Dose Calculation (Desired Over Have or Formula)


Article Author:
Tammy Toney-Butler


Article Editor:
Lance Wilcox


Editors In Chief:
Chaddie Doerr


Managing Editors:
Avais Raja
Orawan Chaigasame
Carrie Smith
Abdul Waheed
Khalid Alsayouri
Trevor Nezwek
Radia Jamil
Patrick Le
Anoosh Zafar Gondal
Saad Nazir
William Gossman
Hassam Zulfiqar
Hussain Sajjad
Steve Bhimji
Muhammad Hashmi
John Shell
Matthew Varacallo
Heba Mahdy
Ahmad Malik
Sarosh Vaqar
Mark Pellegrini
James Hughes
Beata Beatty
Beenish Sohail
Nazia Sadiq
Hajira Basit
Phillip Hynes


Updated:
7/30/2019 3:17:44 PM

Introduction

There are 3 primary methods for calculation of medication dosages; Dimensional Analysis, Ratio Proportion, and Formula or Desired Over Have Method. We are going to 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 the use of conversion factors, for example when converting from pounds to kilograms or liters to milliliters. Simplistic in design, this method affords clinicians the opportunity 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 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 affords us the opportunity to work with various units of measurement, converting factors to find our answer. Useful in checking the accuracy of the other methods of calculation as above mentioned, 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 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 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 like 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 

In colon format, one would use H:V::D:X and multiply means DV and Extremes HX.

  • 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 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 (Chen, Hsiao, Shen, & Wu, 2017). 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 on drug dosage calculation essential to decrease medication errors during the preparation of intravenous drugs (Di Muzio, Tartaglini, De Vito, & La Torre, 2016).

High-risk medications such as heparin and insulin often require a second check on dosage amounts by more than one provider before administration of 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, as well as 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 (Schwappach, Taxis, & Pfeiffer, 2018).


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Dose Calculation (Desired Over Have or Formula) - Questions

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A patient presents with a temperature of 39.8 C and relates a 2-day history of a cough and body aches. An order for acetaminophen 15 mg/kg orally every 4 to 6 hours as needed for fever has been entered by the provider. How many milligrams (mg) are required if the patient weighs 65 kg?



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A patient presents with a temperature of 39.8 C and relates a 2-day history of a cough and body aches. An order for acetaminophen 15 mg/kg orally every 4 to 6 hours as needed for fever has been entered by the provider. The weight of this patient is 65 kg. On hand, there are acetaminophen 325 mg tablets. How many tablets should be administered to carry out the prescribed order?



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A client presents with a benzodiazepine overdose and apnea. The overdose occurred as a one-time ingestion while at a party with friends. A provider orders flumazenil 0.2 mg IV push immediately and 0.4 mg IV repeat dose as needed for apnea. The crash cart is stocked with a flumazenil 0.5 mg/5 mL vial. How many milliliters (mL) are drawn up in the syringe to administer the as needed dose? Select all that apply.



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You have been given two concentrations of drug X. One vial contains 2.5% and the another vial contains 240 g of a 0.25%. In order to make a 1% cream, how much of the 2.5% vial would you mix with the 240 g of the 0.25% cream?



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Prepare 36 mL of a 1:4 solution of drug X. You have in stock a 40% solution. How many milliliters of the solution should you use?



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For a 150 pound patient, dopamine 200 mg in 500 mL of normal saline at 5 mcg/kg/min is ordered. What is the final concentration of the solution in mcg/mL?



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A patient has been admitted for sickle cell crisis and requests pain medicine to relieve his 10/10 back pain. Hydromorphone 4 mg IV q 4 hours PRN is ordered for severe pain of 7 to 10. The pharmacist has you sign out a 10 mg/mL vial of hydromorphone. How many milliliters should be drawn up in a syringe to deliver the appropriately ordered dose?



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Metoclopramide 1/4 grains (gr) IV now is ordered for a pre-op patient. On hand, you have 10 mg/mL supplied in the automatic dispensing unit. How many mL's will need to be drawn up to administer the correct dose?



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Diltiazem 20 mg IV, one dose, has been entered by the provider. Atrial fibrillation with a rapid ventricular response is present on the cardiac monitor. The patient's blood pressure is 134/92 mmHg and heart rate 146 beats/min. On hand, you have diltiazem 25 mg/5 mL vials stocked in the medication refrigerator on your unit. How many milliliters are required to deliver the appropriate dose?



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Today you have been floated to the pediatric unit and are about to start making rounds. Upon entering the room of your first patient diagnosed with status epilepticus, you note seizure-like activity. An order for diazepam 4.5 mg IV push as needed for seizures, may repeat times one dose after 5 minutes exists on the medication administration record. You verify the dose with the package insert and drug reference text. The recommended safe dose is 0.3 mg/kg over 2 minutes IV/IO up to 10 mg maximum dose in children. On hand, you have 5 mg/mL vials. The admission weight was 33 pounds. How many milliliters will you draw up in the syringe to administer the ordered dose?



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A provider places an order for cefotaxime 1 gram IVPB stat for one dose as a pre-op order. On hand, you have cefotaxime 1 gram in 100 mL of normal saline. You are unsure of how fast to administer this medication via infusion pump. After confirming the rate with the pharmacist on the unit, you learn this antibiotic must be infused over 45 minutes. What rate should you program in the pump to deliver the medicine within the desired time frame, rounding off to the nearest whole number?



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A provider prescribes a brand name medication for a patient with hypothyroidism. This medication comes in 1/4 grain tablets. The order reads for 1/2 grain by mouth daily. How many tablets should you administer to carry out this order, employing the Desired Over Have Method of drug calculations to assist you?



