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Temperature Conversion Formula - Celsius to Fahrenheit Equation

Maram Ghadban, Gerald Lemay, Laura Pennington
  • Author
    Maram Ghadban

    A freelance tutor equipped with a bachelor's of science in chemical engineering. Graduated from the American University of the Middle East with a GPA of 3.87, performed a number of scientific primary and secondary research. Tutored university level students in various courses in chemical engineering, math, and art. Has experience tutoring middle school and high school level students in science courses.

  • Instructor
    Gerald Lemay

    Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

  • Expert Contributor
    Laura Pennington

    Laura received her Master's degree in Pure Mathematics from Michigan State University, and her Bachelor's degree in Mathematics from Grand Valley State University. She has 20 years of experience teaching collegiate mathematics at various institutions.

Read about temperature conversion and understand how to use easy temperature conversion formulas. Learn how to convert using the Celsius to Fahrenheit equation. Updated: 10/20/2021

Temperature Conversion

The most common units of temperature measurement are degrees Celsius , which is denoted as °C, degrees Fahrenheit, denoted as °F, and Kelvin, denoted as K. Perhaps the reader is more acquainted with the former two units, given the fact that they are widely used in everyday applications. Degrees Fahrenheit is used in the United States and other countries, a few of which are Bahamas, Palau, and Belize. Whereas the degrees Celsius is used by countries that adopted the metric system, mainly countries in Europe, Asia, and some countries in America, including Canada. The Kelvin unit is used primarily in scientific calculations and research related to temperature, such as problems that involve the ideal gas law.

In this lesson, the relation between each temperature unit will be discussed thoroughly, and the unit temperature conversion formula for each will be derived. The purpose of converting from one temperature unit to another is to express the same temperature in a unit one is more familiar with. Let's suppose that Alice is more familiar with temperatures expressed in degrees Celsius and that she is planning to go on a trip to the United States of America, where the temperature is expressed in Fahrenheit. Upon planning for the trip, she first examines the weather conditions in the region she will be visiting, and she learns that this week the weather will be pleasant, the skies will be clear, and that it's a perfect time for a holiday, except that it's 68 degrees. At first glance, Alice would think twice before going on this trip since the temperature is a staggering 68 degrees, well, in Fahrenheit. Should she convert this temperature to Celsius, she'd confirm that the weather is indeed pleasant and that it's a perfect time for a holiday.

Solving Problems With Temperature

Planning a trip to Vancouver from Boston includes gathering lots of information. It helps to know local temperatures while deciding on the appropriate clothing to bring. Temperatures in Canada are in degrees Celsius while in the United States, the temperature is measured in degrees Fahrenheit.

With Internet resources, these conversions are easily done but have you ever wondered how to do them yourself? With one simple equation, the conversions with Celsius and Fahrenheit temperatures are easily made. Have you ever wondered where this equation came from? Then there's the temperature measure called the Kelvin. In this lesson, we will see how they are all related.

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Easy Temperature Conversion Formulas

The following table shows the temperatures in Celsius and in Fahrenheit. As the reader can see, 15°C is equal to 59°F, and that 113°F is equal to 45°C.

Celsius Fahrenheit
-55 -67
-50 -58
-45 -49
-40 -40
-35 -31
-30 -22
-25 -13
-20 -4
-15 5
-10 14
-5 23
0 32
5 41
10 50
15 59
20 68
25 77
30 86
35 95
40 104
45 113
50 122

By examining this table alone, it would be difficult to deduce the relationship between these two units. To understand this relationship, we will start by discussing the thermodynamic properties of water (as a basis) then use the standard line equation to derive the conversion formulas.

The following image shows the freezing and the boiling temperatures of water in both Celsius and Fahrenheit. At atmospheric pressure, the water boils at 100°C and it freezes at 0°C. The temperature difference between these two points is equal to {eq}\Delta C = 100 - 0 = 100 {/eq}. And in the Fahrenheit scale, water boils at 212°F and freezes at 32°F, the difference between the temperatures is {eq}\Delta F = 212 - 32 = 180 {/eq}.

