Lippincott Nursing Pocket Card - February 2022

# Common Calculations

## Common Calculations |

Medication administration is a core competency for nurses in every clinical setting. A key skill required to safely dispense drugs is the ability to perform accurate dosage calculations. New technologies such as bar coding medication and smart infusion pumps have helped to reduce medication errors (Cookson, 2013). However, nurses cannot rely completely on these advances. Two dosage calculation techniques are presented below: *traditional formulas* and *dimensional analysis*. Nurses should select one formula and practice to become proficient in that method.

## Universal Formula (Wilson, 2013)

All dosage calculations have these 2 components:

- Medication
*dosage*prescribed by the healthcare provider - Medication
*concentration*supplied by the pharmacy

In the universal formula, the *desired amount (D)* is the dose prescribed by the provider. The *amount on hand (H)* is the dose on the container label. *The volume (V)* is the form and amount in which the drug is supplied (i.e. tablet, capsule, liquid). To use this formula, divide the desired amount by the amount on hand and multiply by the volume.

*Example 1: *

Administer digoxin 0.5 mg IV daily. The drug concentration available from the pharmacy is digoxin 0.25 mg/mL. How many mL will you need to administer a 0.5 mg dose?

D/H x V = Dose

0.5/0.25 x 1 = 2 mL

## Intravenous (IV) Medications (Wilson, 2013)

Continuous IV drip calculations are more complex. Use the universal formula, recognizing that some conversions are usually necessary. First, determine the drug concentration. Then consider the unit in which your drug is measured (units/hour, mg/hour, mg/min, mcg/min, or mcg/kg/minute). Then, depending on how the drug is ordered, use one of the formulas below.

**To find mcg/min:**

If your amount on hand is in milligrams (mg), convert mg to micrograms (mcg) by multiplying by 1,000. Also, convert hours to minutes.

*:*

**Example 2**A patient is on a nitroglycerin drip. The IV pump is running at 8 mL/hour. The label on the bottle reads 50 mg in 500 mL 0.9% sodium chloride solution. What dose of nitroglycerin (mcg/min) is the patient receiving?

50 mg/500 mL x 1000 mcg/1 mg x 8 mL/1 hr x 1 hr/60 min

Answer: 13.3 mcg/min

*Most institutions utilize infusion pumps that can be programmed to the tenth or hundredth decimal place. If your institution does not have infusion pumps with this capability, you may need to round to the nearest whole number.*

**To find mcg/kg/min:**** **

Use the formula for mcg/min and divide by patient’s weight (kg).

* Example 3:* Administer dopamine at 10 mcg/kg/min. The pharmacy provides dopamine 800 mg in 250 mL of D5W. What is the hourly IV pump rate? The patient weighs 85.3 kg.

In this example, solve for mL/hr.

800 mg/250 mL x 1000 mcg/1mg x mL/hr x 1 hr/60 min ÷ 85.3 kg = 10 mcg/kg/min

800,000 mcg/250 mL x mL/hr x 1 hr/60 min ÷ 85.3 kg = 10 mcg/kg/min

3,200 mcg/mL x mL/hr x 1 hr/60 min ÷ 85.3 kg = 10 mcg/kg/min

3,200 mcg/mL x mL/hr x 1 hr/60 min = 853 mcg/min

mL/hr = 853 mcg/min x 1 mL/3,200 mcg x 60 min/hr

mL/hr = 16 mL/hr

**To find units/hour:**** **

First, determine the concentration of the amount on hand. Then, use the universal formula to calculate the rate.

**Example 4:**

Administer heparin 500 units per hour I.V. The pharmacy supplies the heparin infusion as 20,000 units in 500 mL D_{5}W.

*Find the concentration:*

20,000 units/500 mL = 40 units/mL

*Use the universal formula:*

D/H x V = Dose

500 units/hr ÷ 40 units/mL = 12.5 mL/hour

## Dimensional Analysis (Cookson, 2013) |

**Dimensional Analysis (DA) or factor-label method:** uses a series of conversion factors of equivalency from one system of measurement to another but doesn’t require memorizing specific formulas (Koharchik & Hardy, 2013). This method reduces errors and can be used for all dosage calculations.

- Start with the labels needed in the answer to determine what unit of measure is needed to begin setting up the calculation.
- Build the calculation by placing information with the same label as the preceding denominator into the equation in the numerator to cancel out the unwanted labels. Repeat until all units of measure not needed in the answer are cancelled out.
- Calculate to determine the correctly labeled numeric answer. Don’t round any numbers in the equation until you have the final answer.

Using the same examples above, let’s use the dimensional analysis method.

**Example 1:**

Administer digoxin 0.5 mg IV daily. The drug concentration available from the pharmacy is digoxin 0.25 mg/mL. How many mL will you need to administer a 0.5 mg dose?

Step 1: What unit of measure (label) is needed? Place this on the left side of the equation.

mL? =

mL? =

__mL__

0.25 mg

Step 3: Place information with the same label as the preceding denominator into the equation in the numerator to cancel out the unwanted labels. Repeat this step sequentially until all unwanted labels are canceled out.

mL? =__mL__x 0.5

0.25

Step 4. Multiply numbers across the numerator, then multiply all the numbers across the denominator. Divide the numerator by the denominator for the final answer with the correct label.

mL? =__ mL __ x 0.5 ~~mg~~ = __0.5 mL__ = 2 mL

0.25 ~~mg~~ 0.25

* Example 2:* A patient is on a nitroglycerin drip. The pump is running at 8 mL/hour. The label on the bottle reads 50 mg in 500 mL 0.9% sodium chloride solution. What dose of nitroglycerin (mcg/min) is the patient receiving?

