics →Absolute bioavailability compares how much drug reaches the systemic circulation from an oral dose versus an IV dose (which is 100% by definition).
F = (AUC_oral ÷ Dose_oral) × (Dose_IV ÷ AUC_IV)IV 100 mg gives AUC 50; oral 200 mg gives AUC 60. First term: 60 ÷ 200 = 0.30; second term: 100 ÷ 50 = 2; F = 0.30 × 2 = 0.60 = 60%.
Practice bioavailability (f) →Insulin calculations at the pharmacy come down to two things: day supply, and switching between basal products.
Vial = 10 mL = 1,000 units • standard pen = 300 units (box of 5) • Toujeo pen = 450 units (box of 3)Day supply = total units ÷ daily dose, capped at in-use stability (rapid & glargine 28 d, Humulin 31, Novolin 42, Tresiba/Toujeo 56; mixed pens 10, 14 d). Round DOWN.Switching (basal → basal) is 1:1 EXCEPT NPH (BID) → glargine and Toujeo → Lantus/Basaglar, both −20%Lantus 10 mL vial at 25 units/day: 1,000 ÷ 25 = 40 days, but an open glargine vial is stable 28 days → 28-day supply. Switching NPH 30 units BID to glargine: 60 × 0.8 = 48 units daily.
Practice insulin day supply & switching →Opioid math converts between opioids and routes using an equianalgesic table anchored to 30 mg of oral morphine.
Proportion from the equianalgesic table (30 mg PO morphine = anchor)Switching to a different opioid: reduce the calculated dose by 25 to 50% for incomplete cross-toleranceMME/day = daily dose × (30 ÷ that drug's equianalgesic dose) • MME totals risk; it is not a dose conversionOxycodone 10 mg three times daily = 30 mg/day. Table: 20 mg oxycodone ≈ 30 mg morphine, so MME = 30 × (30 ÷ 20) = 45 MME/day.
Practice opioid conversion & mme →Days supply is how long a dispensed quantity lasts, which is what insurance billing and refill timing are calculated from.
days = total quantity (drops, tablets, or puffs) ÷ amount used per dayeye drops assume 20 drops/mL • always round DOWNA 5 mL eye drop bottle (20 drops/mL = 100 drops), 1 drop in each eye twice daily = 4 drops/day. 100 ÷ 4 = 25 days.
Practice days supply calculation →Many drugs, especially in pediatrics, are dosed by body weight in mg/kg.
kg = lb ÷ 2.2 • daily dose = mg/kg/day × weight • per dose = daily dose ÷ number of dosesA 66 lb child on amoxicillin 45 mg/kg/day divided twice daily. Kg = 66 ÷ 2.2 = 30 kg; daily = 45 × 30 = 1,350 mg; per dose = 1,350 ÷ 2 = 675 mg.
Practice weight-based (mg/kg) dosing →Reconstituting a powdered drug adds diluent to reach a target concentration, but the dry powder occupies space of its own.
powder (displacement) volume = final reconstituted volume − volume of diluent addedA 1 g vial reconstituted to 100 mg/mL needs a final volume of 10 mL. If the label says to add 9.5 mL diluent, the powder volume = 10 − 9.5 = 0.5 mL.
Practice reconstitution & powder volume →Specific gravity relates a liquid's weight to its volume, so you can convert between grams and milliliters.
specific gravity = weight (g) ÷ volume (mL), a unitless number because it compares to water at 1 g/mL → weight = volume × SG • volume = weight ÷ SGGlycerin has a specific gravity of 1.25. The weight of 240 mL = 240 × 1.25 = 300 g.
Practice specific gravity →Several bedside calculations adjust or interpret a lab value before you can act on it.
Corrected Ca = measured Ca + 0.8 × (4.0 − albumin)Corrected phenytoin = measured ÷ [(0.2 × albumin) + 0.1]ANC = WBC × (% segs + % bands) ÷ 100 • under 1,500 mild, under 1,000 moderate, under 500 severe neutropeniaAnion gap = Na⁺ − (Cl⁻ + HCO₃⁻) • normal about 8 to 12 mEq/LMeasured calcium 7.5 mg/dL, albumin 2.5 g/dL. Corrected = 7.5 + 0.8 × (4.0 − 2.5) = 7.5 + 1.2 = 8.7 mg/dL.
Practice clinical lab calculation →Most pharmacy calculations round to the nearest value.
containers = total amount needed ÷ amount per container, then up to the next whole containerAn 82 kg patient needs vancomycin 20 mg/kg = 1,640 mg, stocked as 750 mg vials. 1,640 ÷ 750 ≈ 2.19, so you open 3 vials.
Practice dispensing quantity →The mistakes that cost the most points. The specific trap built into each of these topics.