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Drug Calculations
CWFS F1 Programme
Safe Prescribing Module
Drug calculations
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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
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Is my answer feasible?
• The maximum you should give a patient:
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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
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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
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Amount you WANT
Amount you’ve GOT
x VOLUME it’s in
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)
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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
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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.
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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
• 2.5x 1000x 1000
• = 22.5 ml/hour
x 50 x 75 x 60
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