Calculating liquid and solution doses

Liquid medication doses

When preparing a liquid medication, you will see two different units of measure on the bottle label. These two units are the weight of the powdered medications and the volume of liquid. The units typically used include the following:

Weight of the powdered medication

• g
• mg
• mcg

Volume of liquid

• cc
• mL

Note: some medications (such as insulin or heparin) are dosed in units, a measure of biological activity rather than weight. Units aren’t converted to mg - you calculate a units dose against a stock that is also labeled in units, using the same proportion method described below.

For instance, a bottle label states, “50 mg/2 mL.” This means there are 50 mg of powdered medication in every 2 mL of liquid. If you want 50 mg of medication, then you would need to give 2 mL of liquid.

Another example is 1500 mg/mL. This means there are 1500 mg of powdered medicine in each milliliter of liquid. Remember that sometimes 1 mL is indicated by just “mL.”

Liquid medication dose with matching labels

If the unit label of the ordered medication is the same as the stock medication, then the units are considered to match. For instance, in the following problem, the ordered medication dose label is shown in milligrams (mg). The stock medication is 1300 mg/2 mL. The powdered medication label (mg) matches the label on the order.

Pitfall: If the order and the stock label use different units (for example, an order written in grams but a stock labeled in mg/mL), convert one to match the other before setting up the proportion or formula - plugging in mismatched units gives a wrong answer even if the arithmetic is correct. For example, an order of 0.5 g converts to 500 mg before you compare it to a mg/mL stock label. The next chapter, Pharmacology math, covers the full set of metric conversions.

Using the proportion method

The following steps show how to calculate the amount of medication needed for a dose when the labels match.

Problem

Order: ABC medication 1500 mg.

Stock: ABC medication 1300 mg/2 mL.

How much medication (in mL) should be given?

Solution for problem

Set up the problem: Make sure the label information is on the stock side of the equation. The order is on the opposite side. Remember labels need to be in the same location on both sides of the equal sign.

Step 1: Put the stock information into a fraction. You can put either number on top, as long as you keep track of which label goes where - the order side in Step 2 must place its matching label in the same position. Make sure to add the labels.

$$\frac{1300\text{mg}}{2\text{mL}}$$

Step 2: Put the order information on the other side. Make sure the labels are in the exact same location.

$$\frac{1300\text{mg}}{2\text{mL}}=\frac{1500\text{mg}}{x\text{mL}}$$

Step 3: Now solve for the unknown.

Using a calculator: Multiply in the diagonal direction of the two numbers (2 × 1500), then divide by the number in the other direction (1300). Round your answer to the nearest tenth.

$$2\times 1500=3000$$

$$3000÷1300=2.3\text{mL}$$

To solve without a calculator: Multiply diagonally and solve for x. Round your answer to the nearest tenth.

$$1300x=1500\times 2$$

$$1300x=3000$$

$$\frac{3000}{1300}=x$$

$$x=2.3\text{mL}$$

Using the formula method

The formula method uses the same values as the proportion method, just arranged differently. It’s a quicker way to reach the same answer once you know D (desired), H (on hand), and V (vehicle):

$$\frac{D(\text{desired})\times V(\text{vehicle [tablet or liquid]})}{H(\text{on hand})}$$

For the same order and stock used above (order: 1500 mg; stock: 1300 mg/2 mL), D = 1500 mg, H = 1300 mg, and V = 2 mL:

$$\frac{1500\text{mg}\times 2\text{mL}}{1300\text{mg}}=\frac{3000}{1300}=2.3\text{mL}$$

Solutions

In the ambulatory care environment, many anesthetics used for minor surgeries come in a solution. When comparing solutions, the medical assistant should be able to recognize the weaker and stronger solutions. The following sections discuss solutions and how to calculate a dose using a solution.

The makeup of a solution

For instance, a provider asks you to get the strongest Xylocaine vial in the cabinet. You see a 1% and a 2% vial. What does this mean?

When the manufacturer made the medication, the recipe called for powdered drug to be mixed with a liquid:

$$1\%\text{ solution}=1000\text{mg in}100\text{mL}$$

$$2\%\text{ solution}=2000\text{mg in}100\text{mL}$$

(The 100 mL of liquid always remains, regardless of the number in front of the percentage sign.)

Going back to the provider’s request, you would give the provider the 2% vial because it is the strongest solution (or contains the most powdered drug).

Solution dose

If a medical assistant needs to calculate a dose of medication using a stock solution vial, the process is similar to that used for the prior problems. The initial step would require the medical assistant to change the percent into a fraction. For example, the fraction for a 5% solution would be 5000 mg/100 mL. The remaining steps would be the same as for the previous problems.

The following steps show how to calculate the amount of medication needed for a dose when using a solution.

Problem

Order: ABC medication 20 mg.

Stock: ABC medication 2% solution.

How much medication (in mL) should be given?

Solution for problem

Step 1: Change the 2% into a fraction.

Tip: Take the number before the percentage sign. Add 3 zeros and mg after it. Then put it over 100 mL.

$$2\%=\frac{2000\text{mg}}{100\text{mL}}$$

Step 2: Use the fraction created in Step 1 as the stock medication.

$$\frac{2000\text{mg}}{100\text{mL}}$$

Step 3: Put the order information on the other side. Make sure the labels are in the exact same location.

$$\frac{2000\text{mg}}{100\text{mL}}=\frac{20\text{mg}}{x\text{mL}}$$

Step 4: Now solve for the unknown.

Using a calculator: Multiply in the diagonal direction of the two numbers (100 × 20), then divide by the number in the other direction (2000). Round your answer to the nearest tenth.

$$100\times 20=2000$$

$$2000÷2000=1\text{mL}$$

To solve without a calculator: Multiply diagonally and solve for x. Round your answer to the nearest tenth.

$$2000x=100\times 20$$

$$2000x=2000$$

$$\frac{2000}{2000}=x$$

$$x=1\text{mL}$$