### Definition/Introduction

Utilizing pharmacy calculations to administer therapeutics to patients correctly is vital to patient treatment. Health care professionals must dispense drugs in the accurate concentrations, calculate correct doses, and compound and prepare medications accurately to ensure that each particular drug is being administered correctly.

Dose refers to the amount of medication taken at a specific time, whereas the dosage of the drug refers to the administration of a frequency, amount, and the number of doses taken over a particular period of time.

The following definitions can aid in preparing and administering pharmacological drugs.

**Concentration** is the amount of active ingredient per total weight of a substance.

**Alligation**** **involves mixing solutions or solids of varying strengths to obtain another strength of the active ingredient in both.[1]

**Specific gravity** refers to the ratio of the weight of a substance to the weight of an equal volume of water at the same time.

*Specific gravity = number of grams of a substance/number of milliliters of a substance.*

If the specific gravity is known, the volume or weight of the desired quantity can be determined.

The following pharmacy calculations are used to determine the dose and dispense drugs in the correct concentrations [2]:

**Tablet Dosage**

Desired Dose/Stock Strength = Number of Tablets

**Mixtures and Solutions**

[Desired Dose/Stock Stregth] x Stock Volume = Amount of Solution to be given

**IV Rate **

*mL per hour and minute*

Total IV Volume/Time (hour or minute) = mL per hour or minute

*Drops per minute*

[Total IV volume/Time (minute)] X Drop Factor = Drops per minute

*Remaining time of infusion*

[Volume remaining (in mL)/Drop per minute] x Drop Factor = Minutes remaining [3]

**Dilutions**

The relationship between concentration and volume is inversely proportional. (See Figure 1 for a schematic of the inverse relationship between percent of concentration or ratio strength (decreases), and the total quantity of product (increases)).

Thus, if a solution requires a dilution, the active drug in the solution will remain constant, but the volume will increase. [4]

**Isotonicity****:**

It is important to note that when two solutions have equal osmotic pressure and salt concentration, they are said to be isotonic. **Normal saline** has a concentration of 0.90% w/v of NaCl in sterile water and therefore is an isotonic crystalloid.[5]

**Percent Strength[6]:**

Percent strength represents the number of grams contained in 100 mL of product and is very useful in pharmacy calculations.

The following units express percent based on the nature of the ingredient:

Percent Weight in Volume (w/v): Is the number of grams in 100 mL of solution and is expressed as %w/v. Powdered substances suspended in a liquid vehicle would be calculated as w/v.

Percent Volume in Volume (v/v): Is the number of milliliters in 100 mL of solution and is expressed as %v/v. A liquid component in a liquid preparation would be calculated on a v/v basis.

Percent weight in weight (w/w): Is the number of grams in 100 grams of solution and is expressed as %w/w. Powdered substances mixed with a solid or semisolid (ointments) would be calculated as w/w.