Nurses must perform dosage calculations when administering medications, feedings and intravenous fluids. Pharmacology math requires the nurse to know systems of measurement and how to convert within those systems of measurement. Since nurses need to accurately calculate medication dosages, it is essential to understand drug weights and measures.

Math computation skills (addition, subtraction, division, multiplication, fractions, etc) are necessary to calculate medication dosages.

To interpret physician's orders, the nurse must also understand abbreviations used to describe those units of measurement and frequency of administration.

Other instances in which the nurse may use math (pharmacology) includes calculating safe dosages of medications. Nurses may use basic math to determine intake and output.

Sometimes it is necessary to convert before one can calculate a problem. When using the metric system, remember the rules for moving the decimal. If you know one equivalent within a system, then you can use ratio and proportion to solve conversions. Below are some of the most common equivalents used for medication doses.

1 kilogram (kg)	2.2 pounds (lb)
1 pound (lb)	454 grams (g or gm)
1 kilogram (kg)	1000 grams (g or gm)
1 gram (g or gm)	1000 mg (milligrams)
1 milligram (mg)	1000 micrograms (mcg)
1 gram (gm)	1 ml (milliliter)
1 cc (cubic centimeter)	1 ml (milliliter)
1 inch (in)	2.54 cm (centimeters)
1 cup	240 ml (milliliters)
8 ounces (oz)	1 cup
16 ounces (oz)	1 pint (pt)
1 ounce (oz)	30 ml (milliliters)
1 teaspoon (tsp)	5 ml (milliliters)
1 tablespoon (T or Tbs)	15 ml (milliliters)
2 tablespoons (T or Tbs)	1 ounce
3 teaspoons (tsp)	1 Tablespoon (T or Tbs)
1 liter	1000 ml (milliliters)
37.0? C (Centigrade)	98.6? F (Fahrenheit degrees)

Setting up the Problem:

Doctor's order:	0.25 mg of digoxin oral
On hand:	0.5 mg tablets

Tip: Your exams may use varied terms to designate the 2 components necessary to calculate the correct dosage to administer. The key is to clarify the 2 parts of the equation (what to give and what is available).

Process:

Set up your skeleton until you become comfortable with the process:

?	=	?		X=___		X is what you want to find out, in this case how much digoxin to give.
?		x

Fill in the 2 units of measurement you are dealing with. Make the equation's labels/units match. In the example below: "mg" on top of both sides of the equation and “tab” on the bottom of both sides of the equation.

mg	=	mg			Add the information from the problem	0.25 mg	=	0.5 mg
tab		tab				X tab		1 tab

Make sure both sides of the equation match in terms of the units. As necessary, change mg to mcg, grams to milligrams, etc. so the units match. It is easier to calculate if the conversion is changed to the measurement one has "one hand". Cross multiply. Place the X on the left side of the equation: Xtab x 0.5 mg = 0.25 mg x 1 tab.

Then by dividing both sides of the equation in order to leave the “X” alone on one side of the equation. Dividing both sides of the equation by 0.5 mg, gives you an equation: Xtab = 0.25 mg*tab / 0.5 mg. The "mg" cancels out leaving 0.25/0.5 = 0.5 tab = X

TIP:

Critical vs. Extraneous Information: an important principle in setting up your problem is to identify what is critical information for calculation and what is extraneous to calculating the problem.

Example:
John has an order:“Oxicillin 550 mg IVPB Q 6 hours”. The nurse has a one gram vial with the following information on the vial: Mix 5.7 ml of sterile water to yield 250 mg/1.5 ml. How many ml will the nurse withdraw from the reconstituted vial?

What is the critical information?

• The dosage (550 mg)
• The end concentration (250ml/1.5 ml)

What is extraneous information not needed for calculating?

• Mixing instructions (Adding the 5.7 ml to the vial tells you that this is the volume necessary to add to the powder to yield a specific concentration.) Can you figure how much volume the powder has in the vial? (0.3 ml)
• Q 6 hours (Since you are calculating a single dose, this information is not necessary to calculate.)
• 1 Gram vial (This is not important because the end concentration is given to you in this case.)

