Sir M.Farooque Soomro

RN, BSN (LUMHS), B.Com (UOS)

Calculations of Medication for Various Routes

Unit VI

MATHEMATICS FOR NURSES

Generic BSN 2^st year

3^st semester

Objective

At the end of this unit, students will be able to;

1. Interpreting scales on syringes
2. Oral medications
3. Parenteral medications
4. Special types of injections

Understanding syringe adjustments is important for correct medication administration.

Interpreting scales on syringes�Objective 01

Types of syringes

• 5-ml Syringe
• Commonly used for larger volume injections.
• Markings typically increment by 0.2 ml.
• Example: A dose of 4.6 ml will be measured between the 4.4 ml and 4.8 ml markings.
• 3-ml Syringe
• Frequently used for smaller, precise volumes.
• Markings typically increment by 0.1 ml.
• Example: A dose of 1.7 ml will be measured between the 1.6 ml and 1.8 ml markings.
• Insulin Syringe (1-ml, marked in units)
• Used specifically for insulin administration.
• Typically marked in units (U-100 insulin = 100 units per ml).
• Example: A dose of 35 units is measured by aligning with the 35 marking.

Oral Medications�Objective 02

Oral medications include solids (e.g., tablets, capsules), liquids (e.g., syrups, suspensions), and powders (reconstituted before administration). Accurate calculations ensure the correct dose is delivered, maintaining safety and efficacy.

1. Solid Medications

• Solid medications are usually measured in number of tablets or capsules based on the prescribed dose.
• Example:
• Ordered: 250 mg
• Stock: 500 mg/tablet
• Formula = Desire Does x Tablet

Available Dose

2. Liquid Medications

• Liquid medications are measured in milliliters (ml) of Syrups or Suspensions.
• The volume to administer depends on the medication's concentration.
• Example:
• Ordered: 200 mg
• Stock: 100 mg/5 ml

3. Powder Medications

• Powder medications require mixing with a specified volume of diluent (e.g., sterile water) to create a liquid of known concentration.
• Example:
• Vial contains 1 g (1000 mg) of medication as powder.
• Reconstituted with 10 ml of sterile water to given 100 mg/ml.
• Ordered dose: 300 mg.
• Stock: 1000 mg/10 ml

Calculating dosages for Oral liquid & Powder medications

• The following formula is commonly used for dosage calculations:
• Dose to administer = Desire Does x Volume

Available Dose

Parenteral Medications� Objective 03

Parenteral medications involve drug administration through routes other than the digestive system. This guide focuses on interpreting syringe scales and calculating dosages for subcutaneous (SC), intramuscular (IM), and intravenous (IV) routes.

Subcutaneous Injections (SC)

• Delivered just beneath the skin, typically in small volumes (≤1 ml).
• Students will practice calculating the volume required for subcutaneous injections, considering the concentration of the drug in the vial.
• Example: Administer 0.5 ml of a medication if the ordered dose is 50 mg, and the vial contains 100 mg/ml.

Intramuscular Injections (IM)

• Similar to SC, but often larger volumes of medications are injected into the muscle tissue (up to 3 ml in adults).
• Example: Administer 2 ml of a medication if the ordered dose is 200 mg, and the vial contains 100 mg/ml.

Calculating dosages for S/C & I/M medications

• The following formula is commonly used for dosage calculations:
• Dose to administer = Desire Does x Volume

Available Dose

Intravenous Infusions (IV)

• Delivered directly into the bloodstream for immediate effect.
• IV medications may require volume-based calculations, or in some cases, continuous infusion rates, which can be calculated based on the ordered dose.
• When an IV infusion is ordered, it is often necessary to calculate how many milliliters per hour the medication should be infused.
• Dosages may require infusion rate calculations.

Intravenous Infusions (IV)

• This can be calculated using the formulas:

​

1. Infusion Rate (ml/hour) = Total Volume (ml)

Time (hours)

​

2. Drops per minute (gtt/min) = Total Volume (ml) × Drop Factor (gtt/ml)

Time (minutes)

Infusion Rate (ml/hour)

Example: Administer 500 ml over 4 hours.

Formula = Total volume

Time in hours

​

Rate (ml/hour) = 500 = 125ml/hour Or 125ml/h.

4

Drops per minute (gtt/min)

Example: Administer 500 ml over 4 hours. using a standard set (15gtts/ml).

Formula = Total volume x Drop factor

Time in mints

​

Drops per minute: 500 ×15= 31.25 drops/mint or ≈ 31 gtt/min

240

​

SELF PRACTICE

Practice # 01

• Medication order states: dose of Flagyl is 2000mg q8h. Available is 2000mg/5ml. How many ml will you give?

Practice # 02

• Dose ordered is 160 mg PO. Available is 0.08gm/tab. How many tab/s will you give?

Practice # 03

• Give gentamycin 4 mg/kg q8hrly. Available is 80 mg/2 ml. child’s weight is 5 kg. How many ml will you give each time?

Practice # 04

• IV fluid order states: give 1000 ml of Inj. D/S at 125 ml/hr, using the pediatric set. calculate the flow rate?

Practice # 05

• Order states: 1500 ml of Inj 5% D/W is to infused in 10 hours with regular set. Calculate
• a. How many ml/hr
• b. Flow rate

Practice # 06

• Give 1000 units of heparin in 500 ml of N/S to run over 06 hours, using the regular IV set
• a. Calculate ml/hr?
• b. How many drops/min?

Special Injection Problems �Objective 04

Calculate special types of liquid injection problems when stocks are ratio or percentage.

Stock as a Ratio

• Some medications are available in a stock solution with a specified ratio, such as 1:10 or 1:1000. Students will practice converting between ratios and standard units (e.g., mg, ml) to determine the appropriate dose.
• A 1:1000 solution means there is 1 g of active ingredient in 1000 ml of solution, or equivalently, 1 mg in 1 ml.

Understanding the Ratio

• Example: If the stock is 1:1000, and you need 500 mg of the medication:
• First, determine the concentration of the stock solution in mg/ml:
• Concentration = 1 g = 1000mg = 1mg/ml

1000ml 1000ml

​

• Next, calculate the volume needed:

​

• Volume to administer = Desire Dose = 500mg = 500ml Concentration 1mg/ml

Stock as a Percentage

• Medications can also be provided in percentage solutions (e.g., 5% solution). Students will learn to convert percentages to mg/ml to calculate the correct dose for injections or infusions.
• For example, a 5% solution means 5 g in 100 ml, or 50 mg/ml.
• Conversion Formula: concentration in mg/ml = Percentage × 10
• For a 5% solution: Concentration = 5 × 10 = 50 mg/ml

Understanding the Ratio:

• Example: If you need to administer 10 mg of a drug from a 5% solution:
• First, calculate the concentration of the solution: Concentration=50 mg/ml
• Next, determine the volume to administer:

​

• Volume to administer = Desire Dose = 10mg = 0.2ml Concentration 50mg/ml

Example #02

• Desire Dose needed = 10 mg
• Concentration = 50 mg/ml (from the 5% solution)
• To calculate the volume to administer, use the formula:

​

• Volume to administer = Desire Dose = 10mg = 0.2ml Concentration 50mg/ml

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If you have any…!

Questions…?

or

Confusion…?

Good luck