Drug Calculations Notes and Worksheet, Exercises of Nursing

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Drug Calculations

Workbook

2 |Corporate Practice Development Team. South Tees Hospital (NHS) Trust IV Drugs and infusion management workbook

Drug Calculations Workbook Registered nurses & Operating department practitioners Introduction

Practitioners administering medicines must be aware of their own accountability within a framework of legislation and professional regulation and guidance.  The Code (NMC 2015)  Professional guidance on the safe and secure handling of medicines (2018)  The Health and Care Professional Council (2016) Standards of conduct, performance and ethics for allied health professional  The Health and Care Professional Council (2014) Consultation on proposed profession-specific standards of proficiency for operating department practitioners

A golden rule of any calculation that you have to carry out is to have some idea of what a sensible answer should be (Hutton 2005).

Numeracy Skills

Weights When administering drugs the amounts given to patients are relatively small. Doses are often measured in grams, milligrams and sometimes nanograms.

Converting Units To convert big to little: Multiply. To convert little to big: Divide:

From To Do This Kilograms grams Multiply by Grams milligrams Milligrams micrograms Micrograms nanograms

Nanograms micrograms Divide by 1000 Micrograms milligrams Milligrams grams Grams kilograms

To change grams to milligrams x by 1000 ( OR move the decimal point 3 places to the RIGHT)

eg: 1.0g = 1000 milligrams 4.2g = 4200 milligrams 0.07g = 70 milligrams

To change milligrams to grams (g) ÷ by 1000 ( OR move the decimal place 3 points to the LEFT)

eg: 100milligrams = 0.1g 62,000milligrams = 62g 35milligrams = 0.035g

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2. 50 milligrams is prescribed, tablets are 12.5 milligrams each: how many tablets will you give?
3. 1 milligram is prescribed, tablets are 500 micrograms: how many tablets will you give?
4. 625 milligrams prescribed, tablets are 1.25 g each: how many tablets will you give?
5. 3 tablets each contain 250 milligrams. What is the total dose in milligrams?

Drugs in Liquid Form

When drugs are in liquid form, the available dose is given in terms of the concentration of the solution or suspension. As an example, pethidine hydrochloride is available as 50milligrams/ml. This means that 50 milligrams of pethidine hydrochloride are dissolved in every millilitre of liquid.

The formula to be used is:

Volume Needed = What You Want x Volume it’s in What You’ve Got

e.g. A drug is available as 25 milligrams/ml and 75 milligrams are required. What volume would be given?

A. 75x 1 = 3ml 25

Drug Calculations – Questions III

Please answer the following:

1. An injection of morphine 8 milligrams is required. Ampoules available contain 10 milligrams in 1 ml. What volume is drawn up for injection?
2. Digoxin ampoules available contains 500 microgram in 2ml. What volume is needed when 350 microgram is prescribed
3. A patient is prescribed 250 milligrams of gentamicin by IV injection. Stock ampoules contain 80milligrams in 2 ml. What volume is needed for the injection?
4. A patient is to be given erythromycin 120 milligrams by injection. Stock vials contain 300 milligrams/10 ml. Calculate the required volume.
5. Stock heparin has strength of 5000 units per ml. What volume must be drawn up to give 6500 units?
6. A patient is to receive Frusemide 80mg IV, the preparation available is Frusemide 250mg in 25mls. Calculate the volume required.
7. A patient is prescribed bumetanide 0.8 milligrams IM. Stock ampoules contain 2 milligrams/4 ml. What volume would be drawn up

5 |Corporate Practice Development Team. South Tees Hospital (NHS) Trust IV Drugs and infusion management workbook

IV Drip Rates

The rate of flow down intravenous infusion lines must be regulated and this is often controlled by a device known as an infusion controller or volumetric pump.

A volumetric infusion pump receives fluid from a giving set. The pump has an adjustable rate of flow and converts fluid into very fine drops, within the machine before delivering the fluid to a patient.

An infusion pump can be accurately set and is designed to maintain a steady flow rate. However, the patient receiving the infusion must still be checked at regular intervals.

Flow Rate (When duration is given in HOURS)

Volume in mLs Duration in hours

e.g. If a patient requires 250 ml in 6 hours, the flow rate is 250 = 41.67 ml/hr 6

Flow Rate (When duration is given in MINUTES)

Volume in mLs Duration (in minutes) ÷ 60 minutes

Example: A patient is to be given 100 ml of medication over 15 mins. What is the flow rate using an infusion pump? (It is advisable to work out Duration in Minutes divided by 60 first). 15 ÷ 60 =0.25.

