Pediatric Math Calculations: Fluid Maintenance, Caloric Intake, Dilutions and Concentrations

Math in pediatrics includes prior knowledge in addition to some new material. First, it would be important to know the essentials when it comes to calculating pediatric dosages. Keep in mind the following:

  • All medication dosages are rounded to TWO DECIMAL PLACES. Keep in mind that previous math exams mostly required one decimal place rounding.
  • Only round your final answer. If for example, you need to calculate a patient’s weight, don’t round that off to 2 decimal places.
  • IV infusion raes, daily fluid maintenance and calorie amounts are rounded to WHOLE NUMBERS.

It would be beneficial to know these conversions:

  • 1 kg = 2.2 lbs
  • 1 in = 2.54 cm
  • 1 oz = 30 mL
  • 1 lb = 16 oz
  • 1 cup = 240 mL
  • 1 L = 1000 mL
  • 1 mg = 1000 mcg
  • 1 g = 1000 mg
  • 1 mL = 1 gm (when weighing diapers)

Now to introduce the new material:

DAILY FLUID MAINTENANCE NEEDS

In pediatrics, patients are under strict intake and output as the potential for overload or deficit is high in this population. It is important for us to know the daily fluid requirements for each patient to maintain that balance between fluid consumption and release. This may be helpful to determine the amount of fluids a child needs orally without the need of IV infusions.

The following is the forumla:
First 10 kg of body weight – x 100 mL/kg/day
Second 10 kg of body weight – x 50 mL/kg/day
Anything above 20 kg of body weight – x 20 mL/kg/day

It may seem complicated, but it may be easier to see a visual. Let’s try out this problem:

A child weighs 18.60 lb. What would be this patient’s daily fluid maintenance needs?

First, you would need to convert pounds to kilograms. Recall that 1 kg = 2.2 lbs. Therefore, 18.60 lb/2.2 = 8.454545 kg (remember don’t round up at this point).
Next, looking at the forumla, multiply the first 10 kg by 100. (in this example, the patient weighs less than 10 kg, therefore you would only multiply his weight by 100 and you would have your answer.

8.454545 x 100 = 845.4545 = 845 mL/day (round to whole number)

Let’s try a heavier child.

A child weighs 45 kg. What would be this patient’s daily fluid maintenance needs?

Since this patient’s weight is in kg, we don’t need to convert.
Take the first 10 kg and multiply by 100. (10 x 100 = 1000 mL/day)
Now, you have “35 kg left over”. Multiply the second 10 kg by 50. (10 x 50 = 500 mL/day)
Now, you have “25 kg” left over”. Multiple this 25 by 20. (25 x 20 = 500 mL/day)
Finally, add all the values to get your total fluid maintenance needs for this child: 1000 + 500 + 500 + = 2000 mL/day.

Simple, right?!

CALORIC INTAKE

Daily caloric intake is a simple calculation. It is important to know how many calories in one ounce, how many ounces of formula in one bottle and how bottles consumed in 24 hours. Take this sample question:

Infant’s total intake for 24 hours: 4 bottles
Each bottle contained: 2 oz of forumla
Formula: 25 calories/oz
Infant weight: 2.5 kg
Infant age: 4 weeks
How many calories did the infant receive in 24 hours?
In the past 24 hours, did the infant receive calories at or above the minimum?

I bolded text above is the information needed for the first part of the question – the infant’s total caloric intake for 24 hours. All you need to do is simply multiply calories/oz by total oz in one bottle (25 calories/oz x 2 oz/bottle = 50 calories/bottle). Next multiple this value by the number of bottle the infant consumed in 24 hours (50 cals/bottle x 4 bottles/day = 200 calories/day)

Now you need to determine whether this patient’s total caloric intake is sufficient for estimated total caloric intake. Here is the formula: 108 cal/kg/day. All you need to do is simply multiply 108 by how many kg the patient weighs, like so: 108 x 2.5 kg = 270 cals/day.

Now compare, does the patient’s caloric intake (200 calories/day) equal or exceed the expected caloric intake (270 calories/day)? In this situation, NO. Therefore, the answer would be no, caloric intake is BELOW the minimum.

DILUTIONS AND CONCENTRATIONS

It is important to know how much diluent to add to a medication to have the correct concentration. Take the following example:

Ordered: Ciprofloxacin 200 mg IV q12h
Available in vial: 200 mg in 1.6 mL
Correct concentration: 10 mg/mL
How many mL of normal saline would you need to add to dilute 200 mg of Ciprofloxacin and have the correct concentration?

The answer is simple.
First, use the ratio method to determine how many mL are in 200 mg of Cipro – cross multiple to get 20 mL.

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Now you know that the total volume needed for correct concentration is 20 mL. Now look at what is available – 200 mg of Cipro in 1.6 mL vial. Now you need to subtract the amount of mL in the available vial (1.6 mL) from the volume needed for correct concentration (20 mL). 20 mL – 1.6 mL = 18.4 mL.

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