2 Measurement Systems and Conversions

Why units matter

Pharmacy calculations often require changing a quantity from one unit to another before calculating a dose or volume. Dimensional analysis, also called the factor-label method, keeps units visible so you can check that each step leads to the desired unit.

Metric units and conversions

The metric system is based on powers of ten. Common pharmacy units include grams ($\text{g}$) for mass, liters ($\text{L}$) for volume, and meters ($\text{m}$) for length. A prefix indicates how a unit relates to its base unit:

• Kilo- ($\text{k}$): $1{,}000$ base units.

• Base unit: $1$ base unit.

• Milli- ($\text{m}$): $0.001$ base unit.

• Micro- ($\text{mcg}$ or $\mu$): $0.000001$ base unit.

Useful mass and volume relationships include:

• $1\ \text{kg}=1{,}000\ \text{g}$

• $1\ \text{g}=1{,}000\ \text{mg}$

• $1\ \text{mg}=1{,}000\ \text{mcg}$

• $1\ \text{L}=1{,}000\ \text{mL}$

• $1\ \text{mL}=1{,}000\ \text{mcL}$

Convert from a larger metric unit to a smaller one by multiplying, and from a smaller unit to a larger one by dividing. For example:

Household and U.S. customary measures

Common household equivalents help with recognizing units in medication directions:

• $1$ teaspoon (tsp) = $5\ \text{mL}$.

• $1$ tablespoon (Tbsp) = $15\ \text{mL}$, or $3$ tsp.

• $1$ U.S. fluid ounce (fl oz) is about $30\ \text{mL}$.

• $1$ cup is about $240\ \text{mL}$.

• $1\ \text{kg}\approx 2.2\ \text{lb}$.

Household equivalents are rounded for convenience. More exact U.S. customary conversions differ slightly; for example, a U.S. teaspoon is about $4.93\ \text{mL}$. Use the conversion specified by the problem or reference. For measuring liquid medicine, use a properly marked oral syringe or dosing cup rather than a kitchen spoon, and check that the device's units match the prescribed dose.

Do not confuse fluid ounces, which measure volume, with ounces, which measure mass. The abbreviation $\text{oz}$ alone may be ambiguous, so identify what quantity is being measured.

Conversion factors and unit cancellation

A conversion factor is a fraction made from equivalent quantities, so its value is $1$. Choose its orientation so the unwanted unit cancels and the desired unit remains. For example:

To convert $0.75\ \text{g}$ to milligrams, multiply by the factor with grams in the denominator:

The grams cancel, leaving milligrams. If units do not cancel as intended, reorient the conversion factor before calculating.

Applying the method to a dose

Suppose a dose of $250\ \text{mg}$ is prescribed and the available liquid contains $125\ \text{mg}$ per $5\ \text{mL}$. The volume that supplies the prescribed dose is:

The milligrams cancel, leaving milliliters. As a reasonableness check, $250\ \text{mg}$ is twice $125\ \text{mg}$, so the volume should be twice $5\ \text{mL}$, or $10\ \text{mL}$. Dimensional analysis uses the same cancellation method for longer calculations involving multiple conversions.

A reliable calculation routine

Use this routine for a conversion or pharmacy calculation:

1. Identify the quantity you need and its unit.

2. Write down the given quantity with its unit.

3. Select equivalent conversion factors and orient each fraction to cancel unwanted units.

4. Multiply and divide, then check that only the desired unit remains.

5. Check whether the result's size is reasonable, and round only as directed.

Use unambiguous abbreviations and clear notation. In medication calculations, avoid a trailing zero: write $5\ \text{mg}$, not $5.0\ \text{mg}$. For amounts less than one, use a leading zero: write $0.5\ \text{mg}$, not $.5\ \text{mg}$.