GPhC Calculations Formulas You Need to Know

Part 1 of the General Pharmaceutical Council (GPhC) Registration Assessment tests 40 calculations in 2 hours. Some formulas may be given in the question stem, but you cannot rely on that. Knowing the key formulas from memory means you spend your time calculating, not trying to recall or derive them.

Here are the essential formulas, what they do, and how to apply them.

Dosing formulas

Weight-based dose

$\text{Dose} = \text{dose per kg} \times \text{patient weight (kg)}$

Used for most weight-based prescriptions. Always check whether the dose given is per dose or per day — getting this wrong doubles or halves your answer.

Dose from a liquid formulation

$\text{Volume to give} = \frac{\text{required dose}}{\text{concentration of liquid}}$

If the concentration is expressed as mg per 5 mL (common for oral suspensions), convert to mg/mL first or use:

$\text{Volume} = \frac{\text{required dose (mg)}}{\text{strength (mg)}} \times \text{volume that contains that strength (mL)}$

Example: To give 250 mg from a 125 mg/5 mL suspension → (250 ÷ 125) × 5 = 10 mL.

Cockcroft-Gault equation (creatinine clearance)

For males:

$\text{CrCl (mL/min)} = \frac{(140 - \text{age}) \times \text{weight (kg)} \times 1.23}{\text{serum creatinine (micromol/L)}}$

For females:

$\text{CrCl (mL/min)} = \frac{(140 - \text{age}) \times \text{weight (kg)} \times 1.04}{\text{serum creatinine (micromol/L)}}$

Used to estimate renal function for dose adjustment. The question should specify which constant to use (1.23 or 1.04) or state the patient's sex.

Concentration formulas

Percentage w/v

$\text{Percentage w/v} = \frac{\text{weight of solute (g)}}{\text{volume of solution (mL)}} \times 100$

Or equivalently: X% w/v means X grams per 100 mL.

Percentage w/w

$\text{Percentage w/w} = \frac{\text{weight of ingredient (g)}}{\text{total weight of preparation (g)}} \times 100$

X% w/w means X grams per 100 grams of final product.

Percentage v/v

$\text{Percentage v/v} = \frac{\text{volume of solute (mL)}}{\text{volume of solution (mL)}} \times 100$

X% v/v means X mL per 100 mL.

Ratio strength to mg/mL

A ratio strength of 1 in N means 1 gram in N mL (for solutions).

$\text{1 in 1,000} = \frac{1 \text{ g}}{1,000 \text{ mL}} = 1 \text{ mg/mL}$

$\text{1 in 10,000} = \frac{1 \text{ g}}{10,000 \text{ mL}} = 0.1 \text{ mg/mL} = 100 \text{ micrograms/mL}$

Know the adrenaline concentrations cold:

• 1 in 1,000 = 1 mg/mL
• 1 in 10,000 = 100 micrograms/mL (0.1 mg/mL)

Parts per million

$1 \text{ ppm} = 1 \text{ mg per litre (for aqueous solutions)}$

Or equivalently:

$1 \text{ ppm} = 1 \text{ mg per kg (for solids)}$

Dilution formula

$C_1 V_1 = C_2 V_2$

Where:

• $C_1$ = concentration of the stock solution
• $V_1$ = volume of stock solution needed
• $C_2$ = required concentration of the diluted solution
• $V_2$ = required total volume of the diluted solution

Both concentrations must be in the same units. Solve for whichever variable is missing.

Example: Make 500 mL of 1% solution from 10% stock. 10 × V1 = 1 × 500 → V1 = 50 mL. Take 50 mL of stock and make up to 500 mL.

Infusion rate formulas

Volume over time

$\text{Rate (mL/hour)} = \frac{\text{total volume (mL)}}{\text{time (hours)}}$

Drop rate

$\text{Drops/min} = \frac{\text{volume (mL)} \times \text{drop factor (drops/mL)}}{\text{time (minutes)}}$

Common drop factors:

• Standard giving set: 20 drops/mL
• Microdrop (paediatric) giving set: 60 drops/mL

Dose-based infusion rate

When a dose is prescribed in mg/hour or micrograms/kg/min:

$\text{Rate (mL/hour)} = \frac{\text{dose required per hour (mg/hour)}}{\text{concentration of solution (mg/mL)}}$

If the dose is in micrograms/kg/min, first calculate:

$\text{Dose (mg/hour)} = \frac{\text{dose (micrograms/kg/min)} \times \text{weight (kg)} \times 60}{1000}$

Then divide by the concentration to get mL/hour.

Moles formulas

Moles from mass

$\text{Moles} = \frac{\text{mass (g)}}{\text{molecular weight (g/mol)}}$

Millimoles from mass in milligrams

$\text{Millimoles} = \frac{\text{mass (mg)}}{\text{molecular weight}}$

Mass from millimoles

$\text{Mass (mg)} = \text{millimoles} \times \text{molecular weight}$

For electrolyte calculations, remember that some salts dissociate. For example, NaCl gives 1 mmol Na⁺ per 1 mmol NaCl. KCl gives 1 mmol K⁺ per 1 mmol KCl. CaCl₂ gives 1 mmol Ca²⁺ per 1 mmol CaCl₂.

Displacement values

When reconstituting a powder for injection:

$\text{Volume of diluent to add} = \text{desired final volume} - \text{displacement volume of the powder}$

The displacement value tells you how much volume the powder itself occupies when dissolved. It is usually stated as a volume per weight (e.g., 0.2 mL per 500 mg).

To draw up the correct dose after reconstitution:

$\text{Volume to draw up} = \frac{\text{required dose}}{\text{concentration after reconstitution}}$

Key unit conversions

The last one is worth memorising: 1% w/v = 10 mg/mL. It removes a conversion step and makes practice faster.

Which formulas are provided in the exam?

The GPhC may provide specific formulas within individual question stems, particularly for less common calculations. However, you should not assume any formula will be given. Treat all of the above as "must know" — if a formula happens to be provided, that is a bonus, but you should not be relying on it.

The formulas you should be able to recall instantly without any prompt:

• Weight-based dose calculation
• Percentage concentration definitions (w/v, w/w, v/v)
• Ratio strength conversions
• C1V1 = C2V2
• Infusion rate (volume/time and dose-based)
• Drop rate formula
• Moles = mass/molecular weight
• Unit conversions

Quick FAQs

• Should I make flashcards for these formulas? Yes — this is one of the best uses of flashcards. Put the formula name or a brief scenario on one side and the formula on the other. Use spaced repetition to ensure you can recall them all under pressure.
• What is the most common formula in the exam? There is no single formula worth treating as the only priority. Weight-based dosing, percentage concentrations, dilutions and infusion rates are all core topics, so you should aim to recall each of them without hesitation.
• How do I remember the Cockcroft-Gault constants? 1.23 for males, 1.04 for females. Some candidates remember it as "males have the higher constant." In practice, the question may provide the equation — but if it does not, you need to know both constants.
• Is 1% w/v really 10 mg/mL? Yes. 1% w/v = 1 g per 100 mL = 1,000 mg per 100 mL = 10 mg/mL. This shortcut appears so often that memorising it saves time on multiple questions.