Medicines Prep

Pharmacy Calculations

Before we dive into the essentials of pharmacy, let’s set the stage. Success in pharmacy isn’t just about memorizing drug name, it’s about mastering the mathematical and scientific foundations that underpin every calculation, formulation, and clinical decision.

Prerequisites you should cover first:

  • Standard Form
  • Exponentials
  • Ratios
  • Proportions Between Ratios
  • Common Units
  • Converting Between Units
  • Significant Figures, Decimal Points, & Rounding
  • Mass & Moles

Once you’re confident with these, you’re ready to explore the 10 fundamental concepts that shape your journey as an MPharm student.

  1. Pharmacy Calculations
    1. C1 / V1 = C2 / V2
    2. C1 x V1 = C2 x V2
    3. 1 in 1000 (Ratio Strength)
    4. Infusion Rates
    5. W/V vs V/V vs W/W
    6. Alligation
    7. Using A Recipe
    8. PPM and PPB
    9. Milli equivalence
    10. Bioavailability

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C1 / V1 = C2 / V2

Pharmacy calculations often highlight proportionality, and this is where the ratio form comes in. The equation can also be expressed as C1 / V1 = C2 / V2, which emphasizes the relationship between concentrations and volumes as ratios.

There are 3 ways to express comparative ratio:

a:b=c:da:b = c:d
a:b::c:da:b :: c:d
ab=cd\frac{a}{b} = \frac{c}{d}

It is option 3 that directly corresponds to the pharmacy equation C1 / V1 = C2 / V2. This form is especially useful when switching between percentage strengths or checking proportionality. However, there is considerable overlap with C1 X V1 = C2 X V2.

Let’s look at an example

Mouthwash was prescribed at concentration 2% w/v. A single dose requires 2 drops diluted in 10ml. Each drop contains 0.125ml of solution. What is the final concentration?

Step 1 (Identify the initial % strength):

  • 2% w/v OR 2g per 100ml

Step 2 (What are they asking for):

Final concentration (C2) at 0.25ml of volume

C1V1=C2V2\frac{C1}{V1} = \frac{C2}{V2}

Step 3 (Rearrange):

Multiple by V2 on both sides

C1∗V2V1\frac{C1*V2}{V1}

Step 4 (Calculate):

2%∗0.25ml10ml\frac{2\%*0.25ml}{10ml}

Which gives us 0.05% w/v

C1 x V1 = C2 x V2

The dilution equation (C1 × V1 = C2 × V2) is one of the most important formulas in pharmacy practice. It is used when you have a stock solution (C1, V1) and need to prepare a smaller volume at a different concentration (C2, V2). In most cases, students calculate V2, which represents the volume of solvent added to dilute the stock solution and achieve the desired percentage concentration.

Let’s look at an example

250ml of a 25% solutions is diluted to 1000ml. What is the final concentration of the solution?

Step 1 (Identify the stock):

25% of a 200ml solution

C1∗V1C1 * V1

Step 2 (What are they asking):

Final concentration at 1000ml

C2∗V2C2 * V2

Step 3 (Rearrange the equation):

Here, we need to isolate C2, as this is the final concentration

C1∗V1=C2∗V2C1 * V1 = C2 * V2

Divide by V2 on both sides

C1∗V1V2=C2\frac{C1*V1}{V2} = C2

Step 4 (Calculate):

25%∗250ml1000ml\frac{25\% * 250ml}{1000ml}

The final concentration would be 6.25%

1 in 1000 (Ratio Strength)

Ratio strength is another way of expressing percentage strength, especially when dealing with very weak formulations such as fluoride toothpaste or dilute antiseptic solutions. Instead of presenting strength as parts per 100 (the usual % w/v or % w/w), ratio strength expresses concentration as parts per 1000 or even higher.

This method is particularly useful because it makes extremely small concentrations easier to understand and compare. For example, a formulation written as 1:1000 means 1 part of active ingredient in 1000 parts of the total preparation. Below are some common formulations and their respective units.

FormulationStrength
Solid in Liquid1g in 1000ml
Liquid in Liquid1ml in 1000ml
Solid in Solid1g in 1000g

Let’s look at an example

What is 0.09% as a ratio strength?

