Drug Calculations

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Drug Calculations
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Drug Administration

• Five rights of administration
• Right drug
• Right dose
• Right route
• Right time
• Right patient
• Prescriber, pharmacist, and nurse are equally
  responsible for safety of order

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Drug Orders

• Patients name
• Drug name (trade or generic)
• Dose
• Route of administration (oral, intravenous)
• Frequency of administration (i.e. daily, every 4
  hours, etc.)

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Medication Order Examples(omitting name of pt)

• Augmentin 250 mg po q12hr x 7D
• Digoxin 0.125 mg po qD
• Inderal 20 mg ii tabs po BID
• Azithromycin 500 mg IV qD x1, then azithromycin
  250 mg IV qD x 4
• Cortisporin Otic susp ii gtt AU TID and HS
• NS 100 cc/hr IV x 1 L then KVO

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Systems of Measurement

• Metric most common
• Apothecary very old, phasing out, you may see
  grains
• Household phasing out, you may teaspoon and
  ounce

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Metric System

• Base unit is meter for length, gram for weight,
  liter for volume
• Common prefixes are kilo-, centi-, milli-, micro-
• Each unit is 3 decimal places away from next
  unit. Exception centi- (100th of base, 2
  decimal places away from meter)
• Ex) kilometer, meter, centimeter, millimeter,
  micrometer
• Decimals only (round dose to nearest tenth), no
  fractions
• 1 mL 1 cubic centimeter (cc)

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Converting From One Unit to Another Within Metric
System

• Remember that kilo-, base unit, milli-, and
  micro- are each 3 decimal places away from next
  unit
• Kilo- is 3 decimal places away from the base unit
• Milli- is 3 decimal places away from the base
  unit in one direction, and 3 decimal places away
  from micro- in the other direction
• To know which direction to move the decimal,
  remember LMNOPQRS (L stands for larger, S stands
  for smaller)
• If you are converting from larger units to
  smaller, move decimal to the right
• If you are converting from smaller units to
  larger, move decimal to the left

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Converting From One Unit to Another Within Metric
System

• Ex Convert 500 mL to L
• Milliliter is 3 decimal places away from liter
• Milliliters are SMALLER than liters, so move 3
  places to the LEFT
• 500 mL 0.5 L
• Ex Convert 0.3 g to mg
• gram is 3 decimal places away from milligram
• Grams are LARGER than milligrams, so move 3
  places to the RIGHT
• 0.3 g 300 mg

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Apothecary System

• Uses roman numerals (IV, iv), fractions (not
  decimals), symbols
• Most common units are grains (gr), ounce
• Unit of measure precedes numeric value (gr ¼, not
  0.25 gr)
• gr i 60 mg

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Converting from Grains to Milligrams (Apothecary
system to Metric system)

• gr i 60 mg
• gr ¼ x mg
• gr ¼ ¼ x 60/1 mg
• gr ¼ 15 mg
• gr 1/30 x mg
• gr 1/30 1/30 x 60/1 mg
• gr 1/30 2 mg

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Household System

• Uses Arabic numbers and fractions
• Abbreviation follows amount
• Ex) 1/2 t (1/2 teaspoon)
• 1lb 16oz
• 2.2lb 1kg
• 1t 60 gtt (drops) 5mL

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Converting out of Household System to Metric
System

• Convert 30lb to kg
• 1lb 2.2lb 30 2.2 13.6kg
• Convert ½ t to mL
• 1t 5mL ½ x 5 5/2mL 2.5mL
• Convert 3t to mL
• 1t 5mL 3t 15 mL

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Calculate Oral Dosages

• Step 1 convert all units of measurement to same
  system and to same size units. Convert larger
  units to smaller units.
• Step 2 use formula to calculate dosage
• D(desired)/H(have) x Q (quantity) X (amount)
• When solving dosage problems for drugs supplied
  in tablets or capsules, Q is always 1, because
  supply dosage is per 1 tablet or capsule

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Calculate Oral Dosages

• Ordered Lopressor 100 mg po BID
• Available Lopressor 50 mg tablets
• Calculate one dose.
• Step 1 Convert. Same system (metric) and same
  unit size (mg) are used. No conversion necessary.
• Step 2 Calculate. (D/H) x Q X
• (100 mg/50 mg) x 1 tablet 2 x 1 tablet 2
  tabs
• Answer Give 2 tablets per dose.

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Calculate Oral Dosages

• Ordered Ampicillin 0.5 g po QID
• Available Ampicillin 250 mg capsules
• Calculate one dose.
• Step 1 Convert. Same system (metric), but
  different unit sizes (g and mg).
• 0.5 g 500 mg
• Step 2 Calculate. (D/H) x Q X
• (500 mg/ 250 mg) x 1 capsule 2 x 1 cap 2
  capsules
• Answer Give 2 capsules.

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Calculate Oral Dosages

• OrderedBetapen-VK 100 mg po QID
• Available Betapen-VK 250 mg/5mL
• Calculate one dose.
• Step 1 Convert. Same system, same unit. No
  conversion necessary.
• Step 2 Calculate. (D/H) x Q X
• (100 mg/250mg) x 5mL 2/5 x 5mL 2 mL
• Answer Give 2 mL.

