What is the formula for intravenous injection?

The provided reference focuses on calculating intravenous (IV) infusion rates, not a general formula for intravenous injections. Therefore, I will provide a formula to calculate the IV infusion rate based on the information given in the reference.

The reference details a method for determining the ml/hr infusion rate based on patient weight, desired dosage, and IV strength. Let's rephrase the question as: "How do you calculate the intravenous infusion rate (ml/hr) for a medication?"

Here's a breakdown of the calculation, adapted from the reference:

Calculating IV Infusion Rate (ml/hr)

Here's a step-by-step approach to calculate the correct IV infusion rate:

1. Determine Patient Weight (kg):

   • If the weight is in pounds (lbs), convert it to kilograms (kg) using the conversion factor: 1 kg = 2.2 lbs.
   • Example: 48 kg (as seen in the reference where 1 x 2.2 = 2.2, implying 48 kg patient weight derived from an initial weight in pounds).

2. Determine Desired Dosage:

   • This is the amount of medication the doctor wants the patient to receive per unit of time, usually expressed as mcg/kg/minute.
   • Example: 70 mcg/kg/minute

3. Determine IV Strength (Concentration):

   • This is the amount of medication present in a specific volume of the IV solution (e.g., mg/ml or mcg/ml). You'll need this to determine how much volume of the IV solution contains the correct dosage.

4. Convert Units as Needed:

   • Ensure all units are compatible before performing calculations. For instance, convert mg to mcg if necessary (1 mg = 1000 mcg).
   • Convert minutes to hours if your final answer needs to be in ml/hr.

5. Reduce the Units:

   • Perform dimensional analysis to cancel out unwanted units, ensuring you're left with ml/hr. This involves setting up the equation so that units in the numerator and denominator cancel each other out.

6. Perform the Math:

The general formula derived from the steps above can be represented as:

Infusion Rate (ml/hr) = (Patient Weight (kg) * Dosage (mcg/kg/min) * 60 min/hr) / Concentration (mcg/ml)

Example:

Let's say we have the following information:

• Patient Weight: 48 kg
• Desired Dosage: 70 mcg/kg/minute
• IV Strength: 1600 mcg/ml

Calculation:

Infusion Rate (ml/hr) = (48 kg * 70 mcg/kg/min * 60 min/hr) / 1600 mcg/ml
= (201600 mcg/hr) / (1600 mcg/ml)
= 126 ml/hr

Therefore, the IV infusion rate should be 126 ml/hr.