Drug Calculations

CWFS F1 ProgrammeSafe Prescribing Module

Drug calculations

• Principles• Units• Strengths• Calculating dosages• IV calculations

Principles

• Keep to a method you understand• Have some idea where your answer

should be so you can ask yourself: • Is my answer reasonable?• IF IN ANY DOUBT –STOP AND GET

HELP !!!

Is my answer feasible?

• The maximum you should give a patient:

• TABLETS = Not more than 4 for any one dose*• LIQUIDS= 5 -20 mL for any one dose• INJECTIONS = 1 -10 mL for any one dose• INFUSIONS = 2-3L per day• *Exceptions –prednisolone, methotrexate

Units

• Always work in the same units !!!

• Avoid decimal points

• Do not use abbreviations –write micrograms and nanograms in FULL to avoid confusing yourself

Be alert to high numbers of dose units

• A female patient aged 65 was prescribed 2,500U of dalteparin sodium subcut o.d under the hospital's post thoracoscopy DVT prophylaxis protocol. The prescribed dose was misread and two nurses checking each other gave five pre-filled syringes i.e. 25,000 units to the patient in error. So much heparin was required that another patient's supply had to be used as well. Error came to light when ward made request to pharmacy for 25,000 unit doses of dalteparin. When the error was discovered the patient's coagulation status was checked; she fortunately came to no harm.

• Taken from: Pharmacy in Practice 2001; 6: 194

Prescribing micrograms -one rule for all?

• O/a to hospital, a patient taking levothyroxine replacement presented her GP’s referral letter which stated that her maintenance dose was 0.025mg od. The clerking FY1 incorrectly converted this dose and prescribed 250 micrograms rather than the 25 micrograms required. A dose was administered before the error was detected by the ward pharmacist the next morning.

• All hospitals have a standard that microgram doses are prescribed as such, not as fractions of milligrams. However, no such requirements laid down in primary care. In complying with this standard the FY1 made an error in converting the dose from that stated by the GP.

• Taken from: Pharmacy in Practice 1994;4:124

Converting a larger unit to a smaller unit

• Decimal point moves 3 places to the RIGHT

• 0.1 2 5 mg 1 2 5 microgram

Converting a smaller unit to a larger unit

• Decimal point moves 3 places to the LEFT• 5 .0 mg 5000 micrograms

Micrograms and milligrams

• 1 milligram = 1000 micrograms

• 0.125mg = 125 micrograms

• 0.025mg = 25 micrograms

Drug Strengths

• There are various ways of expressing how much drug is present in a medicine for liquids (oral/parenteral) or topical prep’s

• Percentage• mg/ml• ‘1 in …….’or ratio strengths

Percentage strength

• Most commonly w/v (weight per volume)

• (but can be w/w and v/v)

• % w/v= number of grams in 100ml

• 2% lignocaine =

• 2g in 100ml

mg/ml strength

• Defined as the number of mg of drug per ml of liquid

• But oral liquids –often mg in a standard 5 mL spoonful

• Injections -mg per 1 mL OR the number of mg per volume of the ampoule

mg/ml Strength

• Percentage w/v to mg/ml• E.g. 2%= 2g in 100ml= 2000 mg per 100ml i.e.

20 mg/ml

• mg/ml to percentage w/v• E.g. 10 mg/ml = 1000 mg per 100ml i.e.• 1g in 100ml=1%

‘1 in …….’or Ratio Strengths

• Used occasionally• Written as 1 in ………• One gram in however many ml• 1 in 10,000= 1gm per 10,000 ml i.e. 1mg/10ml or

0.1mg/ml

• 1 in 1,000 = 1g in 1,000ml = 1mg/ml

EXCEPTION: Tuberculin

• 1 in 10,000(10 units/ml)• 1 in 1,000(100 units/ml)• 1 in 100(1,000 units/ml)

• NOT 1g in 10,000ml BUT a dilution:

• 1ml diluted 10,000 times

• Undiluted tuberculin = 100,000 units/ml

Question 1

• What is the concentration (in mg/ml) of an 8.4% sodium bicarbonate infusion?

• = 8.4g in 100ml• = 84 mg/ml

Question 2

• You have a 10 ml ampoule of adrenaline 1 in 10,000.

• How much adrenaline (in mg) does the ampoule contain?