100 ÷ 0.25 = 400 Therefore = run the infusion pump at 400 mLs / hour

Drip Rate Formula

A drip chamber is part of a giving set or administration set. It has a fixed drop size and an adjustable rate of flow. There are four main types of giving set in general use- these break fluid into either 10, 15, 20 or 60 drops per ml (drop factor).

Drip Rate = Volume needed (in mLs) x Drop Factor (No. of drops per ml delivered by the set) Duration of the Infusion (in Minutes)

If a patient is to be given 500 ml by Intravenous Infusion (IVI) using a drip factor of 20 drops/ml over 6 hours

(it is advisable to convert hours to minutes first)

Therefore 6x 60= 360 minutes

Drop rate = 500 x 20 = 27.77 or 28 drops/min to nearest decimal place 360

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1. Morphine is supplied in a syringe containing 20 milligrams of Morphine in 50 mls of solution. What is the concentration (milligrams/ per ml) of morphine in the syringe?
2. The drug Aminophylline is supplied in a syringe containing 500 milligrams of Aminophylline in 50 ml of solution. What is the concentration (milligrams/ per ml) of Aminophylline in the syringe?
3. Heparin is supplied in a syringe containing 10,000 units of Heparin in 50 ml of solution. What is the concentration (milligrams/ per ml) of heparin?
4. Insulin is supplied in a bag containing 50 units of Regular Insulin in 100 ml of solution What is the concentration (units/ per ml) of insulin in the bag?

Mixed Bag of Questions

Please answer the following:

1. Calculate the volume to be given when the prescribed dose is penicillin 500 milligrams and dose available is syrup 125/5 ml
2. Calculate the volume to be given when the prescribed dose is chloramphenicol 750 milligrams, and the available dose is a suspension of 125 milligrams/5 ml
3. An infusion pump is to be used to give 1 litre of fluid over 11 hours. At what rate should the pump be set?
4. Aminophylline 0.5 milligrams/kg/hr is prescribed for an 80 kg man; 500 milligrams in 500 ml infusion is prepared. At what rate should the infusion run (in ml/hr.)?
5. A patient is to receive a litre of Hartmann’s solution over 12 hours. Calculate the drip rate if the administration set gives 15 drops/ml
6. A patient is to be given 180 milligrams of paracetamol. Stock elixir contains 120 milligrams/5 ml. Calculate the volume to be given orally.
7. A patient is prescribed penicillin 400 milligrams orally. Stock syrup has strength of 125 milligrams/5 ml. Calculate the volume of mixture to be given.
8. A patient weighing 70kg is prescribed Acetylcysteine 150mg/kg in 200mLs of 5% Dextrose. The ampules available are 2g in 10mls. What volume of Acetylcysteine must be added to the 200ml bag?
9. A patient is ordered erythromycin 800 milligrams, stock available is a mixture 125 milligrams/5 ml. Calculate the volume to be given.
10. How much morphine must be drawn up for a 10 milligrams dose if a stock ampoule contains 15 milligrams in 1ml.

8 |Corporate Practice Development Team. South Tees Hospital (NHS) Trust IV Drugs and infusion management workbook

11. Digoxin ampoules on hand contain 500 microgram in 2ml. What volume is needed for an injection of 275 microgram?
12. A patient weighing 45kg is prescribed intravenous paracetamol 15 milligrams/kg.. How many milligrams of paracetamol are required?
13. Pethidine 85 milligrams is to be given IM. Stock ampoules contain pethidine 100 milligrams in 2 ml. Calculate the volume of stock required.

10 |Corporate Practice Development Team. South Tees Hospital (NHS) Trust IV Drugs and infusion management workbook

Answers to Drug Calculations – Questions IV

1. A patient is to receive half a litre of dextrose 5% over 4 hours. The giving set delivers 20 drops/ml. Calculate the required drip rate in drops/min

42 drops/min 500 ml x 20 drops/ml 4h x 60 = 500x20 = 125 drops/min = 41 and 2/3rds = 42 drops minutes 4x60 3

2. If a patient is to be given 750 ml by IVI using a controller with a drip factor of 20 drops/ml over 12 hours, what would you set the drip rate to (round to the nearest number)

= 20x750 = 20.88 = 21 drops/min 12x 60

3. 750 ml of normal saline is to be given to a patient over 9 hours using giving set which emits 10 drops/ml. Calculate the required drip rate in drops per min.

