Doing math in nursing and nursing school is a lot harder and more critical than you think. One wrong interpretation and calculation can compromise your patients’ safety and health.

Despite that, however, pharmacology for nurses shouldn’t make you feel scared or overwhelmed. Here’s an in-depth yet easy-to-understand guide to help you out.

## Abbreviations used in drug preparation and administration

Abbreviations rule the medical world. It is important to know the recognized abbreviations in clinical setting so you will not be lost when preparing medications for your patient. Here are the most commonly used abbreviations when preparing drugs:

**Routes**

**IM**– Intramuscular

**IO**– Intraosseous

**IV**– Intravenous

**IVP**– Intravenous Push

**ID** – Intradermal

**IN** – Intranasal

**IP** – Intraperitoneal

**IT** – Intrathecal

**IVPB** – Intravenous piggyback

**p.o** – By mouth

**SC / SubQ** – Subcutaneous

**SL** – Sublingual

**top.** – Topical

**vag**. – Vaginally

**Measurements**

**Kg**– kilogram

**gm**– gram

**mg**– milligram

**mcg**– microgram

**mEq-** milliequivalent

**L**– liter

**mL**– milliliter

**µg**– microgram

**gtt** – drop

**µgtt** – micro drop

**tbsp** – tablespoon

**tsp** – teaspoon

**mg/dL** – milligrams per deciliter

## Conversions

Before mastering drug dosage formula, you should first learn how to convert the commonly used units of measurements in drug preparation. It is essential so you will not get lost between drug calculations as physicians commonly order a medication available in a different preparation.

The most common conversion factors you will use for drug dosage calculations are the following:

**Solid Conversions**

gr 1 = 60 mg

gr 15 = 1 g

2.54 cm = 1 in

2.2 lb = 1 kg

**Liquid Conversions**

30 mL = 1 oz

1 tsp = 5 mL

1 standard measuring cup = 240 mL

**Mass**

mcg ← mg ← g ← kg ( x by 1,000 )

mcg → mg → g → kg ( ÷ by 1,000 )

lb ← kg ( x by 2.2 )

lb → kg ( ÷ by 2.2 )

**Volume**

mcL ← mL ← L ← kL ( x by 1,000 )

mcL → mL → L → kL ( ÷ by 1,000 )

**Time**

min ← hr ( x by 60 )

min → hr ( ÷ by 60 )

*Examples:*

- Convert 0.008 kg to mg

mcg ← *mg ← g ← kg* ( x by 1,000 )

0.008 L x 1,000 = 8 mg

8 mg x 1,000 = *8,000 mg*

- Convert 1,000 mcL to mL

*mcL → mL* → L → kL ( ÷ by 1,000 )

1,000 L ÷ 1,000 = *1 mL*

- Convert 480 minutes to hour

*min → hr* ( ÷ by 60 )

480 ÷ 60 = *8 hr*

## Drug Calculation Formulas

Below are the four most important calculation formulas that you should know in preparing medications and drips.

**Calculating Tablet Dosages**

In calculating tablet dosages, the following formula is useful:

Desired dosage ÷ stock strength = number of tablets

The desired dosage is the ordered dosage of the physician while the stock strength is the amount of drug present in each tablet. Stock strength is also known as stock dose.

*Example:*

- The physician orders 1,500 mg of calcium carbonate for the patient. The drug is available in 250 mg tablets. How many tablets should be given to the patient?

*Desired dosage ÷ stock strength = number of tablets*

1,500 mg ÷ 250 mg = *6 tablets*

- The patient is ordered to have 2 g of potassium chloride. The drug is available in 500 mg tablets. How many tablets should be given?

Convert 2 g to mg = 2 x 1,000 = 2,000 mg

*Desired dosage ÷ stock strength = number of tablets*

2,000 mg ÷ 500 mg = *4 tablets*

**Calculating Mixtures and Solutions**

The following formula is useful in calculating mixtures and solutions:

Desired dosage ÷ stock strength x stock volume = amount of solution to be given

The desired dosage is the ordered dosage of the physician. The stock strength is the amount of drug present in the preparation while the stock volume is the amount of the solution where the drug is diluted.

*Example:*

- The physician orders 375 mg of cefuroxime for the patient. The drug is available in 750 mg vial. You plan to dilute it in 10 mL of sterile water. How much should you give to your patient?

*[Desired dosage ÷ stock strength] x stock volume = amount of solution to be given*

[375 mg ÷ 750 mg] x 10 mL = amount of solution to be given

0.5 mg x 10 mL = *5 mL*

- A pediatric patient recovering from accidental fall is about to be given with 130 mg paracetamol syrup. The drug is available in 250 mg per 5 mL preparation. How much should you give to your patient?

*[Desired dosage ÷ stock strength] x stock volume = amount of solution to be given*

*[130 mg *÷ 250 mg] x 5 mL = *amount of solution to be given*

0.52 x 5 mL = *2.6 mL*

**Calculate IV Rate – mL per hour and minute**

It is easy to calculate the running rate of IV fluids in terms of mL per hour or mL per minute:

Total IV volume ÷ time (hour or minute) = mL per hour or minute

The total IV volume is the amount of fluid to be infused while the time is the number of running hours or minutes.

