Opening the book…
Measuring Temperature
When you touch something and it feels warm or cold, what is that really telling you about that substance? Temperature is a measure of how fast atoms and molecules are moving in a substance, whether that be the air, a stove top, or an ice cube. The faster those atoms and molecules move, the higher the temperature.
In the metric system, temperature is measured using the Celsius (°C) scale. Because temperature is a condition of the physical properties of a substance, the Celsius scale was created with 100 degrees separating the point at which water freezes, 0 °C, and the point at which water boils, 100 °C. Scientifically, these are the points at which water molecules change from one state of matter to another—from solid (ice) to liquid (water) to gas (water vapor).
When reading temperatures, it’s important to look beyond the degree symbol to determine which temperature scale the units express. For example, 13 °C reads “13 degrees Celsius,” indicating that the temperature is expressed using the Celsius scale, while 13 °F reads “13 degrees Fahrenheit,” indicating that the temperature is expressed using the Fahrenheit scale.
Did you know that in addition to Fahrenheit and Celsius, there is a third temperature scale widely used throughout the world? The Kelvin scale starts at absolute zero, the lowest possible temperature at which there is no heat energy present at all. It is primarily used by scientists to measure very high or very low temperatures when water is not involved.
Converting Between Fahrenheit and Celsius Temperatures
Understanding how to convert between Fahrenheit and Celsius temperatures is an essential skill in understanding metric temperatures. You likely know that below \(32\)°F means freezing temperatures and perhaps that the same holds true for \(0^{\circ} \mathrm{C}\). While it may be difficult to recall that water boils at \(212^{\circ} \mathrm{F}\), knowing that it boils at \(100^{\circ} \mathrm{C}\) is a fairly easy thing to remember.
But what about all the temperatures in between? What is the temperature in degrees Celsius on a scorching summer day? What about a cool autumn afternoon? If a recipe instructs you to preheat the oven to \(350^{\circ} \mathrm{F}\) , what Celsius temperature do you set the oven at?
Figure lists common temperatures on both scales. Since we don’t use Celsius temperatures daily, it’s challenging to recall them. Fortunately, we don’t have to. Instead, we can convert temperatures from Fahrenheit to Celsius and from Celsius to Fahrenheit using a simple algebraic expression.
The following example uses the chart above to estimate the temperature in various situations.
Celsius to Fahrenheit: \[\text{F} =\dfrac{9}{5}\text{C} +32\nonumber\]
Celsius to Kelvin: \[\text{K}=\text{C} +273.15\nonumber\]
Fahrenheit to Celsius: \[\text{C}=\dfrac{5}{9}(\text{F} -32)\nonumber\]
Kelvin to Celsius: \[\text{C}=\text{K} -273.15\nonumber\]
Fahrenheit to Celsius
Subtract \(30\) from Fahrenheit and and divide by \(2\).
\[C=\frac{F-30}{2}\nonumber\]
Celsius Fahrenheit
Multiply Celsius by \(2\) and add \(30\).
\[F=2C+30 \nonumber\]
Celsius Fahrenheit
Example \(\PageIndex{2}\): F to C
- Convert \(73^{\circ} \mathrm{F}\) to Celsius.
- Convert \(28^{\circ} \mathrm{C}\) to Fahrenheit.
- Convert \(3763\) K to Fahrenheit.
- Answer 1
-
To convert from Fahrenheit to Celsius, we need the equation \(\text{C}=\dfrac{5}{9}(\text{F}-32)\). Substitute in the given value for Fahrenheit to find the answer. Round to the nearest degree.
\[
\begin{array}{l}
C=\frac{5}{9} (F-32) \\
C=\frac{5}{9}(73-32) \\
C=\frac{5}{9}(41) \\
C=23.3^{\circ }C
\end{array}
\nonumber \] - Answer 2
-
Use the formula to determine the temperature in degrees Fahrenheit.
\[
\begin{array}{l}
F=\frac{9}{5} C+32 \\
F=\frac{9}{5}(28)+32=82.4 \\
\end{array}
\nonumber \]A temperature of \(82.4^{\circ} \mathrm{F}\) is equal to \(28^{\circ} \mathrm{C}\).
