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**Drug Calculations CWFS F1 Programme Safe Prescribing Module**

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**Drug calculations Principles Units Strengths Calculating dosages**

IV calculations

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**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:**

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

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**Units Always work in the same units !!! Avoid decimal points**

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

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**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

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**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

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**Converting a larger unit to a smaller unit**

Decimal point moves 3 places to the RIGHT mg microgram

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**Converting a smaller unit to a larger unit**

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

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**Micrograms and milligrams**

1 milligram = 1000 micrograms 0.125mg = 125 micrograms 0.025mg = 25 micrograms

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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

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**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

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**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

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**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%

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**‘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

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**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

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

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**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

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**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

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**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

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**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)

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**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

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**Question 4 Dose prescribed is 3 micrograms/kg/min**

Patient's weight = 85 Kg What is the dose in microgram/min? = 255 micrograms/min

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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

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**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)

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**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

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**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

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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

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**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

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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

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**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

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**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

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**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

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**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

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