Use the formula noted above to calculate the solution.

550 mg = 250 mg X ml 1.5 ml

Cross Multiply: 250 mg*Xml = 550 mg*1.5 ml Then divide leaving X on one side of the equation.

Xml X 250 mg = 550 mg X 1.5ml   250 mg 250 mg

X=550/250 ml = 3.3 ml

Calculating Drip Rate:

The drip rate is the number of drops per minute to be infused (drops per minute).
Drip factor of the tubing is found on the manufacturer's packaging. This is expressed in drops/ml (gtt/ml). If the tubing states it is microdrop tubing, then the drip factor of the tubing is 60 drops/ml.

Formula:

Total # of mililiters (volume)	X	Drip factor (drops)	= drop/minute
Total # of minutes (time)		ml

Example:
The physician orders IV fluids to hydrate a client. The order is written as “D5NS 1 liter over 6 hours.” The package indicates the drip factor of the tubing is 20 gtt/ml. What is the drip rate?

Critical information:

• Volume = 1 liter
• Time = 6 hours
• Drip factor of tubing = 20 gtt/ml

Tip: Make conversions first into the units you are going to use.

• Convert the hours to minutes first. 6 hours X 60 minutes/hr = 360 minutes
• Convert the liters to milliliters. 1 liter = 1000 ml

1000 ml	X	20 drops	=	1000 * 20 drops	=	20000 gtt	=	56 drops/min
360 minutes		ml		360 minutes		360 minutes

Example: Order: Run current IV fluids at 175 ml/hr for 2 hours.

Critical Information

• Volume = 175 ml
• Time 1 hour (60 minutes)
• What is the drip factor of the tubing? (The package reads 15 gtt/ml.)

Extraneous Information for Calculating:

• 2 hours (but important for carrying out the order)

175 ml	X	15 drops	=	175 * 15 drops	=	2625 gtt	=	44 drops/min
60 minutes		ml		60 minutes		60 minutes

Example: client's K+ is 2.0 mEq/dl and the physician orders a potassium bolus of 40 mEq of KCl in 200 ml of NS to be delivered at a rate of 10 mEq/hr. What is the drip rate in microdrops?

Critical Information:

• How many ml is needed to provide 10 mEq?
• Flow rate = 10 mEq/hr
• Drip factor = 60 gtt/ml

TIP: This is a 2-part problem. Calculate the concentration of the KCl in the NS solution to give you the volume of fluid which contains 10 mEq of K+.

40 mEq	=	10 mEq
200 ml		X ml

Cross Multiply: 40 mEq * Xml = 10 mEq * 200 ml.
Divide each side by 40 mEq: X = 10 * 200 ml/40 = 50 ml

Xml	X	40 mEq	=	10mEq	X	200 ml	=	2000 ml	=	50 ml
		40 mEq		40 mEq				40

Now calculate the drip rate for the infusion.

50 ml	X	60 drops	=	50 * 60 drops	=	3000 gtt	=	50 drops/min
60 minutes		ml		60 minutes		60 minutes

Calculating Flow Rate: Flow rate refers to the number of ml of fluid to be infused over one hour (ml/hr).

Formula:

Total # of mililiters (volume)	= ml/hr
Total # of hours (time)

Example: Give 500 ml of Pedialyte over 3 hours.

Critical Information:

• Volume = 500 ml
• Time = 3 hours

500 ml	= 167 ml/hr
3 hour

Calculating time if given the flow rate:

The nurse needs to know how long a volume of fluid in the IV bag at the current flow rate will last. When will a new bag need to be hug?

Formula:

Volume	= Infusion time
Flow Rate

Example: The nurse makes rounds and notes that the current bag contains approximately 450 ml. The flow rate is 150 ml/hr. How long will it be before the nurse must hang a new bag?

Critical Information:

• Volume = 450 ml
• Flow rate = 150 ml/hr

450 ml	= 3
150 ml

For more pharmacology math and tutorial on line go to: www.accd.edu/sac/nursing/math.