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# Dosage Calculation Demystified: Understanding the Basics and Beyond

As a healthcare professional, one of the most important responsibilities is ensuring that patients receive the right amount of medication at the right time. Accurate dosage calculation is a critical part of this process, as administering too little or too much medication can have serious consequences for patient health.

The universal formula: Examples:

1. Basic Calculation

Administer heparin 5,000 units I.V. push. Available is heparin 10,000 units/mL. How many mL will you need to administer to achieve a 5,000 unit dose?

D/H x Q = Dose

5,000 units / 10,000 units x 1 mL = 0.5 mL

2. Calculations in units/hour

Heparin 20,000 units in 500 mL D5W is ordered to run at 1,000 units/hour. How will the I.V. pump be set?

20,000 units / 500 mL = 40 units/ml

D/H x Q = Dose

1,000 units / 40 units x 1 mL = 25 mL/hour

Example:

Heparin 20,000 units in 500 mL D5W is infusing at 20 mL/hour. At how many units/hour is the heparin infusing?

20,000 units / 500 mL = 40 units/mL

40 units / 1 mL x 20 mL / 1 hour = 800 units/hour

Dosage by weight:

This formula is used to calculate a patient's medication dosage based on their weight. The formula is: Dose (in mg) = Weight (in kg) x Desired Dose (in mg/kg)

Let's say you have a patient who weighs 70 kilograms (kg), and the medication they need is prescribed at a dosage of 0.1 milligrams (mg) per kilogram of body weight.

The formula you would use to calculate the patient's dosage is:

Dosage = patient weight (in kg) x dosage per kg

So in this case, the calculation would look like this:

Dosage = 70 kg x 0.1 mg/kg Dosage = 7 mg

Therefore, the patient would require a dosage of 7 mg of the medication based on their weight.

Dosage by body surface area:

This formula is used to calculate a patient's medication dosage based on their body surface area. The formula is: Dose (in mg) = Body Surface Area (in m2) x Desired Dose (in mg/m2)

Let's say you have a patient with a body surface area (BSA) of 1.8 square meters (m²), and the medication they need is prescribed at a dosage of 2 milligrams (mg) per square meter of body surface area.

The formula you would use to calculate the patient's dosage is:

Dosage = BSA x dosage per m²

So in this case, the calculation would look like this:

Dosage = 1.8 m² x 2 mg/m² Dosage = 3.6 mg

Therefore, the patient would require a dosage of 3.6 mg of the medication based on their body surface area.

Flow rate for IV infusion:

This formula is used to calculate the flow rate for an IV infusion. The formula is: Flow rate (in mL/hour) = Total Volume (in mL) / Time (in hours)

Let's say you have a patient who needs to receive 500 milliliters (ml) of IV fluid over the course of 4 hours. To calculate the flow rate, you would use the following formula:

Flow rate (in mL/hour) = Total Volume (in mL) / Time (in hours)

So in this case, the calculation would look like this:

Flow rate (in mL/hour) = 500 mL / 4 hours Flow rate (in mL/hour) = 125 mL/hour

Therefore, the IV infusion should be set at a flow rate of 125 mL/hour to deliver the 500 mL of fluid over the 4-hour time period.

Flow rate for IV infusion:

The formula to get the flow rate of IV infusion for the gtts/min is: Flow rate (in gtts/min) = (Volume to be infused in ml ÷ Time for infusion in minutes) × Drop factor

Let's say you have a patient who needs to receive 1000 milliliters (ml) of IV fluid over the course of 6 hours. The IV tubing has a drop factor of 15 drops per milliliter (15 gtts/ml).

To calculate the flow rate, you would use the following formula:

Flow rate (in gtts/min) = (Volume to be infused in ml ÷ Time for infusion in minutes) × Drop factor

So in this case, the calculation would look like this:

Flow rate (in gtts/min) = (1000 ml ÷ 360 minutes) × 15 gtts/ml Flow rate (in gtts/min) = 41.6 or 42 gtts/min (rounded up to the nearest whole number)

Pediatric dosage calculation:

Pediatric dosage calculation is based on the child's weight and is usually calculated in mg/kg/day. The formula is: Total daily dose (in mg/kg/day) = Desired dose (in mg/kg/day) x Weight (in kg)

Let's say a pediatrician has prescribed a medication to a child at a dosage of 10 milligrams per kilogram per day (10 mg/kg/day), and the child weighs 20 kilograms. To calculate the total daily dose, you would use the following formula:

Total daily dose (in mg/kg/day) = Desired dose (in mg/kg/day) x Weight (in kg)

So in this case, the calculation would look like this:

Total daily dose (in mg/kg/day) = 10 mg/kg/day x 20 kg Total daily dose (in mg/kg/day) = 200 mg/day

Therefore, the child would require a total daily dose of 200 milligrams of the medication based on their weight and the prescribed dosage.

After getting the patient's total daily dose follow the formula D/H x Q = Dose

Note: Watch out if you need to convert the patient's weight from lbs to kg wherein you have divide the patient's weight in lbs to 2.2 = weight in kg

You also need to check if they are asking you a divided dose:

Example:

A child is prescribed erythromycin. The recommended dosage is 40 mg/kg/day, 4 doses daily. If the child’s weight is 15 kg, calculate the size of a single dose.

15 kg × 40 mg/kg/day = 600 mg/day

Then

600 mg ÷ 4 doses = 150 mg/dose

Reconstitution of medication:

This formula is used to calculate the amount of diluent needed to reconstitute a medication. The formula is: Volume of diluent (in mL) = Final volume (in mL) - Volume of medication (in mL)

Let's say a medication comes in a vial that contains 1.5 milligrams (mg) of medication in 0.5 milliliters (mL) of solution. The prescribed dosage is 2.5 mg, and the medication needs to be reconstituted with additional diluent to a total volume of 1 mL.

To calculate the volume of diluent needed, you would use the following formula:

Volume of diluent (in mL) = Final volume (in mL) - Volume of medication (in mL)

So in this case, the calculation would look like this:

Volume of diluent (in mL) = 1 mL - 0.5 mL

Volume of diluent (in mL) = 0.5 mL

Therefore, 0.5 mL of diluent is needed to reconstitute the medication to the desired volume of 1 mL.

Concentration of medication:

This formula is used to calculate the concentration of a medication. The formula is: Concentration (in mg/mL) = Total amount of medication (in mg) / Total volume of diluent (in mL)

Let's say you have a vial of medication that contains a total of 500 milligrams (mg) of medication, and it needs to be diluted with 100 milliliters (mL) of diluent to create the desired concentration.

To calculate the concentration, you would use the following formula:

Concentration (in mg/mL) = Total amount of medication (in mg) / Total volume of diluent (in mL)

So in this case, the calculation would look like this:

Concentration (in mg/mL) = 500 mg / 100 mL

Concentration (in mg/mL) = 5 mg/mL

Therefore, the concentration of the medication is 5 mg/mL.

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