dosage calculations

DOSAGE CALCULATION PRACTICE NOTES

TWO STEP MEDICATION ADMINISTRATION BASED ON WEIGHT

1. Weight Conversion
      - If the client's weight is presented in pounds (lbs), convert to kilograms (kg) by dividing the weight by 2.2.
      - Keep the result rounded to the nearest tenth.

2. Medication Units Conversion
      - Convert the ordered medication into the same units as the available medication, if applicable.

3. Calculating Dosage
      - Multiply the ordered medication amount by the client's weight in kg to obtain the dose to be given.

4. Equation Setup
      - Set up the equation with the ordered medication on the left and the available medication on the right-hand side.

EXAMPLE CALCULATIONS

Example 1: Vancomycin Administration

• Physician Order: Administer Vancomycin 10 mg/kg IVPB every 6 hours for diarrhea.

• Client Weight: 50 lbs

• Medication Available: Vancomycin 500 mg Reconstituted with 10 mL of sterile water.
  

Calculation:

1. Convert weight:
      - $ext{Weight in kg} = rac{50}{2.2} = 22.7 ext{ kg}$

2. Calculate ordered medication:
      - $ext{Dose} = 10 imes 22.7 = 227 ext{ mg}$

3. Set up equation based on available medication:
      - $rac{227 ext{ mg}}{ ext{X mL}} = rac{500 ext{ mg}}{10 ext{ mL}}$

4. Solve for X:
      - $X = rac{227 ext{ mg} imes 10 ext{ mL}}{500 ext{ mg}} = 4.5 ext{ mL}$

Example 2: Gentamicin Administration

• Physician Order: Administer Gentamicin 2.5 mg/kg IV every 8 hours for cellulitis.

• Client Weight: 60 lbs

• Medication Available: Gentamicin 40 mg/mL.
  

Calculation:

1. Convert weight:
      - $ext{Weight in kg} = rac{60}{2.2} = 27.3 ext{ kg}$

2. Calculate ordered medication:
      - $ext{Dose} = 2.5 imes 27.3 = 68.3 ext{ mg}$

3. Set up equation based on available medication:
      - $rac{68.3 ext{ mg}}{ ext{X mL}} = rac{40 ext{ mg}}{1 ext{ mL}}$

4. Solve for X:
      - $X = rac{68.3 ext{ mg} imes 1 ext{ mL}}{40 ext{ mg}} = 1.7 ext{ mL}$

Example 3: Ceftriaxone Administration

• Physician Order: Administer 5 mg/kg of Ceftriaxone to a client who weighs 144 lbs.

• Medication Available: Ceftriaxone 500 mg/2.5 mL.
  

Calculation:

1. Convert weight:
      - $ext{Weight in kg} = rac{144}{2.2} = 65.5 ext{ kg}$

2. Calculate ordered medication:
      - $ext{Dose} = 5 imes 65.5 = 327.5 ext{ mg}$

3. Set up equation based on available medication:
      - $rac{327.5 ext{ mg}}{ ext{X mL}} = rac{500 ext{ mg}}{2.5 ext{ mL}}$

4. Solve for X:
      - $X = rac{327.5 ext{ mg} imes 2.5 ext{ mL}}{500 ext{ mg}} = 1.6 ext{ mL}$

Example 4: Lovenox Administration

• Physician Order: Administer 10 mg/kg of Lovenox for a client weighing 320 lbs.

• Medication Available: Lovenox 80 mg/1 mL.
  

Calculation:

1. Convert weight:
      - $ext{Weight in kg} = rac{320}{2.2} = 145.5 ext{ kg}$

2. Calculate ordered medication:
      - $ext{Dose} = 10 imes 145.5 = 1455 ext{ mg}$

3. Set up equation based on available medication:
      - $rac{1455 ext{ mg}}{ ext{X mL}} = rac{80 ext{ mg}}{1 ext{ mL}}$

4. Solve for X:
      - $X = rac{1455 ext{ mg} imes 1 ext{ mL}}{80 ext{ mg}} = 18.2 ext{ mL}$

THREE STEP MEDICATION ADMINISTRATION PROBLEMS

Example 1: Propofol Administration

• Physician Order: Administer Propofol 250 mcg/min.

