1. Drug Calculations CWFS F1 Programme Safe Prescribing Module

2. Drug calculations Principles Units Strengths Calculating dosages
IV calculations

3. 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 !!!

4. Is my answer feasible? The maximum you should give a patient:
TABLETS = Not more than 4 for any one dose*
LIQUIDS= mL for any one dose
INJECTIONS = mL for any one dose
INFUSIONS = 2-3L per day
*Exceptions –prednisolone, methotrexate

5. Units Always work in the same units !!! Avoid decimal points
Do not use abbreviations –write micrograms and nanograms in FULL to avoid confusing yourself

6. 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

7. 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

8. Converting a larger unit to a smaller unit
Decimal point moves 3 places to the RIGHT
mg microgram

9. Converting a smaller unit to a larger unit
Decimal point moves 3 places to the LEFT
5 .0 mg micrograms

10. Micrograms and milligrams
1 milligram = 1000 micrograms
0.125mg = 125 micrograms
0.025mg = 25 micrograms

11. 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

12. 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

13. 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

14. 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%

15. ‘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

16. 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

17. Question 1
What is the concentration (in mg/ml) of an 8.4% sodium bicarbonate infusion?
= 8.4g in 100ml
= 84 mg/ml

18. 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

19. 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

20. 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

21. 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)

22. 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

23. Question 4 Dose prescribed is 3 micrograms/kg/min
Patient's weight = 85 Kg
What is the dose in microgram/min?
= 255 micrograms/min

24. Question 5
You need to give a treatment dose of tinzaparin (175 units/kg) to a patient who is 85kg
You have syringes giving units/ml which can measure quantities to 0.05ml. What volume should you prescribe?
175 x 85 = units
14875 ÷20000 = 0.74 ml
Therefore prescribe 0.75ml

25. 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)

26. 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

27. 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

28. 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

29. 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

30. 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?
x 2 x 68 x 60
800 x 1000
Amount of Drug = 5 ml/hour

31. 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 = mcg/minute
3750x60 = mcg/hour = 225mg/hour
2.5g in 250ml = 10mg/ml
225/10 = 22.5ml/hour

32. 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

33. 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?
x 50 x 75 x 60
2.5x 1000x 1000
= 22.5 ml/hour

34. 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