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Calculate Oral Dosages

• Ordered Morphine Sulfate gr 1/6 IM q 3-4hr prn
  pain
• Available Morphine Sulfate 15 mg per mL
• Calculate one dose.
• Step 1 Convert (different systems)
• gr i 60 mg
• gr 1/6 1/6 x 60/1 10 mg
• Step 2 Calculate. (D/H) x Q X
• (10 mg/15mg) x 1mL (2/5 x 1 mL) 2/5 mL 0.7
  mL
• Answer Give 0.7 mL

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Pediatric Oral Dosages

• Drugs for infants and children are based on body
  weight (such as mg/kg)
• Step 1 Convert childs weight from lbs to kgs
• Step 2 Calculate dosage in mg/kg or mcg/kg as
  recommended by drug reference
• Step 3 Compare ordered dose to recommended dose
  and decide if ordered dosage is safe
• Step 4 If safe, calculate dose. If unsafe,
  contact prescriber

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Calculate Pediatric Oral DosagesSingle dosage
drugs (one time only or prn)

• Ordered Morphine sulfate 1.8 mg IM stat
• Available Morphine sulfate 2 mg/mL
• Weight 79 lbs
• Calculate one dose.
• Step 1 Convert lb to kg. 1 kg 2.2 lbs
• 79 2.2 35.91 35.9 kg
• Step 2 Calculate dose based on references
  recommendation
• Drug reference states IM dose is 0.05mg/kg/dose
• 0.05 mg x 35.9 kg 1.79 mg 1.8 mg/ dose
• Step 3 Is order safe? Yes.
• Step 4 Calculate one dose
• Convert. No conversion necessary.
• Calculate. (D/H) x Q X (1.8mg/2mg) x 1
  mL 0.9 mL x 1 mL 0.9mL
• Answer Give 0.9 mL IM stat.

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Calculate Pediatric Oral DosagesSingle Dosage
Range (recommended dosage of single dose med
indicates min and max range)

• Ordered Vistaril 10 mg IM q 4-6hr prn nausea
• Available Vistaril 25 mg/mL
• Weight 44 lbs
• Calculate one dose.
• Step 1 Convert lb to kg. 1 kg 2.2 lbs
• 44 2.2 20 kg
• Step 2 Calculate dose based on references
  recommendation- Drug reference states IM dose is
  0.05 mg -1 mg/kg/dose q 4-6hr prn
• Min per dose 0.5 mg x 20 kg 10 mg/dose
• Max per dose 1 mg x 20 kg 20 mg/dose
• Step 3 Is order safe? Yes, it falls within
  range.
• Step 4 Calculate one dose
• Convert. No conversion necessary.
• Calculate. (D/H) x Q X (10mg/25mg) x 1
  mL 2/5 x 1 mL
• 2/5 mL 0.4 mL
• Answer Give 0.4 mL IM

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Calculate Pediatric Oral DosagesRoutine/Round-the
-Clock Drugs (Recommended as total daily dosage
mg/kg/day divided into some number of doses)

• Ordered Ceclor 100 mg po TID
• Available Ceclor 125 mg/5ml
• Weight 33 lbs
• Calculate one dose.
• Step 1 Convert lb to kg. 1 kg 2.2 lbs
• 33 2.2 15kg
• Step 2 Calculate dose based on references
  recommendation- Drug reference indicates
  20mg/kg/day in three divided doses
• Calculate total daily dosage 20mg x 15kg 300
  mg/day
• Then, divide total daily dose into 3 doses 300
  3 doses 100 mg/dose
• Step 3 Is order safe? Yes
• Step 4 Calculate one dose
• Convert. No conversion necessary.
• Calculate. (D/H) x Q X (100 mg/125 mg) x
  5 mL 4/5 x 5 mL 4 mLs
• Answer Give 4 mL Ceclor

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Calculate Pediatric Oral DosagesRecommended Min
and Max mg/kg range per day divided into some
number of doses

• Ordered Amoxil 200 mg po q8hr
• Available Amoxil 100mg/5mL
• Weight 22lb
• Calculate one dose.
• Step 1 Convert lb to kg. 1 kg 2.2 lbs
• 22 2.2 10 kg
• Step 2 Calculate dose based on references
  recommendation- Drug reference states
  20-40mg/kg/day in divided doses every 8hr
• Min total daily dose 20mg x 10kg 200 mg/day
• Min dosage for each single use 200 3 doses
  66.7 mg/dose
• Max total daily dose 40mg x 10kg 400mg/day
• Max dosage for each single use 400 3 doses
  133.3 mg/dose
• Step 3 Is order safe? No. Ordered dose exceeds
  max dosage for each single use as well as max
  total daily dose. Contact prescriber.

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Calculate Pediatric Oral DosagesTotal Daily
Dosage range per kg with max daily allowance
(i.e., mg/kg/day recommended, with max allowable
total amount per day)

• Ordered cefazolin 2.1g IV q8hr
• Available cefazolin 0.72g in 50 cc NS for IV use
  only
• Weight 95 lb
• Calculate one dose.
• Step 1 Convert lb to kg. 1 kg 2.2 lbs
• 95 2.2 43.2kg
• Step 2 Calculate dose based on references
  recommendation- Drug reference states IM or IV
  dosage is 50-100mg/kg/day divided every 8hr max
  dosage is 6g/day
• Min mg/kg/day 50 x 43.2 2160mg/day
  2.16g/day
• Min mg/dose 2160 3 doses 720mg/dose
  0.72g/dose
• Max mg/kg/day 100 x 43.2 4320mg/day
  4.32g/day
• Max mg/dose 4320 3 doses 1440mg/dose
  1.44g/dose
• Step 3 Is order safe? No. Ordered dose exceeds
  max g/dose and max g/day. Contact prescriber.