Welcome, In this med calculation blog series, we review several drug dosage calculation methods. Three primary methods for calculation of medication dosages exist, and these include **dimensional analysis, ratio proportion, and formula or desired-over-have method.** In our first blog, we discussed the universal formula, or “desired over have” method. In Part 2, we take a look at the use of dimensional analysis (with examples and practice questions) in drug dose calculations. **Dimensional Analysis (DA)** is helpful in calculating weight-based dosing and more complex continuous intravenous (IV) infusions. This article explores dimensional analysis in more detail.

**After reading this blog you are able to calculate:**

- Simple medicine dose calculations
- Solid medication dose calculations
- Liquid medication dose calculations
- IV Dose Calculations

Before we dive deeper lets take a look at these frequently asked questions about use of dimensional analysis in drug dosage calculations

### FAQs

**What is**

**Dimensional Analysis**?Dimensional analysis, as the name represents, explores dimensions or units of measurements called factors. Commonly used in solving chemistry and physics problems, dimensional analysis is fast becoming the go-to method for dosage calculations in nursing and the medical profession.

**What is another name for Dimensional Analysis?**

DA is also known as Factor-Label Method or the railroad method.

**Where to use Dimensional Analysis in Dosage Calculation?**

Dimensional Analysis (DA) is helpful in calculating weight-based dosing and more complex continuous intravenous (IV) infusions.

**How is dimensional analysis used to convert units of measure?**

The formula is used to calculate the dose of a drug, often utilized when converting different units of measurements such as pounds to kilograms or kilograms to grams.

**When to not use dimensional analysis or unit-factor method?**

Converting degrees Celsius to degrees Fahrenheit is not possible with this unit-factor method of calculation. A comparison is not feasible between units that have different dimensions and do not have a linear relationship.

## Dimensional Analysis

**Factor-label method or Dimensional analysis (DA)** uses a series of conversion factors of equivalency from one system of measurement to another but doesn’t require memorizing specific formulas. This method reduces errors. It can be used **for all dosage calculations**.

- To set up the equation, start with the label or unit of measure needed in the answer.
- Build the equation by placing information with the same label as the preceding denominator in the numerator so that unwanted labels will cancel out. Repeat until all units of measure not needed in the answer are cancelled out.
- Calculate to determine the correctly labelled numeric answer. Don’t round any numbers in the equation until you have the final answer.

Let’s take a look an example to illustrate this method step by step.

**Step-by-Step Dimensional Analysis Dosage Calculation Example: For IV Dose**

**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?**

**What do you need?**Identify the Required Unit of Measure.What is the needed unit of measure (label)? Place this on the left side of the equation

**Set Up Given Information**On the right side, place the information given with the same label needed in the numerator. In this example, we know that the drug concentration available is 0.25 mg/mL. Place mL in the numerator and 0.25 mg in the denominator.

**Cancel Unwanted Units.**The desired dose is 0.5 mg. 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, and cancelled out all unwanted labels.

**Solve the problem**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.

*Answer: Administer 2 mL of digoxin daily.*

**Dimensional Analysis Calculator**

Medi Calculators Team carefully designed the DA calculator which will help you to calculate simple medications dosage in no time.

How to use Dimensional Analysis Calculator to calculate medications dosage?

- Just click on the below link to open calculators page and fill up the given information and press calculate.
- Encase if there are different units in available and ordered dose do not worry click on advance tab and fill up the given information, select respective units and calculate.
- For weight base calculations switch on weight tab in advance mode and do your calculations with ease.

To avoid any confusion we created solid and liquid dosage calculators separately.

For liquid and IV medications doses such as (syrups, emulsions, suspensions, injections etc)

**Dimensional Analysis Calculator for Liquid Dosage Form**(Click here for calculator)

For solid forms of medication dosage such as (e.g., tablets, caplets, capsules, lozenges).

**Dimensional Analysis Calculator for Solid Dosage Form**(Click here for calculator)

**Dimensional Analysis (DA) ****Practice Questions****:**

How about giving it a try? Using the Dimensional Analysis Dosage Calculation method to calculate the following dosage.

- Atenolol are supplied in 0.05 g capsules. MD orders 100 mg. How many capsules

should be administered to the patient? - The order says, “erythromycin suspension 600 mg PO q6h.” The supply on hand is erythromycin 400 mg per 5 mL. How many millilitres of medication should be given to the patient?
- Doctor orders “valporic acid 0.5 g PO TID.” The bottle of valporic acid on hand says 50 mg per 1 mL. How many millilitres should be given?
- The physician ordered “penicillin V potassium 400 000 units PO QID”. You have penicillin V potassium 200 000 units per 5 mL. How many milliliters should be given to the patient?

Please leave your answer in the comments!

#### Dimensional Analysis Practice Question 1: For Solid Dosage Form

**Atenolol are supplied in 0.05 g capsules. MD orders 100 mg. How many capsules should be given to the patient?**

**Given Information:**

- We have Atenolol = 0.05 g Capsules
- Ordered Dose is = 100 mg
- Capsules given = ?