• Available Medication: Propofol 50 mg in 100 mL D5W.
  

Calculation:

1. Convert mcg to mg:
      - $250 ext{ mcg} = rac{250}{1000} = 0.25 ext{ mg}$

2. Setup to calculate from mg to ml/hr:
      - $ext{Rate (mL/hr)} = rac{0.25 ext{ mg/min} imes 60 ext{ min/hr}}{50 ext{ mg}} imes 100 ext{ mL} = 0.3 ext{ mL/hr}$

Example 2: Amrinone Administration

• Physician Order: Administer Amrinone 8 mcg/kg/min IV for congestive heart failure.

• Patient Weight: 198 lbs

• Available Medication: Amrinone 100 mg/100 mL in 0.9% Normal Saline.
  

Calculation:

1. Convert weight:
      - $ext{Weight in kg} = rac{198}{2.2} = 90 ext{ kg}$

2. Convert mcg to mg:
      - $8 ext{ mcg} = rac{8}{1000} = 0.008 ext{ mg}$

3. Calculate the hourly rate:
      - $ext{Rate} = 0.008 ext{ mg} imes 90 ext{ kg} imes 60 ext{ min/hr} = 43.2 ext{ mg/hr}$

4. Set up equation with available medication:
      - $rac{43.2 ext{ mg/hr}}{ ext{X mL/hr}} = rac{100 ext{ mg}}{100 ext{ mL}}$

5. Solve for X:
      - $X = rac{43.2 ext{ mg/hr} imes 100 ext{ mL}}{100 ext{ mg}} = 43.2 ext{ mL/hr}$

Example 3: Dobutamine Administration

• Physician Order: Administer Dobutamine 1.7 mcg/kg/min for a client weighing 68 kg.

• Available Medication: Dobutamine 200 mg in 250 mL 0.9%.
  

Calculation:

1. Convert mcg to mg:
      - $1.7 ext{ mcg} = rac{1.7}{1000} = 0.0017 ext{ mg}$

2. Calculate the hourly rate:
      - $ext{Rate} = 0.0017 ext{ mg} imes 68 ext{ kg} imes 60 ext{ min/hr} = 6.9 ext{ mg/hr}$

3. Set up equation with available medication:
      - $rac{6.9 ext{ mg/hr}}{ ext{X mL/hr}} = rac{200 ext{ mg}}{250 ext{ mL}}$

4. Solve for X:
      - $X = rac{6.9 ext{ mg/hr} imes 250 ext{ mL}}{200 ext{ mg}} = 8.625 ext{ mL/hr}$

Example 4: Ampicillin Administration

• Physician Order: Administer Ampicillin 100 mg/kg/day IV, divided into two doses.

• Client Weight: 3.778 kg

• Available Medication: Ampicillin 250 mg/3 mL.
  

Calculation:

1. Daily Dose Calculation:
      - $ext{Total Dose} = 100 ext{ mg} imes 3.778 ext{ kg} = 377.8 ext{ mg/day}$

2. Dose per administration:
      - $ext{Dose per administration} = rac{377.8 ext{ mg}}{2} = 188.9 ext{ mg}$

3. Set up equation with available medication:
      - $rac{188.9 ext{ mg}}{ ext{X mL}} = rac{250 ext{ mg}}{3 ext{ mL}}$

4. Solve for X:
      - $X = rac{188.9 ext{ mg} imes 3 ext{ mL}}{250 ext{ mg}} = 2.27 ext{ mL}$

EXTRA PRACTICE

• Engage with another student and complete the dosage calculation quiz found in the Module 4 class folder.