1 Medication Measurement and Conversion

Units and common equivalents

Medication calculations depend on choosing the correct unit and converting it correctly. Household equivalents are rounded for convenience, and calculation examples do not replace a medication order or product instructions.

Metric and volume relationships

• $1\,\mathrm{kg}=1{,}000\,\mathrm{g}$.

• $1\,\mathrm{g}=1{,}000\,\mathrm{mg}$.

• $1\,\mathrm{mg}=1{,}000\,\mathrm{mcg}$.

• $1\,\mathrm{L}=1{,}000\,\mathrm{mL}$.

• $1\,\mathrm{mL}=1\,\mathrm{cm}^{3}$, also called $1\,\mathrm{cc}$.

Approximate household equivalents

• $1$ U.S. teaspoon (tsp) is approximately $5\,\mathrm{mL}$.

• $1$ U.S. tablespoon (Tbsp) is approximately $15\,\mathrm{mL}$, or $3$ tsp.

• $1$ U.S. cup is approximately $240\,\mathrm{mL}$.

• $1$ U.S. fluid ounce (fl oz) is approximately $30\,\mathrm{mL}$.

• $1\,\mathrm{kg}$ is approximately $2.2\,\mathrm{lb}$.

These household conversions are approximate: a U.S. teaspoon is about $4.93\,\mathrm{mL}$, and a U.S. tablespoon is about $14.79\,\mathrm{mL}$. A fluid ounce measures volume, while an ounce by weight measures mass; they are not interchangeable.

For actual liquid medicines, measure the prescribed dose in $\mathrm{mL}$ with a suitable calibrated device, such as an oral syringe, rather than an ordinary household spoon. Household conversions are for learning calculations and do not replace the labeled dose or dosing device.

A reliable conversion method

Use a Conversion factor written as a fraction equal to one. Arrange it so the unwanted unit cancels:

For example, convert $0.75\,\mathrm{g}$ to milligrams:

The $\mathrm{g}$ units cancel, leaving $\mathrm{mg}$. Since milligrams are smaller than grams, the numerical value increases in this conversion.

For metric conversions, multiply when changing from a larger unit to a smaller unit, using the number of smaller units in one larger unit. Divide when changing from a smaller unit to a larger unit. For example:

Write the units and conversion factor rather than relying only on moving a decimal point; this makes the conversion direction clear.

Fractions, decimals, and safe notation

A Fraction represents division: $\frac{3}{4}=3\div4=0.75$. Convert a fraction to a decimal by dividing the numerator by the denominator. Convert a decimal to a fraction using its place value, then simplify.

Common equivalents include $\frac{1}{2}=0.5$, $\frac{1}{4}=0.25$, $\frac{3}{4}=0.75$, $\frac{1}{5}=0.2$, and $\frac{1}{10}=0.1$.

For example, $\frac{3}{4}$ of a tablet is the mathematical quantity $0.75$ tablet. Whether a tablet may be split depends on the product and its directions. Also, $0.6=\frac{6}{10}=\frac{3}{5}$, and $1\frac{1}{2}=1+\frac{1}{2}=1.5$.

In medication notation, write a Leading zero for a value below one, such as $0.5$, rather than $.5$. Avoid a Trailing zero after a decimal: write $5\,\mathrm{mg}$, not $5.0\,\mathrm{mg}$. Decimal misreading can cause a tenfold error.

Ratios, proportions, and unit rates

A Ratio compares two quantities, while a Proportion states that two ratios are equal. Keep corresponding units aligned, and simplify ratios when useful.

Suppose $2\,\mathrm{mL}$ contains $10\,\mathrm{mg}$. To find the amount in $6\,\mathrm{mL}$, set up equal ratios:

Cross-multiplying gives $2x=60$, so $x=30\,\mathrm{mg}$.

