1. Computing Dosage for Infants and Children
SSAC2007.WY159.JZ1.1
Computing Dosage for Infants and Children
Calculation of Dosage Using the Body Weight Method
Calculate pediatric dosage using the child’s weight in kilograms and the manufacturer’s recommended daily dose based on the weight in kilograms.
Core Quantitative Issue
Ratio and proportion
Supporting Quantitative Skill
Unit conversions
Prepared for SSAC by
*JIAN ZOU – SOUTH SEATTLE COMMUNITY COLLEGE*
© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. *YEAR*

2. Math and Meds
Calculating dosage is a fundamental skill for nurses. The calculations hinge on understanding ratios and proportions.
The textbook/workbook Math and Meds for Nurses by Dolores F. Saxton, Norma Ercolano and Colleen Glavinsplehs (Delmar Learning, 2005; first edition by Saxton and Ercolano, 1998) covers the subject in great detail and with many examples. We will work through a variation on one of those examples in this module to demonstrate how such calculations are facilitated by using a spreadsheet.
Problem:
Ryan’s pediatrician has prescribed 25 mg/kg/day amoxicillin oral suspension in three divided doses. From the drug book, you find that the manufacturer recommends 20 – 40 mg/kg/day in three divided doses every 8 hours. Your pharmacy supplies bottles of oral suspension labeled 125 mg per 5 mL. Ryan weighs 40 lb. How many mL should you administer every 8 hours?
-- adapted from Saxton and Ercolano, 1998,
p. 211, problem 2.

3. Overview of Module
According to Math and Meds (1998, p. 207), “Even minor mistakes in administering medication to an infant or child can be extremely serious because of differences in their ability to absorb, distribute, metabolize, and excrete substances such as drugs.” This module is designed to show you how to calculate the amount of medication to be administered to an infant or a child according to the physician’s prescription, the manufacturer’s recommended daily dose per kilograms of body weight, and the body weight of the child.
Slides 4-6 Build the pound-to-kilogram conversion spreadsheets.
Slide Gives the formulas to use to calculate the dosage in mg.
Slides 8-9 Build the spreadsheets to calculate the dosages.
Slide 10 Calculates the dosage in mL.
Slides Build the spreadsheet to calculate the dosages in ml
Slides 13 End of module assignment

4. Solving dosage question: Pound-kilogram conversion
Infants and children should take only the amount of medication that is considered safe for their body weight. This immediately introduces a problem: whereas the patient’s body weight is generally measured in pounds, most drug books and drug manufacturers give recommended pediatric dosages in terms of body weight in kilograms, and many physicians also prescribe medications using these units. The first goal, then, is to become proficient in converting between pounds and kilograms.
You often hear that one kilogram is the same as 2.2 pounds. So to convert a child’s weight from pounds to kilograms, you divide the number of pounds by 2.2.
Example:
a child weighs 44 lb,
44 ÷ 2.2 = 20 kilograms,
so the child weighs 20 kilograms.
We can be more accurate and say that one kilogram is the same as pounds. So to convert pounds to kilograms, divide the number of pounds by With Excel, dividing by is as easy as dividing by 2.2.

5. Solving dosage question: Pound-kilogram conversion spreadsheet
Instead of converting pounds to kilograms one by one, we are going to build a conversion table by Excel.
In a new Excel worksheet,
type pounds in Cell B2 and kilograms in Cell C2;
enter numbers 5 through 20 in the pounds column;
type the Excel formula that divides the value in B3 by hence converting the number of pounds in Cell B3 to number of kilograms;
copy Cell C3 and paste it through C4 to C18, converting pounds in all the cells to kilograms. We obtain a table like the one on the left.
Task #1:
Create a similar Excel conversion table that converts pounds to kilograms for 12 – 40 pounds.
= cell with a number in it
= cell with a formula in it
All formulas in Excel start with a = sign.

6. Solving dosage question: Pound-kilogram conversion spreadsheet (2)
Your completed Task #1 should look like this
= cell with a number in it
= cell with a formula in it
You can enter numbers 12 through 40 in the pounds column without typing them one by one: enter 12, 13, and 14 in Cells B3, B5, and B5; highlight these three cells; place your cursor at the lower right corner of the highlighted block and drag the corner down.

