General Pharmaceutical Council Registration Assessment (GPhC Assessment) Pharmaceutical Calculations Syllabus

Pharmaceutical Calculations syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Pharmaceutical Calculations in General Pharmaceutical Council Registration Assessment (GPhC Assessment), not a summary of it.

1. 1

   Fundamentals of Pharmaceutical Numeracy

   4 topics

   • Units, Conversions and SI Prefixes
     • Mass, volume and amount-of-substance units
     • Micrograms, nanograms and unit abbreviations (avoiding error-prone abbreviations)
     • Converting between metric units
   • Expressions of Concentration
     • Percentage w/w, w/v and v/v
     • Parts per million and ratio strengths (1 in x)
     • Converting between concentration formats
   • Moles, Millimoles and Molarity
     • Calculating millimoles from mass and molecular weight
     • Electrolyte content of infusion fluids
   • Rounding, Significant Figures and Estimation
     • Appropriate rounding for doses and devices
     • Sense-checking implausible answers
2. 2

   Dosing Calculations

   4 topics

   • Dose Determination by Body Weight and Surface Area
     • mg/kg dosing
     • Body surface area and chemotherapy dosing
     • Ideal and adjusted body weight
   • Paediatric and Neonatal Dosing
     • Age- and weight-banded dosing
     • Maximum dose limits and safety capping
   • Frequency, Duration and Quantity to Supply
     • Calculating total quantity for a course
     • Days' supply and repeat quantities
   • Dose Adjustment in Renal and Hepatic Impairment
     • Creatinine clearance (Cockcroft-Gault) and eGFR
     • Dose reduction based on renal function
3. 3

   Formulation and Compounding Calculations

   4 topics

   • Dilutions and Concentrations
     • Serial dilutions
     • Stock solution preparation
   • Mixing Strengths and Alligation
     • Combining two concentrations to a target strength
   • Master Formulae and Scaling Recipes
     • Scaling up and down from a formula
     • Amount required versus minimum weighable quantity
   • Displacement Values
     • Reconstitution of injectable powders
     • Suppository and pessary calculations
4. 4

   Infusion, Parenteral and Specialist Calculations

   4 topics

   • Infusion Rate Calculations
     • mL/hour and drops per minute
     • Dose-based rates (mg/kg/hour, micrograms/kg/minute)
   • Reconstitution and Final Concentration
     • Final volume and resulting strength
     • Stability and infusion duration limits
   • Pharmacokinetic Calculations
     • Loading and maintenance doses
     • Half-life and clearance
   • Molecular and Electrolyte Balance
     • Osmolarity and tonicity
     • Total parenteral nutrition components

Pharmaceutical Calculations flashcards for General Pharmaceutical Council Registration Assessment (GPhC Assessment)

19 of 56 cards from the Pharmaceutical Calculations deck — real questions with worked answers.

1. What are the seven SI base units, and which one is most relevant to pharmaceutical mass calculations?

   The seven SI base units are the metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance) and candela (luminous intensity). For pharmaceutical mass calculations the kilogram (and its sub-multiples the gram, milligram and microgram) is most relevant.

2. List the common SI prefixes from kilo down to nano with their factors.

   kilo ($k$) $=10^{3}$; (base unit) $=10^{0}$; milli ($m$) $=10^{-3}$; micro ($\mu$) $=10^{-6}$; nano ($n$) $=10^{-9}$. Each step down is a factor of $1000$ ($10^{3}$).

3. How do you convert a mass in grams to milligrams and to micrograms?

   Multiply by $1000$ at each step: $1\text{ g}=1000\text{ mg}$ and $1\text{ mg}=1000\ \mu\text{g}$, so $1\text{ g}=10^{6}\ \mu\text{g}$. To convert g to mg multiply by $10^{3}$; to convert g to $\mu$g multiply by $10^{6}$.

4. In UK pharmacy practice, why should 'micrograms' and 'nanograms' be written in full rather than abbreviated?

   Abbreviations such as '$\mu$g' or 'mcg' and 'ng' are easily misread (e.g. mistaken for 'mg'), which can cause 1000-fold dosing errors. Safe-practice guidance requires the words 'micrograms' and 'nanograms' to be written out in full on prescriptions.

5. What is the relationship between millilitres, litres and cubic centimetres?

   $1\text{ L}=1000\text{ mL}$, and $1\text{ mL}=1\text{ cm}^{3}$. Therefore $1\text{ L}=1000\text{ cm}^{3}=1\text{ dm}^{3}$.