*Examples:*

- Start venoclysis with D5 0.9 NaCl 1 L to be infused for 16 hours. How many mL of the IV fluid should you infuse per hour?

*Total IV volume ÷ time (hour or minute) = mL per hour *

1 L ÷ 16 hours = mL per hour

[1 L x 1,000] ÷ 16 hours = mL per hour

1,000 mL ÷ 16 hours = 62.5 mL per hour

- You are going to start IV infusion with Plain Lactated Ringer’s Solution 1 L. By regulating it for 11 hours, how much fluid are you going to infuse per minute?

*Total IV volume ÷ time (hour or minute) = mL per minute*

1 L ÷ 11 hours = mL per minute

[1 L x 1,000] ÷ [11 hours x 60] = mL per minute

1,000 mL÷ [11 hours x 60] = mL per minute

1,000 mL ÷ 660 = *1.5 mL per minute*

**Calculate IV Rate – drops per minute**

Calculating for drops per minute is simple with the following formula:

[Total IV volume ÷ time (minute)] x drop factor = drops per minute

The total IV volume is the amount of IV fluid to be infused while time is the duration of how long the IV fluid should be infused in terms of minutes.

The drop factor is the “drops per milliliter” delivered to the patient and it depends on the macrodrip used for the infusion. The common drop factors used in different hospitals are 10, 15 and 20.

*Examples:*

- The physician orders to start venoclysis with D5 0.3 NaCl 1 L solution. The IV fluid will be infused for 14 hours and the drop factor of the macrodrip used is 20. It should be regulated to how many drops per minute?

*[Total IV volume ÷ time (minute) ] x drop factor = drops per minute*

[1 L ÷ 14 hours] x 20 = drops per minute

[{1 L x 1,000} ÷ {14 hours x 60} ] x 20 = drops per minute

[1,000 mL ÷ 840 minutes] x 20 = drops per minute

1.19 x 20 = *23 to 24 drops per minute*

- You are going to regulate D5 0.9 NaCl 500 mL solution for 7 hours. The macrodrip used has 15 drop factor. You should regulate the IV fluid for how many drops per minute?

*[Total IV volume ÷ time (minute) ] x drop factor = drops per minute*

[500 mL ÷ 7 hours] x 15 = drops per minute

[500 mL ÷ {7 hours x 60}] x 15 = drops per minute

[500 ÷ 420] x 15 = drops per minute

1.19 x 15 = *17 to 18 drops per minute*

**Calculate IV Rate – Remaining Time of Infusion**

Calculating for the remaining time of infusion for a certain IV fluid is possible with the following formula:

[Volume remaining (in mL) ÷ drops per minute] x drop factor = minutes remaining

The volume remaining is the amount of IV fluid remaining for the infusion while the drops per minute is the regulation of the IV infusion. The drop factor can be determined in the macrodrip used in the hospital.

*Example:*

- You see that your patient has D5 0.9 NaCl IV infusion at 400 mL level. It is regulated to run for 22 drops per minute using a macrodrip set with drop factor 20. How many minutes are remaining before you are due to change the IV fluid?

*[Volume remaining (in mL) ÷ drops per minute] x drop factor = minutes remaining*

[400 mL ÷ 22] x 20 = minutes remaining

18.18 x 20 = *363 minutes or 6 hours*

- A patient has 350 mL of Plain 0.9 NaCl solution as IV infusion regulated at 20 drops per minute. Drop factor 10 was used for the patient’s macrodrip set. Considering the IV fluid level of the patient, for how many minutes will it run?

*[Volume remaining (in mL) ÷ drops per minute] x drop factor = minutes remaining*

[350 mL ÷ 20] x 10 = minutes remaining

17.5 x 10 = *175 minutes or 3 hours*

## Helpful Videos to Watch

Here are some of the most popular videos about drug calculations. It is easy to understand and practice the formulas presented above using these audio-visual learning tools:

**Infusion Rates**

**Dosage calculations for nurses – drug math made easy!**

**Dosage Calculation – Everything you need to know!**

## Additional Tips:

As long as you know the basic formulas of drug calculations, you will never be lost in finding the desired dosage for your patient.

The trick in mastering drug calculations is to know unit conversions by heart. Once you are regularly working in a clinical setting, you will get used to the common formulas used in determining desired dosages or IV regulations for the patient.

It takes a lot of practice to master drug calculations and you don’t need to memorize it. Answer practice questions at home and in a short period of time, nursing pharmacology will just be a piece of cake for you.

### Recommended Articles:

**Nursing Pharmacology Mnemonics & Tricks** – Learn nursing pharmacologythe fun way using these easy-to-memorize mnemonics and useful study guides.

**Top 10 Best Online Drug Guides for Nurses** – Say goodbye to bulky nursing drug handbooks. This article features the ten of the best free drug guides for nurses online that you must consider.

**The nurse’s quick guide to I.V. drug calculations** – This article will provide a simple and concise method for accurate computation using basic calculations.

**Dimensional analysis: Calculate dosages the easy way** – This article introduces the DA method of performing dosage calculations to practicing nurses.