- Answer 3
-
First, we need to convert to Celsius, then we can convert to Fahrenheit. Round to two decimal places.
\(\text{C}=\text{K}-273.15=3763-273.15=3489.85^{\circ}\text{C}\)
\[
\begin{array}{l}
F=\frac{9}{5} C+32 \\
F=\frac{9}{5}(3489.85)+32 \\
F=6281.73+32 \\
F=6313.73^{\circ}C
\end{array}
\nonumber \]Thus, \(3763\) K \(=6313.73\; F\)
Example \(\PageIndex{3}\): Using Benchmark Temperatures to Determine Reasonable Values for Temperature
- Which is the more reasonable value for the temperature of a freezer? \(5^{\circ} \mathrm{C}\) or \(-5^{\circ} \mathrm{C}\)?
- The average body temperature is generally accepted as \(98.6^{\circ} \mathrm{F}\). What is a reasonable value for the average body temperature in degrees Celsius? \(98.6^{\circ} \mathrm{C}\) or \(64.3^{\circ} \mathrm{C}\) or \(34.3^{\circ} \mathrm{C}\)?
- Answer
-
- We know that water freezes at \(0^{\circ} \mathrm{C}\). So, the more reasonable value for the temperature of a freezer is \(-5^{\circ} \mathrm{C}\) which is below \(0^{\circ} \mathrm{C}\). At a temperature of \(5^{\circ} \mathrm{C}\), it is above freezing.
- To estimate the average body temperature in degrees Celsius, subtract \(30\) from the temperature in degrees Fahrenheit, and divide the result by \(2\).\[\frac{98.6-30}{2}=\frac{68.6}{2}=34.3\nonumber\]A reasonable value for average body temperature is \(34.3^{\circ} \mathrm{C}\).
Example \(\PageIndex{4}\): Using Conversion to Determine Reasonable Values for Temperaturesk
Which is a reasonable temperature for storing chocolate: \(28^{\circ} \mathrm{C}\) or \(18^{\circ} \mathrm{C}\) or \(2^{\circ} \mathrm{C}\)?
- Answer
-
Use the formula in Table \(\PageIndex{2}\) to determine the temperature in degrees Fahrenheit.
\[
\begin{array}{l}
F=\frac{9}{5} C+32 \\
F=\frac{9}{5}(28)+32=82.4 \\
F=\frac{9}{5}(18)+32=64.4 \\
F=\frac{9}{5}(2)+32=35.6
\end{array}
\nonumber \]A temperature of \(82.4^{\circ} \mathrm{F}\) would be too hot, causing the chocolate to melt. A temperature of \(35.6^{\circ} \mathrm{F}\) is very close to freezing, which would affect the look and feel of the chocolate. So, a reasonable temperature for storing chocolate is \(18^{\circ} \mathrm{C}\), or \(64.4^{\circ} \mathrm{F}\).
Time is used to describe the duration between events. Some common units (along with their abbreviations) for time are listed in the following table.
\[
\begin{array}{l}
1 \text{ minute} &= 60 \text{ sec} \\
1 \text{ day} &= 24 \text{ hours} \\
1 \text{ hour } &= 60 \text{ min} \\
1 \text{ week} &= 7 \text{ days} \\
1 \text{ year } &= 52 \text{ week} \\
\end{array}
\nonumber \]
Example \(\PageIndex{5}\): Hours to Week
Convert \(2,016\) hr to weeks.
- Answer
-
Looking in the unit conversion table under time, we see that \(\text{1 wk = 7 da}\) and that \(\text{1 da = 24 hr}\). To convert from hours to weeks, we first convert from hours to days, then from days to weeks. We need two unit fractions.
