← Pharmacy Calculations – PTCB Exam Prep Flashcards

PTCB Pharmacy Technician Certification Study Guide

Key concepts, definitions, and exam tips organized by topic.

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Pharmacy Calculations – PTCB Exam Prep Study Guide


Overview

Pharmacy calculations are a critical component of the PTCB exam, testing your ability to accurately perform dosage, concentration, flow rate, dilution, and business math. Errors in pharmacy calculations can directly harm patients, making precision and formula mastery essential. This guide consolidates core concepts, formulas, and common pitfalls to prepare you for exam success.


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Section 1: Dosage Calculations


Key Concepts & Formulas


Dosage calculations require unit conversions, weight-based dosing, and ratio-proportion methods.


Essential Conversion:

  • • Pounds to Kilograms: Divide lbs by 2.2

    • - Example: 176 lbs ÷ 2.2 = 80 kg


    Weight-Based Dosing Formula:

    ```

    Dose (mg) = Weight (kg) × Dose (mg/kg)

    ```

  • • Convert lbs → kg FIRST, then multiply by the ordered dose

    • Ratio-Proportion Method:

    ```

    Known concentration / Known volume = Desired dose / Unknown volume

    (C1/V1 = C2/V2)

    ```


    Calculating Total Volume for a Course of Treatment:

    ```

    Total Volume = Dose volume × Doses per day × Number of days

    ```


    Step-by-Step Examples


    | Scenario | Key Steps |

    |---|---|

    | Weight-based pediatric dose | lbs ÷ 2.2 → kg × mg/kg → total daily dose ÷ # of doses |

    | Tablets per dose | Convert g → mg, then mg needed ÷ mg/tablet |

    | Total course volume | mL/dose × doses/day × days |

    | Solution dose | (Volume ordered ÷ Volume per unit) × mg per unit |


    Key Terms

  • • Weight-based dosing – Dose calculated per kilogram of body weight
  • • Divided doses – Total daily dose split into individual administrations
  • • Ratio-proportion – Setting two equivalent ratios equal to solve for an unknown
  • • 1 teaspoon (tsp) = 5 mL
  • • 1 tablespoon (tbsp) = 15 mL

    • Watch Out For

    > ⚠️ Always convert pounds to kilograms BEFORE calculating a weight-based dose. Forgetting this step is the most common error.


    > ⚠️ Unit mismatches: Convert grams to milligrams (× 1000) or milligrams to grams (÷ 1000) before dividing by tablet strength.


    > ⚠️ Divided dose vs. total daily dose: The exam may ask for the per-dose amount — always divide total daily dose by the number of doses.


    ---


    Section 2: Concentrations & Percentages


    Key Concepts & Formulas


    Percent Weight-in-Volume (% w/v):

    ```

    % w/v = grams of solute per 100 mL of solution

    ```

  • • 5% = 5 g per 100 mL
  • • 0.9% NS = 0.9 g NaCl per 100 mL = 9 g per 1000 mL

    • Ratio Strength:

    ```

    1:1000 = 1 g per 1000 mL = 0.001 g/mL = 1 mg/mL

    1:500 = 1 g per 500 mL = 0.002 g/mL = 2 mg/mL

    1:200 = 1 g per 200 mL = 0.5%

    ```


    Converting Ratio Strength to Percentage:

    ```

    % = (1 ÷ ratio denominator) × 100

    ```


    Dilution Formula (C1V1 = C2V2):

    ```

    (Concentration 1)(Volume 1) = (Concentration 2)(Volume 2)

    ```

  • • Use this to find stock solution volume needed or final volume after dilution

    • Milliequivalents (mEq):

    ```

    For monovalent ions: mEq = mmol

    Grams = mmol × molecular weight (g/mol) ÷ 1000

    ```


    Key Terms

  • • % w/v – grams of drug per 100 mL solution
  • • % w/w – grams of drug per 100 g of preparation (creams/ointments)
  • • Ratio strength – concentration expressed as 1 part drug per X parts solution
  • • Stock solution – concentrated solution used to prepare a more dilute solution
  • • mEq (milliequivalent) – unit of measure for electrolyte concentration
  • • D5W – 5% dextrose in water (5 g dextrose per 100 mL)
  • • NS (Normal Saline) – 0.9% NaCl solution

    • Watch Out For

    > ⚠️ When using C1V1 = C2V2, V2 is the TOTAL final volume — subtract V1 to find how much diluent (water) to add.


