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Nursing math and pharmacology

Posted by eLearning Cafe, eLearning Math, eLearning science

Nursing Math and Pharmacology

Nursing math is a fundamental aspect of nursing practice that involves mathematical calculations to determine accurate medication dosages for patients.  

The following worksheets will help you develop the foundational math skills necessary for the calculations you’ll be doing in pharmacology. 

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Modules

Module 1 - Number Systems and Conversions Number Systems and Conversions Key
Module 2 - Decimals Decimals Key
Module 3 - Fractions Fractions Key
Module 4 - Ratio and proportion Ratio and Proportion Key
Module 5 - Percent Percent Key

Check out the “Pharmacology” section below for information on dimensional analysis and dosage calculations. 

Pharmacology

Pharmacology involves applying mathematical calculations to pharmacological concepts and medication administration. It includes dosage calculations to determine accurate medication doses based on factors such as patient weight, concentration, and prescribed dosages. Look at the information below to learn more! 

In nursing, dimensional analysis is particularly valuable when calculating medication dosages or determining appropriate infusion rates.  

The process of dimensional analysis involves the following steps: 

  1. Identify the given and desired units: Begin by clearly identifying the units given in the problem and the units you need to obtain in the final result. 
  2. Determine the conversion factors: Conversion factors are ratios that express the relationship between different units of measurement. They allow you to convert from one unit to another. For example, if you need to convert from milligrams (mg) to grams (g), the conversion factor would be 1 g = 1000 mg. 
  3. Apply conversion factors: Multiply the given value by the appropriate conversion factors to cancel out the undesired units and obtain the desired units. Make sure to set up the conversion factors in a way that the units cancel out appropriately, leaving only the desired units. 
  4. Complete the math: Multiply the numerators, multiply the denominators, and divide the products to produce the wanted quantity.  
  5. Check units: Always check the units in the final calculation to ensure they match the desired units. If the units do not match, it indicates an error in the calculation. 

Put simply, ask yourself: 

  1. What do I KNOW? (eg. Order, Conversions)
  2. What do I HAVE? (eg. How the medication is supplied)
  3. What do I WANT? 

You can reference this image to help you solve conversions between different metric units.

Converting between metric units involves multiplying or dividing by powers of 10. Here's a step-by-step explanation of the process: Understand the metric prefixes: The metric system uses prefixes to indicate different orders of magnitude. The most commonly used prefixes are: Kilo- (k): represents a factor of 1,000 (e.g., 1 kilometer = 1,000 meters) Hecto- (h): represents a factor of 100 (e.g., 1 hectogram = 100 grams) Deca- (da): represents a factor of 10 (e.g., 1 decameter = 10 meters) Base Unit: represents a factor of 1 (For length the base unit is a meter, for weight the base unit is a gram, and for capacity the base unit is a liter) Deci- (d): represents a factor of 0.1 (e.g., 1 deciliter = 0.1 liter) Centi- (c): represents a factor of 0.01 (e.g., 1 centimeter = 0.01 meter) Milli- (m): represents a factor of 0.001 (e.g., 1 milligram = 0.001 gram) Determine the relationship between the starting unit and the target unit. Look at the prefixes and their corresponding factors to determine how many places you need to move the decimal point. If you are converting to a larger unit (e.g., from centimeters to meters), you move the decimal point to the left. Each step to the left represents a factor of 10. So, for every prefix you move up (e.g., from centimeters to meters), you move the decimal point one place to the left (divide by 10 each step). If you are converting to a smaller unit (e.g., from meters to centimeters), you move the decimal point to the right. Each step to the right represents a factor of 10. So, for every prefix you move down (e.g., from meters to centimeters), you move the decimal point one place to the right (multiply by 10 each step). Count the number of places you need to move the decimal point based on the prefixes involved in the conversion. Move the decimal point the corresponding number of places in the appropriate direction. For example: If you want to convert 547.8 millimeters to meters, then you need to move the decimal three spaces to the left. Therefore, 547.8 millimeters = 0.5478 meters

Converting Between Metric Units

Converting between metric units involves multiplying or dividing by powers of 10. Here’s a step-by-step explanation of the process: 

  1. Understand the metric prefixes: The metric system uses prefixes to indicate different orders of magnitude. The most commonly used prefixes are: 
    • Kilo- (k): represents a factor of 1,000 (e.g., 1 kilometer = 1,000 meters) 
    • Hecto- (h): represents a factor of 100 (e.g., 1 hectogram = 100 grams) 
    • Deca- (da): represents a factor of 10 (e.g., 1 decameter = 10 meters) 
    • Base Unit: represents a factor of 1 (For length the base unit is a meter, for weight, the base unit is a gram, and for capacity, the base unit is a liter)   
    • Deci- (d): represents a factor of 0.1 (e.g., 1 deciliter = 0.1 liter) 
    • Centi- (c): represents a factor of 0.01 (e.g., 1 centimeter = 0.01 meter) 
    • Milli- (m): represents a factor of 0.001 (e.g., 1 milligram = 0.001 gram) 
  2. Determine the relationship between the starting unit and the target unit. Look at the prefixes and their corresponding factors to determine how many places you need to move the decimal point.
  3. If you are converting to a larger unit (e.g., from centimeters to meters), you move the decimal point to the left. Each step to the left represents a factor of 10. So, for every prefix you move up (e.g., from centimeters to meters), you move the decimal point one place to the left (divide by 10 each step). 
  4. If you are converting to a smaller unit (e.g., from meters to centimeters), you move the decimal point to the right. Each step to the right represents a factor of 10. So, for every prefix you move down (e.g., from meters to centimeters), you move the decimal point one place to the right (multiply by 10 each step). 
  5. Count the number of places you need to move the decimal point based on the prefixes involved in the conversion. Move the decimal point to the corresponding number of places in the appropriate direction. 

For example: 

If you want to convert 547.8 millimeters to meters, then you need to move the decimal three spaces to the left.  

Therefore, 547.8 millimeters = 0.5478 meters 

Additional Resources

Look at this video for some walk-through examples to help you practice dimensional analysis. 

This dosage calculation cheat sheet gives great step-by-step examples of dimensional analysis.  

Often, the patient’s weight needs to be considered when being given a medication. Watch this video to learn more about weight-based dosage calculations. 

IV Flow Rate Calculations are also standard for nurses, so check out the links provided to watch videos and do practice questions.  

This playlist Dosage Calculations Nursing offers videos on all the topics listed above and is a great resource! 

For practice questions, please check out the resources below: 

References

Some content from the Nursing Math and Pharmacology webpage was generated using ChatGPT. 

 OpenAI. (2023). ChatGPT (Mar 14 version) [Large language model]. https://chat.openai.com/chat 

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