The unit fraction needed for converting from hours to days is \(\dfrac{1 \text{ da}}{24 \text{ hr}}\). The unit fraction needed for converting from days to weeks is \(\dfrac{\text{1 wk}}{\text{7 da}}\).
\(\begin{array} {rcll} {\text{2,016 hr}} & = & {\dfrac{\text{2,016 hr}}{1} \cdot \dfrac{\text{1 da}}{\text{24 hr}} \cdot \dfrac{\text{1 wk}}{\text{7 da}}} & {\text{Divide out common units.}} \\ {} & = & {\dfrac{\text{2,016 } \cancel{\text{hr}}}{1} \cdot \dfrac{\text{1 } \cancel{\text{da}}}{\text{24 } \cancel{\text{hr}}} \cdot \dfrac{\text{1 wk}}{\text{7 } \cancel{\text{da}}}} & {} \\ {} & = & {\dfrac{2,016 \cdot 1 \text{ wk}}{24 \cdot 7}} & {\text{Simplify}} \\ {} & = & {\text{12 wk}} & {} \end{array}\)
Thus, \(\text{2,016 hr = 12 wk}\).
To Your Health: Dosages
A medicine can be more harmful than helpful if it is not taken in the proper dosage. A dosage (or dose) is the specific amount of a medicine that is known to be therapeutic for an ailment in a patient of a certain size. Dosages of the active ingredient in medications are usually described by units of mass, typically grams or milligrams, and generally are equated with a number of capsules or teaspoonfuls to be swallowed or injected. The amount of the active ingredient in a medicine is carefully controlled so that the right number of pills or spoonfuls provides the correct dose.
A medical dose is the amount of medicine given to a person at one time. The correct dose is important because too little medicine may not work, and too much may be harmful. Doctors, nurses, and pharmacists determine the proper dose based on factors such as a person's age, weight, and health condition. Medical doses are commonly measured in units such as milligrams (\(\text{mg}\)) and milliliters (\(\text{mL}\)). Accurate dosing helps ensure safe and effective treatment.
Dimensional Analysis in Medical Dosage Calculations
Dimensional analysis provides a systematic, unified framework for calculating medication dosages by treating units of measurement as algebraic quantities that can be multiplied, divided, and canceled. Rather than memorizing disparate formulas for different clinical scenarios, practitioners set up a continuous string of conversion factors arranged so that unwanted units cancel diagonally, leaving only the desired unit of measurement for the final answer. The calculation typically follows a standard sequence:
Calculating drug dosages for humans from animal studies can be based on weight (e.g., \(\text{mg/kg}\)) or surface area (e.g., \(\text{mg}/\text{m}^2\)). Drug dosage calculation is required if the physician’s order is different from what is available.
When solving dosage problems, it is helpful to identify the target unit first. This will help you choose the correct conversion factors and ensure that your final answer is expressed in the required unit.
Problem: An order calls for Amoxicillin \(500\text{ mg}\) orally. The pharmacy supplies Amoxicillin suspension labeled as \(250\text{ mg}\) per \(5\text{ mL}\). How many milliliters should be administered?
-
Identify the target unit: \(\text{mL}\)
-
Start with the ordered dose: \(500\text{ mg}\)
-
Multiply by the conversion factor arranged to cancel units:
\[ 500\text{ mg}=500\text{ mg} \times \left(\frac{5\text{ mL}}{250\text{ mg}}\right)\nonumber\]
-
Cancel terms and solve:
\[ \frac{500 \times 5}{250}\text{ mL} = \frac{2500}{250}\text{ mL} = 10\text{ mL}\nonumber\]
\[250 \text{ mg per } 5 \text{ mL}= \frac{250\text{ mg}}{5\text{ mL}} \nonumber\]
\[50 \text{ mg per } \text{ tablet}= \frac{50\text{ mg}}{1\text{ tablet}} \nonumber\]
\[30 \text{ mg every } 5 \text{ hours}= \frac{30\text{ mg}}{5\text{ hours}} \nonumber\]
\[80 \text{ mg }/\text{kg}= \frac{80\text{ mg}}{1\text{ kg}} \nonumber\]
Example \(\PageIndex{6}\): Find the Number of Tablets
- A physician ordered \(100\) mg of Demerol. Demerol is available as \(50\) mg per tablet. How many tablets should the nurse administer?