    > ⚠️ Ratio strength direction: 1:1000 is NOT 1000 g per 1 mL — it is always 1 part drug to X parts solution.


    > ⚠️ For creams and ointments, use weight (grams), not volume. Apply the same percentage formula: Total weight × decimal percent = grams of active ingredient.


    ---


    Section 3: IV Flow Rates & Infusions


    Key Concepts & Formulas


    Basic Flow Rate:

    ```

    Flow rate (mL/hr) = Total volume (mL) ÷ Infusion time (hrs)

    ```


    Drip Rate (gtt/min):

    ```

    Drip rate = [Flow rate (mL/hr) × Drop factor (gtt/mL)] ÷ 60 min

    ```


    Time Remaining:

    ```

    Time (hrs) = Volume remaining (mL) ÷ Flow rate (mL/hr)

    ```


    Weight-Based IV Dosing (e.g., dopamine, heparin):

    ```

    Step 1: Dose (mcg/min) = dose (mcg/kg/min) × weight (kg)

    Step 2: Convert to per hour: mcg/min × 60

    Step 3: Convert units if needed (mcg → mg ÷ 1000)

    Step 4: Find bag concentration: mg ÷ mL = mg/mL

    Step 5: Rate (mL/hr) = dose per hour ÷ concentration

    ```


    Heparin Infusion Rate:

    ```

    Rate (mL/hr) = Ordered units/hr ÷ Concentration (units/mL)

    ```


    Microdrip Shortcut:

    ```

    With a 60 gtt/mL microdrip set: gtt/min = mL/hr (numerically equal)

    ```


    Common Drop Factors


    | Tubing Type | Drop Factor |

    |---|---|

    | Macrodrip (standard) | 10, 15, or 20 gtt/mL |

    | Microdrip | 60 gtt/mL |


    Key Terms

  • • Flow rate – Volume of fluid infused per unit time (mL/hr)
  • • Drip rate – Number of drops per minute (gtt/min)
  • • Drop factor – Number of drops per mL delivered by IV tubing
  • • Microdrip – 60 gtt/mL tubing used for precise/low-volume infusions
  • • mcg/kg/min – Common unit for critical care drips (e.g., dopamine, norepinephrine)
  • • Infusion concentration – Total drug ÷ Total volume of bag

    • Watch Out For

    > ⚠️ Unit conversions in IV drips: mcg/min must be converted to mg/hr before dividing by bag concentration in mg/mL. Watch for mcg vs. mg discrepancies.


    > ⚠️ Always divide by 60 when converting mL/hr to gtt/min (there are 60 minutes in an hour).


    > ⚠️ The microdrip shortcut ONLY works because 60 gtt/mL ÷ 60 min = 1, making gtt/min = mL/hr numerically.


    ---


    Section 4: Ratio, Proportion & Dilutions


    Key Concepts & Formulas


    Dilution Using C1V1 = C2V2:

    ```

    (Higher concentration)(Volume of stock) = (Lower concentration)(Final volume)

    Solve for unknown variable

    ```

  • • Volume of diluent to add = Final volume − Stock volume used

    • 1:X Dilution Interpretation:

    ```

    1:10 dilution = 1 part stock in 10 parts TOTAL

    Stock needed = Total volume × (1/10)

    ```


    Alligation Method (mixing two concentrations to achieve a target):

    ```

    Step 1: Place higher % top-left, lower % bottom-left, desired % in center

    Step 2: Subtract diagonally (always subtract smaller from larger)

    Higher % − Desired % = Parts of lower concentration

    Desired % − Lower % = Parts of higher concentration

    Step 3: Total parts = sum of both parts

    Step 4: Volume of each = (Parts / Total parts) × Final volume

    ```


    Alligation Visual Template

    ```

    Higher % \ / Parts of lower = (Higher − Desired)

    Desired %

    Lower % / \ Parts of higher = (Desired − Lower)

    ```


    Key Terms

  • • Alligation – Mathematical method to determine proportions needed to mix two concentrations
  • • Stock solution – Concentrated source solution before dilution
  • • Diluent – Substance used to dilute (usually water or NS)
  • • 1:X ratio dilution – 1 part drug in X parts total volume
  • • w/v ratio – Weight (g) per volume (mL) expression of concentration

    • Watch Out For

    > ⚠️ C1V1 = C2V2 gives you TOTAL final volume (V2) — you must subtract V1 to find how much water to add separately.


