Dose Calculation Desired Over Have Formula Method

Preparation

When clinicians are prepared and know the key conversion factors, they may feel less anxious about the calculation involved. Preparation is vital to accuracy, regardless of which formula or method is used.

Conversion Factors

• 1 kg = 2.2 lb
• 1 gallon = 4 quart
• 1 tsp = 5 mL
• 1 in = 2.54 cm
• 1 L = 1000 mL
• 1 kg = 1000 g
• 1 oz = 30 mL = 2 tbsp
• 1 g = 1,000 mg
• 1 mg = 1,000 µg
• 1 cm = 10 mm
• 1 tbsp = 15 mL
• 1 cup = 8 fl oz
• 1 pint = 2 cups
• 12 in = 1 ft
• 1 L = 1.057 qt
• 1 lb = 16 oz
• 1 tbsp = 3 tsp
• 60 min = 1 h
• 1 cc = 1 mL
• 2 pt = 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 or Treatment

Three primary methods are used to calculate medication dosages, as referenced above. These include the desired over have, or formula, method; dimensional analysis; and ratio and proportion (as cited in Boyer, 2002)[Lindow, 2004].

Desired Over Have or Formula Method

The desired over have, or formula, method uses a formula or equation to solve for an unknown quantity (x), much like the ratio and proportion method. Drug calculations require conversion factors, such as converting from pounds to kilograms or from L to mL. This simple method allows clinicians to work with various units of measurement, using conversion factors to find the answer. The method is useful for checking the accuracy of the other calculation methods mentioned above, thereby serving as a double or triple check.

A basic formula, solving for x, guides clinicians in setting up an equation:

Desired Dose/Amount on Hand × Quantity = x,

Alternatively:

Desired Dose Amount = Ordered Dose Amount × On-Hand Quantity.

For example, a clinician requests lorazepam 4 mg intravenous push for a patient with severe alcohol withdrawal. The clinician has 2 mg/mL vials on hand. How many mL should the clinician draw up in a syringe to deliver the desired dose?

Dose Ordered (4 mg) × Quantity (1 mL)/Have (2 mg) = Amount Wanted to Give (2 mL)

Units of measurement must match, for example, mL and mL, or the clinician needs to convert the values to like units of measurement. In the example above, the ordered dose and the available dose were both in mg, which cancel out, leaving mL; because the answer requires mL, no further conversion is needed.

Dimensional Analysis Method

An order is placed for lorazepam 4 mg intravenous push for a Clinical Institute Withdrawal Assessment for Alcohol (CIWA) score of 25 or higher, with the CAGE protocol used 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 is placed over 1:

x mL = 4 mg/1 x 1 mL/2 mg x (4)(1)/2 x 4/2 x 2/1 = 2 mL,

Continue multiplying or dividing until the desired amount is reached, which is 2 mL in this example. Notice that the fraction was set up with mg and mg strategically placed, so units could cancel each other out, making the equation easier to solve for the desired unit, mL. The answer makes sense, so the calculation is complete.

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 because they are like units in the 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 a clinician multiplies a number by 1, then the number is unchanged. In contrast, if a clinician multiplies a number by zero, the number becomes zero. Examples include:

18 × 0 = 0 and 20 × 1 = 20.

Ratio and Proportion Method

The ratio and proportion method has been around for years and is one of the oldest methods used in drug calculations (as cited in Boyer, 2002)[Lindow, 2004]. The addition principle 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 addition. An example below provides a better explanation using a fraction or colon format:

A clinician orders lorazepam 4 mg intravenous push now for a CIWA score of 25. The clinician has 2 mg/mL vials on hand. How many mL are required to administer the ordered dose?

Have on Hand/Quantity on Hand = Desired Amount/x

2 mg/1 mL = 4 mg/x2x/2 = 4/2x = 2 mL

In colon format, clinicians can use H:V::D:X and multiply the means, DV, and the extremes, HX:

Hx = DVx = DV/H2:1::4:x2x = (4)(1)x = 4/2x = 2 mL

Complications

A 2016 study evaluated the role of confidence in overall arithmetic and drug-calculation skills. Study participants attended remedial math classes, came from a wide range of educational backgrounds and age groups, and were pursuing a first degree in nursing, a foundation degree, or postregistration courses (Shelton, 2016). Results from the study showed that one-third of students felt a lack of confidence, which originated at an earlier stage of education, dating back to the primary school environment (Shelton, 2016). Results from the study also showed that confidence plays a role in dosage calculations and in the overall performance of mathematical calculations, and that it 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 results from a 2016 study of intensive care unit (ICU) nurses, 80% considered knowledge of drug dosage calculation essential to reducing medication errors during intravenous drug preparation.[2]

High-risk medications, such as heparin and insulin, often require a second check on dosage amounts by more than one clinician before drug administration. Clinicians should follow institutional policies and recommendations on the double-checking of dose calculations by another licensed clinician. Results from a 2018 study by a group of oncology nurses across 3 Swiss hospitals discussed the process of double-checking and its limitations in the current healthcare environment, including increased nurse workload, time constraints, distracting environments, and a lack of resources. Results from the study showed 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. Clinicians, nurses, and pharmacists must all be knowledgeable regarding the desired formulas. This technique is invaluable in properly treating patients.