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A young woman with fibromyalgia is experiencing chronic pain and follows up with pain management. She is prescribed oxycodone hydrochloride 100 mg suspension PO Q 4 hours PRN severe pain of 7 to 10. The supplied amount is 20 mg/5 mL. Using the Desired Over Have Method, how many milliliters do you need to give to achieve the ordered dose?



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A female presenting with pedal edema, dyspnea, orthopnea, and rales on auscultation after consuming a large Thanksgiving dinner has a furosemide order placed. The provider prescribes furosemide 80 mg IV push now. The automated dispensing unit has 40 mg/4 mL vials stocked. How many milliliters will be drawn up in the syringe to administer the prescribed dose using the Ratio and Proportion Method?



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A female presenting with pedal edema, dyspnea, orthopnea, and rales on auscultation after consuming a large Thanksgiving dinner has a furosemide order placed. Furosemide 80 mg IV push now is ordered. The automated dispensing unit has 40 mg/4 mL vials stocked. How many milliliters will be drawn up in the syringe to administer the prescribed dose using the Desired Over Have or Formula Method?



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A child presents with a fever, sore throat, and cough. Erythromycin suspension 1200 mg per day is prescribed based on a measured weight of 30 kg. The safe daily dose is between 30 to 50 mg/kg/day according to the drug reference guide. The pharmacist provides you with a 200 mg/5 mL suspension. How many milliliters would you administer in a single dose if ordered every 8 hours and is the ordered dose in the effective yet safe dosing range?



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A female patient presents with chest pain, tachycardia, orthopnea, pulse oximetry reading of 86% on room air, and right leg swelling. She has a diagnosis of deep vein thrombosis and subsequent pulmonary embolus. An order for heparin weight-based protocol, bolus, and drip are initiated by a provider. The protocol calls for an 80 unit/kg bolus IV dose for pulmonary embolism, and 60 unit/kg bolus IV for non-ST-elevation myocardial infarction. Patient bed scale weight measured on arrival was 110 pounds. How many milliliters will this patient receive as an IV bolus dose of heparin if you have 5000 units/mL stocked on your unit?



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Cephalexin 250 mg by mouth four times per day has been ordered for a child weighing 50 pounds. The daily safe dose range is 25 to 50 mg/kg/day. The pharmacist dispensed 125 mg/2 mL suspension for this patient. How many milliliters will you administer to this child?



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Two tablespoons of 90% boric acid solution are diluted to 10% strength. How many 4 oz bottles can be filled with the resulting diluted solution?



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In what proportions should 25% zinc oxide cream be mixed with moisturizing cream base to create a 5% zinc oxide topical product?



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If 60 mL of 10% (w/v) solution is diluted with distilled water to a volume of one pint, what will the resultant solution's strength be?



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You are to prepare 2.0 L of a 1:10 solution from a 30% solution. How much water did you have to add?



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You have a 50% (w/v) solution in your inventory. You are instructed to take 180 mL of this stock solution, and add 8 ounces of water to it. What will be the final concentration percentage (w/v) of the resulting solution?



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A pediatric patient weighs 88 lbs and is prescribed amoxicillin 10 mg/kg TID. Your pharmacy has 200 mg/5mL suspension in stock. How many mL will the patient receive daily?



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You have 10% sodium chloride in stock. How much water would need to be added to 250 mL of the stock solution to make 0.9% NS solution?



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Dose Calculation (Desired Over Have or Formula) - References

References

Maths anxiety and medication dosage calculation errors: A scoping review., Williams B,Davis S,, Nurse education in practice, 2016 Sep     [PubMed]
Increasing nursing students' understanding and accuracy with medical dose calculations: A collaborative approach., Mackie JE,Bruce CD,, Nurse education today, 2016 May     [PubMed]
Educational audit on drug dose calculation learning in a Tanzanian school of nursing., Savage AR,, African health sciences, 2015 Jun     [PubMed]
[Medication administration and dose calculation]., Clavagnier I,, Revue de l'infirmiere, 2013 Jun-Jul     [PubMed]
Enhancing student nurses' medication calculation knowledge; integrating theoretical knowledge into practice., Coyne E,Needham J,Rands H,, Nurse education today, 2013 Sep     [PubMed]
Dose Calculation (Dimensional Analysis, Factor-Label Method), Toney-Butler TJ,Hughes J,,, 2018 Jan     [PubMed]
Students who developed logical reasoning skills reported improved confidence in drug dose calculation: Feedback from remedial maths classes., Shelton C,, Nurse education today, 2016 Jun     [PubMed]
[Prevention of medication errors during intravenous drug administration in intensive care units: a literature review.], Di Simone E,Giannetta N,Spada E,Bruno I,Dionisi S,Chiarini M,Tartaglini D,Di Muzio M,, Recenti progressi in medicina, 2018 Feb     [PubMed]
Oncology nurses' beliefs and attitudes towards the double-check of chemotherapy medications: a cross-sectional survey study., Schwappach DLB,Taxis K,Pfeiffer Y,, BMC health services research, 2018 Feb 17     [PubMed]
Knowledge, behaviours, training and attitudes of nurses during preparation and administration of intravenous medications in intensive care units (ICU). A multicenter Italian study., Di Muzio M,De Vito C,Tartaglini D,Villari P,, Applied nursing research : ANR, 2017 Dec     [PubMed]
The cost-saving effect and prevention of medication errors by clinical pharmacist intervention in a nephrology unit., Chen CC,Hsiao FY,Shen LJ,Wu CC,, Medicine, 2017 Aug     [PubMed]

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