- The doctor’s order is \(1.2\) g of Folic Acid. Folic Acid is available as \(800\) mg per tablet. How many tablets should be taken?
- Answer 1
-
Here, the target unit is the number of tablets. We start with the given, \(100\) mg. We want to change the unit from mg to tablets. There are \(50\) mg in \(1\) tablet (Remember that per tablet means one tablet. From this relationship, we can construct the following conversion factor. \[50\text{~mg} = 1\text{~tablet} \nonumber\]We use the conversion factor that will cancel out the original unit, mg, and introduce the unit we are converting to, which is tablet.\[ 100 \cancel{\rm{mg}} \times \dfrac{1\; \rm{tablet}}{50\; \cancel{\rm{mg}}} = 2\; \rm{tablets} \nonumber \]Hence, the nurse should administer \(2\) tablets..
- Answer 2
-
Here, the target unit is the number of tablets. We start with the given amount, \(1.2\) g, and we want to convert it to the number of tablets. First, we convert \(1.2\) g to mg and then convert mg to tablets. We need a conversion factor for each step. Here are the conversion factors that we can use.
\begin{align*} 800\text{~mg} &= 1\text{~tablet}\\
1,000\text{~mg} &= 1\text{~g} \\
\end{align*}\[ \begin{align*} 1.2 \; \cancel{\rm{g}} \times \dfrac{1,000 \cancel{\rm{mg}}}{1\; \cancel{\rm{g}}} \times \dfrac{1\; \rm{tablet}}{800\; \cancel{ \rm{mg}}} &=1.5 \; \rm{tablets} \end{align*} \nonumber \]
Hence, exactly \(1.5\) tablets should be taken. If we round to the nearest whole number, \(2\) tablets should be taken.
Drug Dosage Calculation based on Body Weight. Many drugs (especially in children) are dosed according to body weight (mg/kg). These calculations are carried in 3-step conversions. The first step is to convert the body weight from pounds (lbs) to kg. The second step is to convert kg to mg (the total mg dose calculated based on body weight). And, finally, the mg dose is converted to the number of tablets.
Example \(\PageIndex{7}\): Find the Number of Tablets
Demerol is ordered \(1.5\) mg/kg for a patient who is \(220\) lbs. Demerol is available as \(50\) mg per tablet. How many tablets should the nurse administer?
- Answer
-
Here, the target unit is tablets. We start with the given, \(220\) lbs. We want to change the unit from lbs to kg, and then from kg to total dose (mg), and then the mg dose to tablets. The first conversion factor will cancel out the original unit, lbs, and introduce the unit we are converting to, which is kg. The second conversion factor will cancel out kg and introduce the unit of the dose (usually mg), and then convert mg to tablets. The following are the conversion factors that we can use.
\begin{align*} 1\text{~kg} &= 2.2\text{~lb}\\
1.5\text{~mg} &= 1\text{~kg} \\
1\text{~tablet} &= 50\text{~mg} \\
\end{align*}\[ 220 \cancel{\rm{lbs}} \times \dfrac{1\cancel{\rm{kg}}}{2.2\; \cancel{\rm{lbs}}} \times \dfrac{1.5\cancel{\rm{mg}}}{1\; \cancel{ \rm{kg}}} \times \dfrac{1\; \rm{tablet}}{50\; \cancel{\rm{mg}}}= 3\; \rm{tablets} \nonumber \]
Hence, the nurse should administer \(3\) tablets.