7. Solving dosage question: Ratio and proportion: Patient’s dosage per day
From the lb-kg conversion spreadsheet, Ryan’s body weight 40 lb = kg. The ratio of prescribed 25 mg per day to 1 kg must equal the ratio of Ryan’s dosage in mg per day to his body weight kg. Write Ryan’s dosage per day as x mg, set up the proportion, and then –
So, Ryan should take mg per day in three divided doses, that is 453.6/3=151.2 mg every 8 hours.
In general, we have or
(patient’s dosage per day)
= (prescribed dosage per kg per day) x (patient’s body weight in kg)

8. Solving dosage question: Patient’s dosage per day: Spreadsheet
We are going to build a spreadsheet to calculate the dosages for patients of body weights from 12 lb through 42 lb with the prescribed dosage of 25 mg/kg/day.
In the first row of a new Excel spreadsheet:
Type Patient’s weight, Prescribed, and Patient’s dosage in Cells B2, D2, and E2, respectively;
Type in lb, in kg, mg/kg/day, and mg/day in Cells B3, C3, D3, and E3, respectively.
The spreadsheet should look like the one on the left.
= cell with a number in it
= cell with a formula in it

9. Solving dosage question: Patient’s dosage per day: Spreadsheet (2)
Enter pound number from 12 through 42 in Cells B4 through B34.
In Cell C4, enter the formula that converts pounds in B4 to kilograms.
Copy C4 and paste it to Cells C5 though C34, converting pounds in Cells B5 through B34 into kilograms.
Enter the prescribed dose per kg body weight per day (25) in Cells D4 through D34.
In E4, enter the formula that multiplies the body weight in kg in Cell C4 by the dose per kg per day in Cell D4, to obtain the dose per day for the patient, and paste it to cells through Cell E5 through E34.
The completed spreadsheet should look like the one on the left.
Ryan weighs 40 lb. So from the table, his daily dose should be mg
= cell with a number in it
= cell with a formula in it

10. Solving dosage question: Ratio and proportion: Med per administration
Now we find out the amount of oral suspension Ryan should take each time.
Divide the daily dose by 3 to get 453.6÷3=151.2 mg. So Ryan should take mg of amoxicillin each time.
The available oral suspension contains 125 mg of amoxicillin per 5 mL. To find the amount of oral suspension in mL, x mL, that contains mg of amoxicillin, we set up the proportion:
Solving the above proportion, we get
The amount of oral suspension for every 8 hours
= (dose per each time) / (the mg to mL ratio of the oral suspension)
Ryan should take 6 mL of the oral suspension each time for three times a day.

11. Solving dosage question: Med per administration: Spreadsheet
We are going to use the spreadsheet to calculate the amount of oral suspension to be taken each time for children of various weights.
Type mg/8hours in cell F3, mg/mL in Cell G3, and mL/8hour in Cell H3
Enter the formula that divides the dose per day by 3 to obtain the dose per 8 hours in Cell F4, then paste it in Cells F5 through F34
Enter the ratio of the mg to mL of the available oral suspension in Cell G4 and paste it in Cells G5 through G34;
Enter the formula that calculates the amount of oral suspension in Cell H4 and paste it in Cells H5 through H34.
The completed spreadsheet is on the next slide.

12. Solving dosage question: Med per administration: Spreadsheet (2)
From the table, with the body weight of 40 lb, Ryan should take 6 mL each time.
= cell with a number in it
= cell with a formula in it

13. Build a spreadsheet that converts 12 through 60 inches to centimeters.
End of Module Assignment
1. One inch equals 2.54 cm. A child is 54 in tall. What is the child’s height in cm?
Build a spreadsheet that converts 12 through 60 inches to centimeters.
A physician has prescribed for a baby of 20 lb a medication 15 mg/kg/day to be administered in divided doses every 12 hours. The drug on hand is labeled 75mg per 2 mL.
(a) Calculate how many mL of the drug the nurse should administer each time?
(b) Build a spreadsheet to calculate the doses to be administered each time for babies with weights varying from 15 lb to 25 lb.

14. Pre and post module test
Write the ratio of 30 students to 40 chairs.
A vial of Kantrex Injection is labeled 75 mg per 5 mL. Write the ratio of mL to mg.
You drove your car 500 miles and used 20 gallons of gas. At the same ratio, how many miles would you expect to drive on 15 gallons of gas?
A nurse finds that the manufacturer’s recommended dosage for a certain drug is 12 mg per kg of body weight per day. At this ratio, what is the daily dosage for a child of 39 lb?
5. One tbsp = 15.0 mL. How many tablespoonfuls (tbsp) are there in 75 mL?