### Introduction

There are 3 primary methods for calculating medication dosages; Dimensional Analysis, Ratio Proportion, and Formula or Desired Over Have Method. We will explore the Desired Over Have or Formula Method, one of these 3 methods, in more detail.

Desired Over Have or Formula Method uses a formula or equation to solve for an unknown quantity (x), much like ratio proportion.

Drug calculations require using conversion factors, for example, when converting from pounds to kilograms or liters to milliliters. Simplistic in design, this method allows clinicians to work with various units of measurement, converting factors to find the answer. These methods are useful in checking the accuracy of the other methods of calculation, thus acting as a double or triple check.

### Preparation

When clinicians are prepared and know the key conversion factors, they will be less anxious about the calculation involved. This is vital to accuracy, regardless of which formula or method is employed.

**Conversion Factors**

- 1 kg = 2.2 lb
- 1 gallon = 4 quart
- 1 tsp = 5 mL
- 1 inch = 2.54 cm
- 1 L = 1,000 mL
- 1 kg = 1,000 g
- 1 oz = 30 mL = 2 tbsp
- 1 g = 1,000 mg
- 1 mg = 1,000 mcg
- 1 cm = 10 mm
- 1 tbsp = 15 mL
- 1 cup = 8 fl oz
- 1 pint = 2 cups
- 12 inches = 1 foot
- 1 L = 1.057 qt
- 1 lb = 16 oz
- 1 tbsp = 3 tsp
- 60 minute = 1 hour
- 1 cc = 1 mL
- 2 pints = 1 qt
- 8 oz = 240 mL = 1 glass
- 1 tsp = 60 gtt
- 1 pt = 500 mL = 16 oz
- 1 oz = 30 mL
- 4 oz = 120 mL (Casey, 2018)

### Technique

There are 3 primary methods for the calculation of medication dosages, as referenced above. These include Desired Over Have Method or Formula, Dimensional Analysis, and Ratio and Proportion (as cited in Boyer, 2002)[Lindow, 2004].

**Desired Over Have or Formula Method**

Desired over Have or Formula Method is a formula or equation to solve for an unknown quantity (x), much like ratio proportion. Drug calculations require the use of conversion factors, such as when converting from pounds to kilograms or liters to milliliters. Simplistic in design, this method allows us to work with various units of measurement, converting factors to find our answer. It is useful in checking the accuracy of the other calculation methods as mentioned above, thus acting as a double or triple check.

- A basic formula, solving for x, guides us in the setting up of an equation:
- D/H x Q = x, or Desired dose (amount) = ordered Dose amount/amount on Hand x Quantity.

For example, a provider requests lorazepam 4 Mg IV Push for a patient in severe alcohol withdrawal. The clinician has 2 mg/mL vials on hand. How many milliliters should he or she draw up in a syringe to deliver the desired dose?

- Dose ordered (4 mg) x Quantity (1 mL)/Have (2 mg) = Amount wanted to give (2 mL)

Units of measurement must match, for example, milliliters and milliliters, or one needs to convert to like units of measurement. In the example above, the ordered dose was in milligrams, and the have dose was in milligrams, both of which cancel out, leaving milliliters (answer called for milliliters), so no further conversion is required.

**Dimensional Analysis Method**

An order placed by a provider for lorazepam 4 mg IV PUSH for CIWA score of 25 or higher, follow CAGE Protocol for subsequent dosages based on CIWA scoring.

- The clinician has 2 mg/mL vials in the automated dispensing unit.
- How many milliliters are needed to arrive at an ordered dose?
- The desired dose os placed over 1 remember, (x mL) = 4 mg/1 x 1 mL/2 mg x (4)(1)/2 x 4/2 x 2/1 = 2 mL, keep multiplying/dividing until the desired amount is reached, 2 mL in this example.
- Notice, the fraction was set up with milligrams and milligrams strategically placed, so units could cancel each other out, making the equation easier to solve for the unit desired or milliliters. The answer makes sense, so work is done.

Zeros can be canceled out in the same way as like units. For example:

- 1000/500 x 10/5 = 2, the 2 zeros in 1000 and 2 zeros in 500 can be crossed out since like units in numerator and denominator, leaving 10/5, a much easier fraction to solve, and the answer makes sense.

We have addressed zeros, and now let us look at 1.

- If one multiplies a number by a 1, then the number is unchanged.
- In contrast, if you multiply a number by zero, the number becomes zero.
- Examples listed below are as follows: 18 x 0 = 0 or 20 x 1 = 20.

**Ratio and Proportion Method**

The Ratio and Proportion Method has been around for years and is one of the oldest methods utilized in drug calculations (as cited in Boyer, 2002)[Lindow, 2004]. Addition principals is a problem-solving technique that has no bearing on this relationship. Only multiplication and division are used to navigate through a ratio and proportion problem, not adding. An example listed below will provide a better explanation using a fraction or a colon format:

A provider orders lorazepam 4 mg IV Push now for a CIWA score of 25. There are 2 mg/mL vials on hand. How many milliliters are required to carry out the ordered dose?

- Have on hand / Quantity you have = Desired Amount / x
- 2 mg/1 mL = 4 mg/x
- 2x/2 = 4/2
- x = 2 mL

One would use H:V::D:X and multiply means DV and Extremes HX in colon format.

- Hx = DV, x = DV/H, 2:1::4:x, 2x = (4)(1), x = 4/2, x = 2 mL

### Complications

A 2016 study evaluated the role confidence plays in overall arithmetic in drug calculation skills. Study participants attended remedial math classes from a wide range of educational backgrounds and age dynamics seeking a first degree in nursing, a foundation degree, or post-registration courses (Shelton, 2016). The study revealed one-third of students feel a lack of confidence, which originated in an earlier stage of education, dating back to a primary school environment (Shelton, 2016). The study concluded that confidence plays a role in dosage calculations and the overall performance of mathematical calculations and can be improved in an environment that fosters a deep-learning approach (Shelton, 2016).

### Clinical Significance

Medication errors can be detrimental and costly to patients.[1] Drug calculation and basic mathematical skills play a role in the safe administration of medications.

According to a 2016 study of intensive care (ICU) nurses, 80% of nurses considered knowledge of drug dosage calculation essential to decrease medication errors during the preparation of intravenous drugs.[2]

High-risk medications such as heparin and insulin often require a second check on dosage amounts by more than one provider before administering the drug. Follow institutional policies and recommendations on the double-checking of dose calculations by another licensed provider.

Published in 2018, one study by a group of oncology nurses in 3 Swiss hospitals discusses the process of double-checking and its limitations in the current healthcare environment and increased nurse workload and time constraints, distracting environments, and lack of resources. The study concluded that oncology nurses strongly believed in the effectiveness of double-checking medication despite reporting limitations of the procedure in clinical practice.[3]

### Enhancing Healthcare Team Outcomes

All members of the interprofessional team are responsible for dose calculations. Physicians, nurses, and pharmacists all must be knowledgeable regarding the desired formulas. This technique is invaluable in properly treating patients.