Example \(\PageIndex{8}\): Find the Number of Tablets in a Week
The antihistamine Benadryl is often prescribed for allergies. A typical dose for a \(95\)-a pound person is \(30\) mg every \(5\) hours. Following this dosage, how many \(10.5\) mg chewable tablets would be taken in a week?
- Answer
-
Note that we are looking for tablets per week, so the "tablet" unit must be in the numerator and the "week" unit must be in the denominator. The following are the conversion factors that we can use.
\begin{align*}
30\text{~mg} &= 5\text{~hr} \\
24\text{~hr} &= 1\text{~days} \\
1\text{~week} &= 7\text{~days} \\
1\text{~tablet} &= 10.5\text{~mg} \\
\end{align*}\[ \dfrac{30\cancel{\rm{mg}}}{5\; \cancel{\rm{hrs}}} \times \dfrac{24\cancel{\rm{hr}}}{1\; \cancel{ \rm{day}}} \times \dfrac{7\; \cancel{\rm{days}}}{1\; \rm{week}}\times \dfrac{1\; \rm{tablet}}{10.5\; \cancel{\rm{mg}}}= 96\; \dfrac{ \rm{tablet}}{\rm{week}}\nonumber \]
Hence, the nurse administers \(96\) tablets in a week.
Example \(\PageIndex{9}\): Doses Calculation
Suppose a dose of \( 9,000\) units/kg of penicillin is prescribed every \(8\) hours for treatment of a bacterial infection. For penicillin, \(400,000\) units = \(250\) mg.
(a) Express the dose in mg per kg of body weight.
(b) How many milligrams of penicillin would a \(22\)-kg child take in one day?
- Answer
-
(a) Note that we are looking for mg per kg, so the "mg" unit must be in the numerator and the "kg" unit must be in the denominator. The following are the conversion factors that we can use.
\begin{align*}
9,000\text{~units} &= 1\text{~kg} \\
400,000\text{~units} &= 250\text{~mg} \\
\end{align*}\[ \dfrac{9,000\cancel{\rm{units}}}{1\; \cancel{\rm{kg}}} \times \dfrac{250\cancel{\rm{mg}}}{400,000\; \cancel{ \rm{units}}} = 5.63\; \dfrac{ \rm{mg}}{\rm{kg}}\nonumber \]
Hence, the dose will be \(5.63\) milligram per kilogram.
(b) Note that we are looking for mg per day, so the "mg" unit must be in the numerator and the "day" unit must be in the denominator. The following are the conversion factors that we can use.
\begin{align*}
9,000\text{~units} &= 1\text{~kg} \\
400,000\text{~units} &= 250\text{~mg} \\
1\text{~day} &= 24\text{~hr} \\
\end{align*}\[ \dfrac{9,000\cancel{\rm{units}}}{1\; \cancel{\rm{kg}}\times 8~ \cancel{\text{hr}}} \times \dfrac{250\rm{~mg}}{400,000\; \cancel{ \rm{units}}} \times \dfrac{22 \cancel{\rm{~kg}}}{1 }\times \dfrac{24 \cancel{\rm{~hr}}}{1\rm{~day} } = 371.25\; \dfrac{ \rm{mg}}{\rm{day}}\nonumber \]
Hence, the dose will be \(371.25\) milligrams per day.
References
- The Use of Body Surface Area as a Criterion of Drug Dosage in Cancer Chemotherapy(opens in new window) [cancerres.aacrjournals.org] "The Use of Body Surface Area as a Criterion of Drug Dosage in Cancer Chemotherapy" D Pinkel. Cancer Research 1958
Contributors and Attributions
- Wikipedia
- Leticia Colmenares (UH-WCC)
Dosage Calculations
This page titled 3.4: Temperature, Time, and Medicine Doses was last modified on Wed, 14 Oct 2026 15:37:14 GMT and is shared under a not declared license and was authored, remixed, and/or curated by Leah Griffith, Veronica Holbrook, Johnny Johnson, and Nancy Garcia.
The book could not be loaded just now.