#### Just the Facts

- Medication math is a high-risk undertaking and accounts for a disproportional number of medical errors each year.
- Similarly labeled medications, varying solution concentrations and difficulty estimating weight are all contributing factors in incorrect medication calculations.
- Each year there are as many as 210,000 deaths attributed to medical error. There may be as many as 10,000 serious complications per day.

#### Key Concept – Human Performance under Stress

- The fight or flight response impairs cognition and decision making. Even the simplest calculations will be more difficult in stressful situations.
- A culture of safety suggests that medication calculations should be avoided unless absolutely necessary. Use resources, standardized references and checklists as a substitute.
- Any medication calculation should be cross-checked with another provider before administration of the drug.

#### Setting Yourself Up for Success

- Before beginning any calculation, double check:
- Weight estimates
- Medication quantities on hand (particularly if a conversion has been necessary)
- Any conversion (weight or quantity)
- Solution concentrations
- Protocol/standard doses

- If you must use calculations, do not multi-task. One person should have singular attention to working on the problem.
- Always preprogram and be familiar with medication administration pumps. Most devices have internal libraries that will eliminate the need for calculation.

#### Definitions

**Desired Dose** – The specific amount of medication necessary to be delivered to achieve the appropriate effect

**Dosage on Hand** – The amount (typically weight) of a medication in a solution.

**Solute **– A substance (such as a medication) dissolved in a solvent to form a solution.

**Solvent **– The liquid in which a solute is dissolved.

**Solution **– A solute dissolved in a solvent.

**Volume on Hand **– The total amount of solution containing a medication.

**Solution Concentration** – The amount of solute (typically the weight of a medication) dissolved in a solvent. Simply put, the amount of medication per volume of the solution.

**Volume to be Administered **– The volume of the solution that must be administered to deliver the desired dose.

#### Common abbreviations:

**mcg or μg **– micro-

** m** – milli- and/or meter

**c** – centi-

**d** – deci-

**k **– kilo-

**g** – gram

**L** – liter

**min.** – minute

**lb **– pound

**gtt **– drop

#### Basic Metric Measurements:

**Weight** = Gram

**Volume** = Liter

**Length** = Meter

#### Common Metric prefixes:

**kilo-** [1000] (for example, there would be 1000 grams in a kilogram)

**deci- **[0.1] (for example, a deciliter would be 1/10th of a liter, or 0.1 liter. There would therefore be 10 deciliters in a liter)

**centi-** [0.01] (for example, a centimeter would be 1/100th of a meter, or 0.01 meters. There are 100 centimeters in a meter.

**milli-** [0.001] (for example, milligram would be 1/1,000th of a gram, or 0.001 grams. There are 1,000 milligrams in a gram.

**micro-** [0.000001] (for example, a microgram would be 1/1,000,000th of a gram, or 0.000001 grams. There are 1,000,000 micrograms in a gram.

#### Metric Conversions

- To convert a base unit (gram, liter, meter) to a smaller unit (a prefix such as micro-, milli-, centi-, or deci-), multiply the base unit by the numeric factor of the prefix. For example, to convert 5 grams to milligrams, you would multiply 5 by 1,000 and determine that 5 grams are equivalent to 5000 milligrams.
- To convert a base unit to a larger unit (such as a prefix like kilo-), divide the base unit by the numeric factor of the prefix. For example, to convert 5 grams to kilograms, you would divide 5 by 1,000 and determine that 5 grams are equivalent to 0.005 kilograms.
- With practice, metric conversions can often be made by simply moving the decimal point to make larger or smaller quantities.
- If in doubt, it is reasonable to first convert prefix quantities to a base unit (milligrams to grams for example) and then convert to other prefixes from there.

#### Weight Conversion

Very commonly in medication math, it is necessary to convert US customary weights (pounds) to metric weights (grams and kilograms). To do this consider the following conversion:

**1 kilogram = 2.2 pounds**

- To convert kilograms to pounds, multiply the number of kilograms by 2.2. (For example, a 10-kilogram child would weigh 22 pounds).
- To convert pounds to kilograms, divide the number of pounds by 2.2. For example, a 220-pound man would weigh 100 kg

#### Temperature Conversion

To convert a temperature measured in Celsius (C) to Fahrenheit (F), use the following formula:

**F = Temp. in C X 1.8 +32**

For example, to convert 34°C to F, you would multiply 34 X 1.8 and then add 32. (61.2+32= 93.2°F)

To convert a temperature measured in Fahrenheit (F) to Celsius (C), use the following formula:

**C = (Temp in F – 32) ÷ 1.8**

For example, to convert 98.6°F to C, you would subtract 32 from 98.6 and then divide that sum by 1.8. 98.6-32= 66.6. 66.6 ÷ 1.8 = 36.7

#### Calculating Volume to be Administered

Medications commonly are packaged in solution volumes larger than what is needed to administer the desired dose. If this is the case, you will need to determine the appropriate volume to be administered.