6. Define the three ways of expressing percentage concentration in pharmacy: %w/w, %w/v and %v/v.

   $\%\text{w/w}$ = grams of constituent per $100\text{ g}$ of product; $\%\text{w/v}$ = grams of constituent per $100\text{ mL}$ of product; $\%\text{v/v}$ = millilitres of constituent per $100\text{ mL}$ of product. Percentage strength of a solid in a liquid is conventionally w/v.

7. How is a ratio strength such as $1\text{ in }1000$ interpreted, and how do you convert it to a percentage?

   $1\text{ in }1000$ means 1 part (g) in 1000 parts (mL) for a solid in liquid, i.e. $1\text{ g in }1000\text{ mL}$. As a percentage: $\frac{1}{1000}\times100=0.1\%\text{ w/v}$. Generally ratio $1\text{ in }x$ equals $\frac{100}{x}\%$.

8. What does a concentration expressed in 'parts per million (ppm)' mean and how does it relate to mg per litre of water?

   $1\text{ ppm}$ = 1 part in $10^{6}$ parts. For dilute aqueous solutions $1\text{ ppm}=1\text{ mg per litre}=1\ \mu\text{g per mL}$ (since $1\text{ L}$ of water weighs $\approx1000\text{ g}=10^{6}\text{ mg}$).

9. Convert a $5\%\text{ w/v}$ solution into mg/mL and into a ratio strength.

   $5\%\text{ w/v}=5\text{ g per }100\text{ mL}=50\text{ mg/mL}$. As a ratio strength: $5\text{ g in }100\text{ mL}=1\text{ g in }20\text{ mL}=1\text{ in }20$.

10. Define the mole and state the value of the Avogadro constant.

    A mole is the amount of substance containing the same number of elementary entities as there are atoms in $12\text{ g}$ of carbon-12. The Avogadro constant is $N_{A}\approx6.022\times10^{23}\ \text{mol}^{-1}$.

11. How do you calculate the number of moles from a mass and the molar mass?

    $$n=\frac{m}{M}$$ where $n$ = amount in moles, $m$ = mass in grams, and $M$ = molar mass in $\text{g mol}^{-1}$. For millimoles use mass in mg with $M$ in $\text{g mol}^{-1}$: $\text{mmol}=\frac{\text{mg}}{M}$.

12. Define molarity and give its formula.

    Molarity is the amount of solute (in moles) per litre of solution. $$c=\frac{n}{V}$$ where $c$ is in $\text{mol L}^{-1}$ (M), $n$ is moles of solute, and $V$ is volume of solution in litres.

13. Sodium chloride has $M=58.5\ \text{g mol}^{-1}$. How many millimoles of $\ce{Na+}$ are in $1\text{ g}$ of $\ce{NaCl}$?

    Moles of $\ce{NaCl}=\frac{1000\text{ mg}}{58.5}=17.1\text{ mmol}$. Since each $\ce{NaCl}$ provides one $\ce{Na+}$, there are $17.1\text{ mmol of }\ce{Na+}$ (and $17.1\text{ mmol of }\ce{Cl-}$).

14. How many grams of solute are needed to prepare $500\text{ mL}$ of a $0.1\text{ M}$ solution of a substance with $M=40\ \text{g mol}^{-1}$?

    $n=c\times V=0.1\text{ mol L}^{-1}\times0.5\text{ L}=0.05\text{ mol}$. Mass $=n\times M=0.05\times40=2\text{ g}$.

15. State the general rules for rounding a number to a given number of decimal places.

    Look at the digit immediately after the last digit to be kept: if it is $5$ or greater, round the last kept digit up; if it is less than $5$, leave it unchanged. Then drop the remaining digits. Only round the final answer, not intermediate values.

16. How do you determine the number of significant figures in a measurement, including the role of zeros?

    All non-zero digits are significant; zeros between non-zero digits are significant; leading zeros are not significant; trailing zeros after a decimal point are significant. E.g. $0.00450$ has 3 significant figures; $1.020$ has 4.

17. Why is rough estimation important before performing a pharmaceutical calculation?

    Estimating the expected magnitude of the answer (e.g. by rounding numbers) provides a sanity check that flags gross errors such as misplaced decimal points or 10/100/1000-fold mistakes before a dose is dispensed, improving patient safety.

18. When should you round a calculated tablet or dose quantity up versus down in practice?

    Doses must be deliverable and safe: round to a practical, measurable amount (e.g. whole tablets or available volumes). Generally avoid rounding up if it would exceed the maximum safe dose, and avoid rounding down if it would give a sub-therapeutic dose; round to the nearest practical quantity that stays within safe limits.

19. What is the formula for a dose based on body weight, and how do you apply it?

    $$\text{Dose}=\text{dose per kg}\times\text{body weight (kg)}$$ Multiply the prescribed dose per kilogram by the patient's weight in kg. For a divided regimen, multiply by frequency and duration to get the total quantity required.

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