Step 1 (Identify the correct equation)

As we are converting between ratios, we would use

C1V1=C2V2\frac{C1}{V1} = \frac{C2}{V2}

Step 2 (Recognise each part of the equation)

  • C1 – 0.09 (0.09%)
  • V1 – 100 (This makes up the latter part of 0.09 in 100)
  • C2 – 1 (As a standard, ratio strengths are 1 in x)
  • V2 – x (This makes up the latter part of 1 in x)

Step 3 (Rearrange):

Our equation currently looks like this:

0.09100=1x\frac{0.09}{100} = \frac{1}{x}

Rearranging for x gives us

x=1∗1000.09x = \frac{1*100}{0.09}

The ratio strength would be 1 in 1111 or 1:1111

Infusion Rates

Common infusion questions will walk you through:

  • Multiplying by weight
  • Multiplying by time
  • Converting between hours and minutes
  • Calculating a total dose and subtracting for each part of the infusion
  • Conversions using percentage weight

Let’s look at an example

For a woman weighing 55kg, what is the total minutes of infusion?

InfusionRate
Drug at 0.25%2 ml/kg/hr for 15 minutes
0.4 ml/kg/hr as a continuous infusion for total 20mg/kg

Step 1 (What can we work out immediately)

Dose for the first 15 minutes (See if you can convert to grams using the %)

2ml/kg/hr∗55kg∗0.25hr=27.5ml2 ml/kg/hr * 55kg * 0.25hr = 27.5ml

Total dose

20mg/kg∗55kg=1100mg20mg/kg *55 kg = 1100mg

Step 2 (Calculations)

  • Consider each part of the infusion as a different stage
  • We have worked out stage 1 (15 minutes)
  • Stage 2 requires us to work out the remaining time at 0.4 ml/kg/hr
    • In order to do this, we need to know the remaining volume

Step 3 (Convert to similar units)

  • Convert 1100mg to ml using the % strength
  • As we are converting between ratios we can use C1/V1 = C2/V2
    • C2 here is the total mass, this is the same as C1 being 0.25g out of 100ml
V2=1.100g∗100ml0.25g=440mlV2 = \frac{1.100g*100ml}{0.25g} = 440 ml
  • Therefore, the remaining volume is 412.5ml

Step 4 (Complete the second stage)

  • Calculate the time for the continous infusion
0.4ml/kg/hr∗55kg=22ml/hr0.4 ml/kg/hr*55kg = 22ml/hr
  • We need to understand that 440ml of fluid was infused at a rate of 22ml/hr
  • Therefore, we need to workout how many minutes this took (look at the units in the question)
440ml22ml/hr/60=1200minutes\frac{440ml}{22ml/hr}\\/\\60=1200 \\minutes

Therefore, our infusion took 1225 minutes

W/V vs V/V vs W/W

As you progress through your degree, the questions will become more complex each year. Sometimes the type of calculation may not be clearly shown, which can feel confusing. That’s why it’s essential to understand when each formula applies, whether you’re working with C1/V1 or C1 × V2, so you avoid mistakes during conversions.

TypeMeaningQuantityExample
W/Wweight per weight1g per 100gSolid or semisolid
V/Vvolume per volume1ml per 100mlLiquids
W/Vweight per volume1g per 100mlSolid in liquid

Alligation

Alligation is a simple method used in pharmacy to mix two solutions of different strengths (concentrations) to create a final preparation with the exact concentration and volume you need.

For example, if you have one strong solution and one weak solution, alligation helps you calculate how much of each to combine to make a total concentration.

Points to find are:

  • Concentration of the final solution
  • The 2 concentrations of the solutions you’re using
  • Total number of parts

Let’s look at an example

Create an IV bag of 500ml at 25% using 40% (solution A) and a 15%(solution B) solution.

Step 1 (Identify the concentrations)

  • 25% is the final concentration
  • Solution A: 40%
  • Solution B: 15%

Step 2 (Calculations)

For solution A :

Required – B = Proportion of A

25%−15%=10%25\% – 15\% = 10\%

For solution B:

A – Required = Proportion B

40%−25%=15%40\% – 25\% = 15\%

In terms of ratios, this means 10 parts of the 40% (A) to 15 parts of the 15% (B)

Step 3 (Ratios)

Using the 500ml total volume and each parts we calculated, the equation we’ll use:

Total volume * (Solution Parts / Total Parts) = Required Volume

  • For solution A:
500ml∗1025=200ml500ml*\frac{10}{25} = 200ml
  • For solution B:
500ml∗1525=300ml500ml * \frac{15}{25} = 300ml

.

