5.4: Equivalencies
- Page ID
- 44539
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The nurse performs a variety of calculations in the clinical setting including intake and output conversions, weight conversions, dosages, volumes, and rates. The metric system is typically used when documenting and performing calculations in the clinical setting. Dosages may be calculated and converted into micrograms (mcg), milligrams (mg), milliequivalents (mEq), and grams (gm); volumes may be calculated in cubic centimeters (cc), milliliters (mL), and liters (L); and rates may be calculated in drops per minute (gtt/min), milliliters per hour (mL/hr), or units per hour (units/hr). Each of these types of calculations will be described in the following sections. Let’s begin by discussing equivalencies.
Equivalency is a mathematical term that refers to two values or quantities that are the same amount. For example, one cup is equivalent to eight ounces. Nurses must memorize common household and metric equivalents to perform drug calculations and convert quantities easily.
Household Equivalencies
The household system of measurement is familiar to patients and includes drops, teaspoons, tablespoons, ounces, cups, and pounds. See Table \(\PageIndex{1}\) for common household measurement conversions and abbreviations that must be memorized by nurses.
| Measurement and Abbreviation | Common Conversions |
|---|---|
| drop (gtt) | 15 -20 gtt = 1 mL |
| teaspoon (tsp) | 1 tsp = 5 mL |
| tablespoon (Tbs) | 1 Tbs = 3 tsp = 15 mL |
| ounce (oz) | 1 oz = 30 mL |
| pound (lb) | 1 lb = 16 oz |
| cup (C) | 1 C = 8 oz = 240 mL |
| pint (pt) | 1 pt = 2 C |
| quart (qt) | 1 qt = 4 C |
| gallon (gal) | 1 gal = 4 qt |
Metric Equivalencies
The metric system is organized by units of 10. The basic units of measurement in the metric system include meter for length, liter for volume, and gram for weight. The decimal point is easily moved either to the right or left with multiplication or division in units of 10. For example, there are 1,000 mL in 1 liter, and 0.5 liters is the same as 500 mL. See Table \(\PageIndex{2}\) for a metric equivalency chart.
When converting to a smaller unit, the decimal moves to the right →→→→→→→→→→
When converting to a larger unit, the decimal moves to the left. ←←←←←←←←←←←
| Kilo-
1000 units |
Hecto-
100 units |
Deca-
10 units |
1
Unit |
Deci-
0.1 units |
Centi-
0.01 units |
Milli-
0.001 units |
|---|
Nurses often need to convert household measurements to metric equivalents or vice versa. See Table \(\PageIndex{3}\) for common metric conversions that nurses must memorize.
| Metric Measurement | Common Conversions |
|---|---|
| 1 kilogram (kg) | 1 kg = 2.2 pounds = 1000 mg |
| 1 centimeter (cm) | 1 in = 2.54 cm = 25.4 mm |
| 37 degrees Celsius | 97.8 degrees F |
| 1 liter | 1000 mL = 1000 cc |
| 1 gram | 1000 mg |
| 1 mg | 1000 mcg |
Metric Table[1]
Metric Conversions[2]
Other Measurements
The nurse encounters other miscellaneous measurements in practice, such as:
- Units (U): Units are used in insulin and heparin dosages.
- International Units (IU): International units are used for vitamins, such as Vitamin D 600 IU.
- Milliequivalents (mEq): Milliequivalents are used in electrolyte replacement, such as Potassium 40 mEq.
- Percentages: Percentages are used in intravenous (IV) fluids, such as 0.9% Normal Saline IV fluid, meaning 9 g of NaCl are diluted in 1000 mL water.
- Ratios: Ratios are used in medications such as Epinephrine 1:1000, meaning 1 gram of Epinephrine is diluted in 1000 mL of fluid (equivalent to 1 mg/mL).
Practice Problems: Household and Metric Equivalents
Practice converting household and metric equivalents using the following problems and referencing Tables \(\PageIndex{1}\)-\(\PageIndex{3}\). The answers are found in the Answer Key (Math Calculations Chapter section) at the end of the book.
- A prescription for a child is written as 1 teaspoon every 4 hours. How many milliliters (mL) will you draw up in an oral syringe?
- A patient’s prescription states to administer one ounce of medication. How many milliliters will you measure in the medication cup?
- A patient’s prescription states to administer 0.5 grams of medication. How many milligrams will you administer?
- A baby weighs 3.636 kilograms. How many grams does this convert to?
- A patient’s pupils are 7 mm in size. How many centimeters does this convert to?
- RegisteredNurseRN. (2015, February 4). What is the metric table for nursing calculations? [Video]. YouTube. All rights reserved. Video used with permission. https://youtu.be/aGMLRnWGanM↵
- RegisteredNurseRN. (2015, February 5). Metric conversions made easy | How solve in metric conversions w/ dimensional analysis (Vid 1). [Video]. YouTube. All rights reserved. Video used with permission. https://youtu.be/0N6SmKVWZdI↵