• = 1g in 10,000ml• = 0.1mg in 1ml• = 1 mg in 10ml

Calculating dosages

• Easiest way: Proportion

• What you do to one side of an equation, do the same to the other side

• ‘ONE’ unit rule

• Make every thing you’ve got equal to ONE then multiply by what you want

• Using a formula

• Amount you WANT x VOLUME it’s in• Amount you’ve GOT

Question 3

• Calculate how many ml you need for a 0.75mg dose of digoxin

• You have digoxin injection 500 micrograms/2ml

• = 250micrograms/ml• ∴750mcg = 3ml of the injection

Dosages based on body parameters

• Calculated on a body weight basis (mg/Kg) or in terms of a patient's surface area (mg/m2)

• WEIGHT• Dose = 3 mg/kg Weight = 68 kg• 3 mg/kg = 3 x 68 = 204 mg• Total dose required = dose/kg x weight (kg)

Dosages based on body parameters

• BODY SURFACE AREA (BSA)• Dose = 500 mg/m2

• Surface area = 1.89 m2

• 500 x 1.89 = 945 mg• Total dose required = dose/m2 x BSA

Question 4

• Dose prescribed is 3 micrograms/kg/min

• Patient's weight = 85 Kg

• What is the dose in microgram/min?

• = 255 micrograms/min

Question 5

• You need to give a treatment dose of tinzaparin (175 units/kg) to a patient who is 85kg

• You have syringes giving 20000 units/ml which can measure quantities to 0.05ml. What volume should you prescribe?

• 175 x 85 = 14875 units• 14875 ÷20000 = 0.74 ml• Therefore prescribe 0.75ml

Calculation Tips

• Keep units the same• Where possible use whole numbers rather

than fractions• If appropriate, round your final answer to a

practical level of accuracy• (5 or more rounds up, 4 or below rounds

down)

Converting dosages to infusion rates (ml/hour)

• Dosages may be expressed as mg/min, mg/kg/min or mcg/kg/min

• When using infusion pumps –convert to ml/hour

• Can use the ‘ONE unit’ rule OR use a formula

Using a formula

• Dose to mL/hour

• Total Volume (ml) x Dose (mcg) x 60• Amount of Drug (mcg)• The DOSE and the AMOUNT MUST be in the

SAME units

Question 6

• You have a 500 ml infusion containing 50 mg glyceryl trinitrate.

• Dose required is 10 micrograms/min• What is the rate in ml/hour?• 10x60 = 600micrograms/hour• 50mg in 500ml = 100micrograms/ml • ∴ 6 ml/hour

Using a formula

• Dose/Kg/min to mL/hour:

• Total Volume (ml) x Dose (mcg/ kg/ min) x weight x 60

• Amount of Drug (mcg)

• The DOSE and the AMOUNT MUST be in the SAME units

Question 7

• You have an infusion of dopamine 800mg in 500ml. Dose required is 2 micrograms/kg/min Patient weighs 68kg

• What is the rate in ml/hour?• 500 x 2 x 68 x 60• 800 x 1000• Amount of Drug = 5 ml/hour

Question 8 –one unit rule method • You have an infusion containing 2.5g esmolol in 250ml

sodium chloride 0.9%.

• Dose required is 50micrograms/kg/minute

• Patient weighs 75kg. What is the rate in ml/hour?

• 50x75 = 3750 mcg/minute

• 3750x60 = 225000mcg/hour = 225mg/hour• 2.5g in 250ml = 10mg/ml

• 225/10 = 22.5ml/hour

Question 8 –formula method• You have an infusion containing 2.5g esmolol in

250ml sodium chloride 0.9%.

• Dose required is 50micrograms/kg/minute

• Patient weighs 75kg What is the rate in ml/hour?

• 250 x (50x75) x 60• 2.5x 1000 x1000• = 22.5ml/hour

Question 8 - formula again – different sum – same answer!

• You have an infusion containing 2.5g esmolol in 250ml sodium chloride 0.9%.

• Dose required is 50micrograms/kg/minute • Patient weighs 75kg What is the rate in ml/hour?

• 250 x 50 x 75 x 60• 2.5x 1000x 1000

• = 22.5 ml/hour

Summary

• Stick to ONE Method that makes sense to you

• SelfCheck - Is your answer sensible?

• If possible, get your answer checked by another

• IF IN ANY DOUBT STOP AND GET HELP• Try the calculations workbook for practice