Do check the total volume is correct (300ml + 200ml = 500ml)

Using A Recipe

A standard recipe, often taken from the British Pharmacopoeia, provides a reliable way to prepare and scale medicines for different prescriptions. These recipes are based on ratios, which means you can easily adjust the quantities up or down depending on the dose required. Typically, they are prepared using potable water (safe drinking water).

In real practice, however, you must remember that when a solid ingredient is added, it will occupy part of the final volume. This displacement needs to be considered to ensure the medicine has the correct strength and consistency.

Lets look at an example

Patient x is prescribed a TDS 50ml mouthwash for 15 days. How much Double Strength Chloroform Water will you use?

Double Strength Chloroform Water500ml
Sodium Bicarbonate50g
Potable WaterMade up to 1000ml

Step 1 (Total volume)

Calculate how much volume will be used

  • 50ml, TDS, for 15 days
15days∗3times∗50ml=2250ml15\\days*3\\times*50ml = 2250ml

Step 2 (Ratios)

In the recipe we are using 500ml for a total of 1000ml

500:1000convertingtox:2250500:1000\\ converting\\to\\ x:2250

We can use C1/V1 as we are dealing with ratios

5001000∗2250=1125ml\frac{500}{1000}*2250 = 1125ml

Giving us a final volume of 1125ml of double strength chloroform water.

PPM and PPB

Part per million (ppm) and parts per billion (ppb) are extreme forms of ratio strengths.

Here 1 PPM is expressed as (6 zeros):

1:1,000,000

And 1 PPB is expressed as (9 zeros):

1:1,000,000,000

Once the ratio strength method is used, simple convert from 1 in x to x in PPM/PPB by multiplying.

Milli equivalence

Milliequivalence or mEq measure the amount of ion in a solution. This is useful in understanding osmotic and oncotic pressure.

Each ion is taken at face value called valence, for example, K+ would be +1. We can convert between Mg, mEq, and milliequivalance per milliliter:

To convert milligrams (mg) to milliequivalents (mEq):

mEq=mg∗ValenceMolecularweightmEq = \frac{mg*Valence}{Molecular\\weight}

To convert milliequivalents (mEq) to milligrams (mg):

mg=mEq∗MolecularweightValencemg=\frac{mEq*Molecular\\weight}{Valence}

To convert milliequivalents per milliliter (mEq/mL) to milligrams per milliliter (mg/mL):

mg/ml=mEq/L∗MolecularweightValencemg/ml=\frac{mEq/L*Molecular\\weight}{Valence}

Let’s look at an example

Calculate, in milligrams per milliliter, 5 mEq of KCl per milliliter?

Step 1 (Calculate weight)

Molecular weight of KCl is 74.5

Step 2 (Identify the correct equation)

mEq/L∗MolecularweightValence\frac{mEq/L*Molecular\\weight}{Valence}

Step 3 (Substitute)

2∗74.51=149mg/ml\frac{2*74.5}{1} = 149\\mg/ml

Bioavailability

The bioavailability of a drug is expressed as a ratio from 0 to 1. The closer to 1, the higher the availability. IV would have a bioavailability of 1 – though tablets may have lower due to first pass metabolism or food particles.

Pharmacy calculations will usually ask you to compare different bioavailability, and ask you to dose a comparable tablet.

Let’s look at an example

If the bioavailability of tablet A in a 100mg tablet is 0.60 compared to the bioavailability of 0.75 in tablet B, calculate the dose of tablet B equivalent to tablet A.

Step 1 (Calculate the amount of drug in tablet A)

Tablet A has a bioavailability of 0.6. In a 100mg tablet, it would have 60mg as the real dose

100mg∗0.6=60mg100mg*0.6 = 60mg

Therefore, we would like tablet B to administer 60mg

Step 2 (Create an equation)

Dose∗Bioavailability=FreeDrugDose*Bioavailability = Free\\Drug
Dose∗0.75=60mgDose*0.75 = 60mg
60mg0.75=Dose\frac{60mg}{0.75} = Dose

80mg tablets of B are required to create an equivalent dose of tablet A.