= 10x 750 = 13.88 = 14drops/min 9x

4. 300 mls of blood is to be transfused over 4 hours using an administration set which gives 10 drops/ml. Calculate the drip rate in drops/min

= 10x300 = 13 drops/min 4x 60

Flow rates

5. If a patient requires 1000 mls in 12 hours what is the flow rate (give your answers to two decimal places)

= 1000 = 83.333 = 83 mls/hr 12

6. 500 mls of Hartmann’s solution is to be given to a patient over 7 hours. What is the flow rate?

= 500/7 = 71ml/hr

7. Over the next 15 hours, a patient is to receive 2 litres of dextrose 5%, what is the flow rate?

= 15/2000 = 133ml/hr.

8. A patient is to receive 500 ml of normal saline. The drip chamber is adjusted to deliver 25 ml/h. How long will the fluid last?

11 |Corporate Practice Development Team. South Tees Hospital (NHS) Trust IV Drugs and infusion management workbook

= 500/25 = 20hrs

9. A patient is to receive half a litre of fluid IV over 6 hours using an infusion pump. At what rate (in ml/h) should the pump be set?

= 500/6 = 83.3333ml/hrs. = 83 mls

10. Calculate the required flow rate of an infusion pump- one litre of fluid to be given over 4 hours

= 1000/4 = 250 mls/hr

Answers to Question V

1. Morphine is supplied in a syringe containing 20 milligrams of Morphine in 50 mls of solution. What is the concentration (milligrams/ per ml) of morphine in the syringe?

= 20 milligrams/50 mls = 0.4 milligrams in 1 ml

2. The drug Aminophylline is supplied in a syringe containing 500 milligrams of Aminophylline in 50 ml of solution. What is the concentration (milligrams/ per ml) of Aminophylline in the syringe?

= 500 milligrams/ 50mls = 10 milligrams in 1ml.

3. Heparin is supplied in a syringe containing 10,000 units of Heparin in 50 ml of solution. What is the concentration (milligrams/ per ml) of heparin?

= 10,000 units/ 50mls = 200 units in 1ml.

4. Insulin is supplied in a bag containing 50 units of Regular Insulin in 100 ml of solution. What is the concentration (units/ per ml) of insulin in the bag?

= 50 units /100 mLs= 0.5units in 1ml

Answers to Mixed Bag of Questions

1. Calculate the volume to be given: ordered penicillin 500 milligrams, on hand syrup 125/5 ml

= 20 ml

2. Calculate the volume to be given: ordered chloramphenicol 750 milligrams, on hand suspension 125/5 ml

= 30 ml

3. An infusion pump is to be used to give 1 litre of fluid over 11 hours. At what rate should the pump be set?

13 |Corporate Practice Development Team. South Tees Hospital (NHS) Trust IV Drugs and infusion management workbook

11. Digoxin ampoules on hand contain 500 microgram in 2 ml. What volume is needed for an injection of 275 microgram?

= 275x2/500 = 1.1 ml

12. A patient weighing 45kg is prescribed intravenous paracetamol 15 milligrams/kg.. How many milligrams of paracetamol are required?

= 15milligrams x 45kgs = 675mg

13. Pethidine 85 milligrams is to be given IM. Stock ampoules contain pethidine 100 milligrams in 2 ml. Calculate the volume of stock required.

= 1.7 ml

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References

 Coben D. Atere-Roberts E. (1996) Carefree Calculations for Health Care Students London, McMillan Publisher.

 The Health and Care Professional Council (2016) ‘Standards of conduct, performance and ethics for allied health professional’ (online) https://www.hcpc- uk.org/standards/standards-of-conduct-performance-and-ethics/ [accessed 27/12/2018]

 Hutton, M. (2005) ‘Paediatric Nursing Calculation Skills’(online): http://hy.health.gov.il/_Uploads/dbsAttachedFiles/pncalculationskills.pdf [accessed 27/12/2018]

 Nursing & Midwifery Council (2015) The Code Professional standards of practice and behaviour for nurses and midwives London, NMC.

 Nursing & Midwifery Council (2010a) Guidelines for Administration of Medicines London, NMC.

 Nursing & Midwifery Council (2010b) Guidelines for Records and Record Keeping London, NMC.

 Royal Pharmaceutical Society (2018) ‘Professional guidance on the safe and secure handling of medicines’ (online) https://www.rpharms.com/recognition/setting- professional-standards/safe-and-secure-handling-of-medicines/professional- guidance-on-the-safe-and-secure-handling-of-medicines [accessed 18/12/18]