The same calculation can use a Unit rate:

Converting weight

A commonly used approximate weight conversion is $1\,\mathrm{kg}=2.2\,\mathrm{lb}$. Convert pounds to kilograms by dividing by $2.2$; convert kilograms to pounds by multiplying by $2.2$:

For example, convert $154\,\mathrm{lb}$ to kilograms:

The $\mathrm{lb}$ units cancel. For clinical calculations, use the patient weight and rounding method specified by the order or applicable protocol; do not round prematurely.

Worked conversion examples

The following worked problems apply the conversion, fraction, ratio, and weight methods.

Metric conversions

• Convert $1.8\,\mathrm{g}$ to milligrams:

  $$1.8\,\mathrm{g}\times\frac{1{,}000\,\mathrm{mg}}{1\,\mathrm{g}}=1{,}800\,\mathrm{mg}$$

• Convert $650\,\mathrm{mcg}$ to milligrams:

  $$650\,\mathrm{mcg}\times\frac{1\,\mathrm{mg}}{1{,}000\,\mathrm{mcg}}=0.65\,\mathrm{mg}$$

• Convert $0.125\,\mathrm{L}$ to milliliters:

  $$0.125\,\mathrm{L}\times\frac{1{,}000\,\mathrm{mL}}{1\,\mathrm{L}}=125\,\mathrm{mL}$$

• Convert $0.04\,\mathrm{g}$ to micrograms:

  $$0.04\,\mathrm{g}\times\frac{1{,}000\,\mathrm{mg}}{1\,\mathrm{g}}\times\frac{1{,}000\,\mathrm{mcg}}{1\,\mathrm{mg}}=40{,}000\,\mathrm{mcg}$$

Household and metric volume

Use the approximate learning equivalents $1\,\mathrm{tsp}=5\,\mathrm{mL}$ and $1\,\mathrm{Tbsp}=15\,\mathrm{mL}$.

• Convert $2\,\mathrm{tsp}$ to milliliters:

  $$2\,\mathrm{tsp}\times\frac{5\,\mathrm{mL}}{1\,\mathrm{tsp}}=10\,\mathrm{mL}$$

• Convert $45\,\mathrm{mL}$ to tablespoons:

  $$45\,\mathrm{mL}\times\frac{1\,\mathrm{Tbsp}}{15\,\mathrm{mL}}=3\,\mathrm{Tbsp}$$

• Convert $\frac{1}{2}$ cup to milliliters using $1$ cup $\approx240\,\mathrm{mL}$:

  $$\frac{1}{2}\times240\,\mathrm{mL}\approx120\,\mathrm{mL}$$

Fractions, decimals, and ratios

• Write $\frac{3}{8}$ as a decimal:

  $$3\div8=0.375$$

• Simplify the ratio $12\,\mathrm{mg}$ to $4\,\mathrm{mL}$ and state the amount per milliliter:

  $$12\,\mathrm{mg}:4\,\mathrm{mL}=3\,\mathrm{mg}:1\,\mathrm{mL}=3\,\mathrm{mg}/\mathrm{mL}$$

• A solution contains $18\,\mathrm{mg}$ in $6\,\mathrm{mL}$. Find the amount in $2\,\mathrm{mL}$:

  $$\frac{18\,\mathrm{mg}}{6\,\mathrm{mL}}=\frac{x\,\mathrm{mg}}{2\,\mathrm{mL}}$$

  Cross-multiplying gives $6x=36$, so $x=6\,\mathrm{mg}$.

Weight

• Convert $132\,\mathrm{lb}$ to kilograms using $2.2\,\mathrm{lb}/\mathrm{kg}$:

  $$132\,\mathrm{lb}\div2.2\,\mathrm{lb}/\mathrm{kg}=60\,\mathrm{kg}$$

Checking calculations and medication use

Before accepting a result, check that the starting and final units are identified and that the conversion factors are oriented so unwanted units cancel. Consider whether the numerical result changes in a sensible direction; converting grams to milligrams, for example, produces a larger number.

Write decimals safely, and round only as directed. Do not use a calculation to override a medication label, order, or required clinical verification. In real medication measurement, follow the prescribed directions and use a calibrated device for liquid doses.

• Metric prefixes