    > ⚠️ Alligation subtraction is always diagonal and always positive — subtract smaller from larger regardless of direction.


    > ⚠️ 1:10 dilution means 1 part in 10 total, NOT 1 part added to 10 parts. This is a common source of error.


    ---


    Section 5: Business & Compensation Calculations


    Key Concepts & Formulas


    Markup (based on cost):

    ```

    Selling Price = Cost + (Cost × Markup %)

    Markup amount = Cost × Markup %

    ```


    Gross Profit Margin (based on selling price):

    ```

    Profit Margin % = [(Selling Price − Cost) ÷ Selling Price] × 100

    ```

    > Note: Markup % uses cost as the base; profit margin % uses selling price as the base.


    AWP (Average Wholesale Price) Reimbursement:

    ```

    Reimbursement = AWP − (AWP × discount %) + Dispensing fee

    ```


    Patient Co-pay:

    ```

    Co-pay = Drug cost × Co-pay %

    ```


    Overtime Pay:

    ```

    Regular pay = Hours (≤40) × Hourly rate

    Overtime rate = Hourly rate × 1.5

    Overtime pay = Overtime hours × Overtime rate

    Gross pay = Regular pay + Overtime pay

    ```


    Key Terms

  • • AWP (Average Wholesale Price) – Reference price used for insurance reimbursement calculations
  • • Markup – Amount added to cost price; calculated as a percentage of the cost
  • • Profit margin – Profit as a percentage of the selling price
  • • Dispensing fee – Flat fee added to drug cost for pharmacist services
  • • Co-pay – Patient's share of prescription cost as flat amount or percentage
  • • Gross pay – Total earnings before taxes and deductions

    • Watch Out For

    > ⚠️ Markup vs. profit margin use different bases: Markup is calculated on COST; profit margin is calculated on SELLING PRICE. They will give different percentages even with the same numbers.


    > ⚠️ Overtime starts after 40 hours — only hours beyond 40 are paid at 1.5×, not the entire week's hours.


    > ⚠️ AWP reimbursement: Apply the discount to AWP first, THEN add the dispensing fee — do not apply the fee before discounting.


    ---


    Key Formulas Quick Reference Card


    | Calculation | Formula |

    |---|---|

    | lbs → kg | lbs ÷ 2.2 |

    | Weight-based dose | kg × mg/kg |

    | Tablets per dose | mg needed ÷ mg/tablet |

    | Total course volume | mL/dose × doses/day × days |

    | % w/v → g/mL | % ÷ 100 |

    | Ratio to % | (1 ÷ denominator) × 100 |

    | Dilution | C1V1 = C2V2 |

    | Flow rate | Total mL ÷ Total hrs |

    | Drip rate | (mL/hr × drop factor) ÷ 60 |

    | Markup price | Cost × (1 + markup %) |

    | Profit margin | [(Price − Cost) ÷ Price] × 100 |

    | Overtime pay | Regular hrs × rate + OT hrs × (rate × 1.5) |


    ---


    Quick Review Checklist


    Before your exam, confirm you can do the following:


  • • [ ] Convert pounds to kilograms (÷ 2.2) and apply to weight-based dosing
  • • [ ] Calculate total volume for a complete prescription course (mL/dose × doses/day × days)
  • • [ ] Use ratio-proportion to find volumes or doses from given concentrations
  • • [ ] Interpret % w/v, ratio strengths (1:X), and convert between them
  • • [ ] Apply C1V1 = C2V2 for dilutions and identify how much diluent to add
  • • [ ] Perform alligation to mix two concentrations to a desired strength
  • • [ ] Calculate IV flow rate (mL/hr) and drip rate (gtt/min) using drop factor
  • • [ ] Work through multi-step weight-based IV infusion problems (mcg/kg/min → mL/hr)
  • • [ ] Apply the microdrip shortcut (gtt/min = mL/hr with 60 gtt/mL tubing)
  • • [ ] Calculate heparin or other unit-based infusion rates
  • • [ ] Distinguish markup (based on cost) from profit margin (based on selling price)
  • • [ ] Calculate AWP reimbursement: subtract discount, then add dispensing fee
  • • [ ] Calculate overtime pay correctly (only hours >40 at 1.5× rate)
  • • [ ] Recognize and avoid the most common unit conversion errors (mcg/mg/g, mL/L)

    • ---


    Remember: On the PTCB exam, always verify your units, set up your formula before plugging in numbers, and double-check that your answer is reasonable in a clinical context.

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