Medication Dosage Calculations and Medical Mathematics

Drug Dosage Formula and Calculations

  • The fundamental formula for calculating medication volume or tablets is: DesireHave×Quantity=Amount to Administer\frac{\text{Desire}}{\text{Have}} \times \text{Quantity} = \text{Amount to Administer}.

  • Dosage calculation examples from the transcript include:

    • Cimetidine HCl (Tagamet): Administering 100 mg100\,mg IM when specific label concentrations are provided.

    • Clindamycin: Calculating volume for a 300 mg300\,mg PO dose at 75 mg/mL75\,mg/mL.

    • Heparin: Calculating volume for 6,000 units6,000\,units or 1,000 units1,000\,units based on available concentrations like 10,000 units/mL10,000\,units/mL or 3,500 units/mL3,500\,units/mL.

    • Digoxin: Determining tablet count for 0.25 mg0.25\,mg dose using 0.125 mg0.125\,mg tablets.

    • Morphine: Calculating 15 mg15\,mg IM dose using 10 mg/mL10\,mg/mL supply.

Weight-Based Dosing and Conversions

  • To calculate weight-based dosages, first convert the patient's weight from pounds to kilograms using the ratio: 1 kg=2.2 lb1\,kg = 2.2\,lb.

  • Daily dosage calculation: Patient weight in kg×mg/kg/day=Total Daily Dosage\text{Patient weight in kg} \times \text{mg/kg/day} = \text{Total Daily Dosage}.

  • Individual dose calculation: Total Daily DosageNumber of doses per day=Amount per Dose\frac{\text{Total Daily Dosage}}{\text{Number of doses per day}} = \text{Amount per Dose}.

  • Safe dosage range screening involves verifying if the ordered total daily amount falls between established limits (e.g., 45 to 65 mg/kg/day45\text{ to }65\,mg/kg/day).

Metric and Measurement Conversions

  • Standard metric conversions:

    • 1 g=1,000 mg1\,g = 1,000\,mg

    • 1 mg=1,000 mcg1\,mg = 1,000\,mcg

    • 1 L=1,000 mL1\,L = 1,000\,mL

    • 3,550 mL=3.55 L3,550\,mL = 3.55\,L

  • Household to metric conversion:

    • 1 fl oz=30 mL1\,fl\,oz = 30\,mL

    • 2 fl oz=60 mL2\,fl\,oz = 60\,mL

  • Roman Numerals: The number 1515 is represented as XVXV.

Medical Abbreviations and Administration Timing

  • Routes of Administration:

    • PO (Per Os): Administered into the mouth.

    • IM: Intramuscular.

  • Frequency and Timing Abbreviations:

    • BID: Twice a day (e.g., 09000900 and 21002100).

    • QID: Four times a day.

    • TID: Three times a day.

    • STAT: Immediately.

    • HS (Hora Somni): At bedtime (e.g., 9 PM9\,PM or 21002100).

    • PRN: As needed.

  • Military Time Conversion: 14001400 is equivalent to 2:00 PM2:00\,PM on a traditional clock.

IV Infusions and Solutions

  • Infusion Duration: To find the time required for a specific volume to infuse at a set rate: Total Volume (mL)Rate (mL/hr)=Total Time (hr)\frac{\text{Total Volume (mL)}}{\text{Rate (mL/hr)}} = \text{Total Time (hr)}.

  • Example: 1,500 mL1,500\,mL at 125 mL/hr125\,mL/hr will take 12 hours12\,hours to infuse.

  • Solutions: Mix calculations for percentages, such as preparing 250 mL250\,mL of a 40%40\% Boost solution.

  • Reconstitution: The process of adding a specific volume of diluent (e.g., sterile water) to a powder vial to reach a target concentration for injection.