To determine the volume to be administered, use the following formula: (Remember that you must first assure that all weights are expressed in the same prefix).

##### Volume to be Administered = (Volume on Hand X Desired Dose) ÷ Dosage on Hand.

Consider the following example: Your protocols indicate that you should administer 4mg of midazolam to stop a pediatric seizure. Your vial of midazolam contains 10mg in 2 mL. Therefore, the equation breaks down into:

- Volume on Hand = 2 mL
- Desired Dose = 4 mg
- Dosage on Hand = 10 mg

Using the equation then, you would multiply the volume on hand (2mL) by the Desired Dose (4mg) and then divide that product by the Dosage on Hand (10mg).

**2 X 4 = 8. 8 ÷ 10 = 0.8.**

Therefore, your Volume to be Administered would be 0.8 mL

#### Cross Multiplying (also known as the Ratio Proportion Method or “solving for “X”)

Volume to be administered can also be determined by comparing the ratio of solution concentrations. For example, you might express the previous problem in the following way:

**10mg/2mL = 4mg/**XmL

By cross multiplying, it would become:

**10X = 8**

Which could then be expressed as:

** X = 8/10 or 8 ÷ 10 = 0.8**

*Whether you utilize a standard formula or use algebra to solve for X, you should approach these problems with consistency and practice your chosen method often.*

#### Calculating Drip/Infusion Rates

An infusion implies that a medication will be administered over time. Most commonly, an infusion is expressed as a drip rate and measured in drops (gtts) per minute.

The rate of infusion will depend greatly upon the IV infusion set used to administer the medication. This consideration is factored as a known Drip Factor. Common drip factors are:

- Microdrip set = 60 drops/mL
- Macrodrip set = 10 drops/mL or 15 drops/mL

*Drip factors are noted on the IV tubing packaging.*

To determine an infusion rate, consider the following formula:

**Drops/Minute = (Volume on Hand X Drip Factor X Desired Dose) ÷ Dosage on Hand**

Consider the following example: Your protocol indicates that you should administer 8 micrograms of norepinephrine per minute. Your premixed bag of norepinephrine contains 4mg in 500mL and you will use a microdrip (60gtt/mL drip factor) set. To determine the infusion rate, you should:

First convert the 4mg of norepinephrine to micrograms* (remember that consistency of prefixes is critical).*

Milli- refers to .001 g and micro- refers to 0.000001g. Therefore, 4mg would be equivalent to 4,000 micrograms.

The equation would then break down into:

- Volume on Hand = 500mL
- Drip Factor = 60 gtt/mL
- Desired Dose = 8μg
- Dosage on Hand = 4000μg

Using the equation then, you would multiply the volume on hand (500mL) by the Drip Factor (60gtt/min) by the Desired Dose (5μg) and then divide that product by the Dosage on Hand (4μg).

500 X 60 X 8 = 240,000. 240,000 ÷ 4000 = 60

Therefore, your infusion rate would be 60 drops per minute.

#### Calculating Volume of a Medication Administered over Time

Occasionally, medications must be administered over a specific period of time. Here you must calculate an infusion rate, but also consider the total amount of time the medication will be infused.

To determine a drip rate over time, use the following formula:

**Drop/Minute = (Volume to be Administered X Drip Factor) ÷ Time in Minutes**

Consider the following Example: Your protocol indicates that you should administer 5 g of magnesium sulfate to a polymorphic ventricular tachycardia patient over 10 minutes using a microdrip set (60gtt/mL). Using the previous formulas, you have determined that to deliver 5g of magnesium sulfate, you must deliver 10mL of the solution it is contained in.

The equation would break down into:

- Volume to be Administered = 10mL
- Drip Factor = 60 gtt/mL
- Time in minutes = 10

Using the equation then, you would multiply the Volume to be Administered (10mL) by the Drip Factor (60 gtt/mL) and then divide that product by the Time in Minutes (10).

10 X 60 = 600. 600 ÷ 10 = 60.

Therefore, your infusion rate to deliver 10mL of the magnesium sulfate solution over 10 minutes would be 60 drops per minute.