The Three Step Method
Most pharmaceutical calculations can be solved with the simple three step method.

1. Write down all the variables. Record all the variables that are known. Also, indicate the unknown variable that you are solving for.
2. Choose the method used to solve the problem. If the problem can be solved using a formula, then write down the formula. If the problem is a conversion, then write down the conversion factors and set up the equation. All the units should cancel out except for the unit of the unknown variable in the numerator. If the problem is a proportion and ratio, then set up the equation. Proportion and ratio problems should have three known variables and one unknown variable.
3. Solve the problem. If it is a problem that can be solved with a mathematical formula, then plug the variables into the formula and solve it. Solve the problem to determine the unknown variable declared in the first step.

Conversions
Make sure that the units that cancel each other out are the same type of units. For example, meters can cancel meters, but meters cannot cancel feet.

• Problem - A medication order for a patient weighing 176 lb calls for 400 µg antibiotic per kg of body weight to be added to 400 mL of isotonic dextrose solution. If the drug is to be obtained from a solution containing 20 mg per 10 mL, how many milliliters should be added to the dextrose solution?
• Known variables; 400 µg antibiotic dose/kg body weight, 176 lb body weight, 400 mL isotonic dextrose solution (this is not a useful variable, it was just thrown in to confuse you), 20 mg/10 mL antibiotic source
• Unknown variable: X mL of antibiotic added to the dextrose solution.
• Conversion factors; 1 kg/2.2 lb, 1 mg/1000 µg.
• Solution:

Proportions
Make sure that the numerators on both sides of the equation have the same units. The denominators on both sides of the equation should also have the same units.

• Problem - A pycnometer weighs 25.0 g. When filled with a liquid (S.G.=1.25) it weighs 55.0 g. How many ml of water will the pycnometer hold?
• Specific Gravity & Density - In order to do this problem, you need to understand specific gravity and density. Density is the mass per unit volume of a substance. It is usually expressed as g per mL. Specific gravity is a ratio, expressed with decimals, of the weight of a substance to the weight of an equal volume of another substance (usually water) chosen as a standard. Both substances have to be at the same temperature or the temperature of both substances has to be known. Because the units cancel out when calculating the specific gravity, it is a dimensionless number. This means that it is a number without a unit.
• Known variables; 55.0 g (weight of pycnometer and liquid) - 25.0 g (weight of pycnometer) = 30.0 g (weight of liquid). Therefore, the known variables are; 30.0 g liquid weight, 1.25 g liquid/1 g water.
• Unknown variable: X mL of water.
• Proportion and ratio: - Since there are three known variables and one unknown variable, the proportion and ratio method is used.
• Solution:

Formulas

• Problem - On a prescription balance having a sensitivity requirement of 0.012 g what is the smallest amount that can be weighed with a maximum potential error of not more than 10%.
• Known variables; 0.012 g Sensitivity Requirement, 10% Permissible Percentage of Error
• Unknown variable: X g Smallest Amount Weighable
• Formula - In order for you to do this problem, you have to know the Percentage of error formula:
  (Sensitivity Requirement x 100%)/Permissible Percentage of Error = Smallest Amount Weighable
• Solution:

Study Conversions Tutorial - Please be patient. This may take 5-10 minutes to download on a dialup connection.

Study Ratio & Proportion Tutorial - Please be patient. This may take 5-10 minutes to download on a dialup connection.