##### Step 1: __? mcg __

min

Step 2: *Convert 50 mg to 50,000 mcg.

__? mcg __ = __50,__~~000~~ mcg = __100 mcg__

min 5~~00~~ mL mL

Step 3: __? mcg __ = __100 mcg __ x __8 __~~mL~~ x __ 1 hour __

min ~~mL~~ ~~hour~~ 60 min

Step 4: __? mcg __ = __100 mcg__ x __ 8 __~~mL~~ x __1 __~~hour~~ = __ 800 mcg __ = 13.3 mcg/min

min ~~mL~~ ~~hour ~~ 60 min 60 min

* Example 3:* Administer dopamine at 10 mcg/kg/min. The pharmacy provides dopamine 800 mg in 250 mL of D5W. What is the hourly IV pump rate? The patient weighs 85.3 kg.

__? mL__

hr

Step 2:

__? mL__=

__250 mL__

hr 800 mg

Step 3:

__? mL__=

__250 mL__x

__1__~~mg~~ x

__10__~~mcg~~ x 85.3

__60__~~min~~

hr 800

Step 4:

__? mL__=

__250 mL__x

__1__~~mg~~ x

__10__~~mcg~~ x 85.3

__60__~~min~~ =

__12,795,000__

hr 800

= 16 mL/hr

* Example 4: *Administer heparin 500 units per hour I.V. The pharmacy supplies the heparin infusion as 20,000 units in 500 mL D

_{5}W.

__? mL__

hr

Step 2:

__? mL__=

__1 mL__

hr 40 units

Step 3:

__? mL__=

__1 mL__x

__500__~~units~~

hr 40

Step 4:

__? mL__=

__500 mL__= 12.5 mL/hr

hr 40 hr

## Calculating Drops Per Minute (Koharchik & Hardy, 2013)

Continuous IV infusions are delivered via infusion pumps. While continuous IV infusions are typically delivered via infusion pumps, there may be times when an electronic pump is not available. This requires calculating the number of drops per minute, as administered through basic IV tubing.

It is important to note that there are two types of IV tubing that will deliver fluid at a specific flow rate, known as the drip factor: macrodrip and microdrip. The drip factor, which can be found printed on the IV tubing package, is the number of drops (gtts) in one mililiter (mL) of solution delivered by gravity. The rate is measured by counting the number of drops that fall into the drip chamber each minute.

- Macrodrip tubing is wider, producing larger drops and is available in three sizes: 10, 15, or 20 drops per mL (gtt/mL). Macrodrip tubing is typically used to infuse fluids at a rapid rate.
- Microdrip tubing is narrower, producing smaller drops with a drip factor of 60 gtts/mL. It is often used to infuse fluids to pediatric and neonatal patients or medications requiring a precise flow rate.

**Example:**

Administer lactated ringer’s solution IV at 75 mL/hour. The drip factor is 10 drops/mL. How many drops per minute will you run the infusion?

**Using the DA method:**

Step 1:

__? drops__

min

Step 2:

__? drops__=

__10 drops__

min mL

Step 3:

__? drops__=

__10 drops__x

__75 mL__x

__1 hr__

min mL hr 60 min

Step 4:

__? drops__=

__10 drops__x

__75__~~mL~~ x

__1__~~hr~~ =

__750 drops__= 12.5 or 13 drops/min

Mn

To simplify, take the infusion rate and divide by the following based on the size of the tubing set.

** Macrodrip**

- 10 gtt/mL - divide the infusion rate by 6
- 15 gtt/mL - divide the infusion rate by 4
- 20 gtt/mL - divide the infusion rate by 3

**Microdrip**

- 60 gtt/mL divided by 60 is 1. Therefore, the drip rate is the same as the flow rate (drip rate = flow rate).

## General Calculation Tips:

- Check that your answer makes sense clinically.
- Double-check your work.
- Have a colleague or pharmacist check your work.
- Know general therapeutic drug dose ranges for common medications.

## Dosage Calculation Conversions

1 kilogram | 1,000 grams | 2.2 pounds | |||

1 pound | 0.45kg | 16 ounces | |||

1 gram | 1,000 mg | 15-16 grains | |||

1 mg | 1,000 mcg | ||||

1 grain | 60 mg | ||||

1 liter | 1,000 mL | 1 quart | 2 pints | 4 cups | 32 ounces |

1 teaspoon | 5 mL | 60 drops | |||

1 tablespoon | 3 teaspoons | 15 mL | |||

1 ounce | 2 tablespoons | 30 mL | |||

1 cup | 1/2 pint | 8 ounces | 240-250 mL | ||

1 pint | 2 cups | 16 ounces | 480 mL | ||

1 quart | 2 pints | 4 cups | 32 ounces | 1 liter | 1,000 mL |

1 gallon | 4 quarts | 8 pints | 16 cups | 128 ounces | 3,785 mL |

**Temperature Conversion:**

T°C = (T°F – 32) x 5/9

T°C = (T°F – 32)/1.8