**Solution:**

1 gram = 1000 mg

0.05 g = 0.05 x 1000 = **50 mg**

You can check dosage calculation conversions unit here.

Now, Follow the same steps:

*What do you need?*

Capsules = ?

Set Up Given Information

$Capsules=\frac{1}{50mg}\times 100mg$Cancel Unwanted Units & Perform the Calculation

$Capsules=\frac{1}{50\overline{)mg}}\times 100\overline{)mg}=\frac{\overline{)100}}{\overline{)50}}={\mathbf{2}}{\mathbf{}}{\mathit{C}}{\mathit{a}}{\mathit{p}}{\mathit{s}}{\mathit{u}}{\mathit{l}}{\mathit{e}}{\mathit{s}}$**Answer:** *Administer 2 Capsules of Atenolol.*

⚠ Warning, Certain medications are not intended to be portioned. Please consult the pharmacist.

#### Dimensional Analysis Practice Question 2: For Liquid Dosage Form

**The order says, “erythromycin suspension 600 mg PO q6h.” The supply on hand is erythromycin 400 mg per 5 mL. How many millilitres of medication should be given to the patient?**

**Given Information:**

- Erythromycin Suspension = 400 mg per 5 mL
- Ordered Dose is = 600 mg PO q6h
- Millilitres Should be given = ?

**Solution: **Follow the steps:

What do you need?

Millilitres (ml) = ?

Set Up Given Information

$\mathit{m}\mathit{L}=\frac{5ml}{400mg}\times 600mg$Cancel Unwanted Units & Perform the Calculation

$\mathit{m}\mathit{L}=\frac{5ml}{400mg}\times 600mg=\frac{3000}{400}={\mathbf{7.5}}{\mathit{m}}{\mathit{L}}$*Answer: Administer 7.5 millilitres of erythromycin suspension* PO q6h*.*

#### Dimensional Analysis Practice Question 3: For Liquid Dosage Form

**The doctor orders “valporic acid 0.5 g PO TID.” The bottle of valporic acid on hand says 50 mg per 1 mL. How many milliliters should be given?**

**Given Information:**

- Valporic acid = 50 mg per 1 mL
- Ordered Dose is = 0.5 g PO TID = 0.5 x 1000 = 500 mg
- Millilitres given = ?

**Solution: **Follow the steps:

What do you need?

Millilitres (ml) = ?

Set Up Given Information

$\mathit{m}\mathit{L}=\frac{1ml}{50mg}\times 500mg$Cancel Unwanted Units & Perform the Calculation

$\mathit{m}\mathit{L}=\frac{1ml}{50mg}\times 500mg=\frac{500}{50}={\mathbf{10}}{\mathbf{}}{\mathit{m}}{\mathit{L}}$*Answer: Administer 10 millilitres of ***valporic acid PO TID***.*

#### Dimensional Analysis Practice Question 4: For Liquid Dose

**The physician ordered “penicillin V potassium 400 000 units PO QID”. You have penicillin V potassium 200 000 units per 5 mL. How many milliliters should be given to the patient?**

**Given Information:**

- Penicillin V potassium = 200 000 units per 5 mL
- Ordered Dose is = 400 000 units PO QID
- Millilitres Should be given = ?

**Solution: **Follow the steps:

What do you need?

Millilitres (ml) = ?

Set Up Given Information

$\mathit{m}\mathit{L}=\frac{5ml}{200000units}\times 400000units$Cancel Unwanted Units & Perform the Calculation

$\mathit{m}\mathit{L}=\frac{5ml}{200000units}\times 400000units=\frac{2000000}{200000}={\mathbf{10}}{\mathit{m}}{\mathit{L}}$*Answer: Administer 10 mL of ***Penicillin V potassium PO QID***.*

### Conclusion

These were simple examples. In the next few blogs we will go into more depth with Dimensional Analysis and work on more complex dosage calculations such IV drip rates like millilitres per hour (mL/hour), micrograms per minute (mcg/min) and micrograms per kilogram per minute (mcg/kg/min). You can check Keep practicing and good luck!

Here is the dimensional analysis calculator which allows you to calculate medication dose in no time:

**Dimensional Analysis Calculator for Solid Dosage Form****Dimensional Analysis Calculator for Liquid Dosage Form**

### Remember these Tips:

- Check that your answer makes sense clinically.
- Double check your work.
- Have a colleague or pharmacist check your work.
- Know general therapeutic drug doses for commonly administered medications.

**References:**

Cookson, K.L. (2013). Dimensional analysis: Calculate dosages the easy way. *Nursing2013*, 43(6), 57-62.

Koharchik, L.S. & Hardy, E.C. (2013). As easy as 1, 2, 3! Dosage calculations. *Nursing Made Incredibly Easy!*, 11(1), 25 – 29.

Wilson, K.M. (2013). The nurse’s quick guide to I.V. drug calculations. Nursing Made Incredibly Easy! 11(2), 1 – 2.