Fahrenheit and Celsius Temperature Scales Indicating the Boiling Point & Freezing Point of Water

Temperature Scale

Recall the line equation, y = mx + b, where m is the slope of the line and b is the constant. Let us first find the slope m, which would be equal to the ratio of the difference in temperatures in Fahrenheit to the difference in Celsius, as shown: {eq}m = \Delta F / \Delta C = 180/100 = 1.8 = 9/5 {/eq}. Next, we will rewrite the line equation this way {eq}T (F) = m T (C) + b {/eq}, which is {eq}T (F) = 1.8 T (C) + b {/eq}

The only component that we have yet to identify is the constant b. Recall that the freezing temperatures of water in Celsius and in Fahrenheit are 0 and 32 degrees respectively. To solve for the constant b in the line equation, we will need a slope and a point. We have already found the slope, and the point that we will be using is the freezing point of water. Substituting the values in the previous equation gives:

{eq}32 (F) = 1.8 * 0 (C) + b {/eq}

Solving for b:

{eq}b = 32 {/eq}

We have identified the slope and the constant for the line equation. Ultimately, we have derived the Celsius to Fahrenheit conversion formula. The following equation is the conversion formula one must use when converting a temperature from Celsius to Fahrenheit.

{eq}T (F) = 1.8 T (C) + 32 {/eq}

To find the Fahrenheit to Celsius conversion formula, one can simply mathematically manipulate the equation discussed earlier, the final format would be the following:

{eq}T (C) = (T (F) - 32)/1.8 {/eq}

To summarize:

Convert C to F: {eq}T (F) = 1.8 T (C) + 32 {/eq}

Convert F to C: {eq}T (C) = (T (F) - 32)/1.8 {/eq}

Other Temperature Conversion Formulas

There are other formulas that can be used to convert temperatures in Celsius and Fahrenheit to Kelvin, which is a temperature unit used to express absolute temperatures, its null point is the absolute zero, which is the lowest temperature possible. The reason why it is important to know how to convert to Kelvin is because this unit is widely used in solving scientific and engineering problems.

Convert C to K: {eq}T ( K ) = T (C) + 273 {/eq}

Convert K to C: {eq}T ( C ) = T (K) - 273 {/eq}

Convert F to K: {eq}T ( K ) = ( T (F) - 32 )/1.8 + 273 {/eq}

Convert K to F: {eq}T (F) = ( T (K) - 273) * 1.8 + 32 {/eq}

Celsius, Fahrenheit & Kelvin Equation Examples

  • Example 1: The weather reporter said that the temperature is 100 degrees Fahrenheit and that the ambience is humid. Convert this temperature to Celsius.

{eq}T (C) = (T (F) - 32)/1.8 = (100 - 32)/1.8= 37.7C {/eq}

  • Example 2: Your weather app reported the following: the weather is mostly cloudy in Istanbul, the humidity is at 67%, and the temperature is 295K. Convert the temperature to Celsius.

{eq}T(C) = T(K) + 273 = 295 - 273 = 22 C {/eq}

The Celsius-Fahrenheit Equation

The temperature in Boston this fine summer morning is 72o F while at the same time in Vancouver, the people are enjoying 15o C. To get to the same temperature scale, whether it's degrees Celsius or degrees Fahrenheit, means that these measurements have a relationship. We can convert from one to the other.

At sea level, water boils at 212o F and freezes at 32o F. That's a difference in temperatures of 212 - 32 = 180. You could say ΔF = 180. On the Celsius scale, water boils at 100o C and freezes at 0o C; a temperature difference ΔC = 100.

Let's think about a slope, m = ΔF / ΔC. The slope is ΔF / ΔC = 180/100 = 1.8.

Remember the equation of a line expressed as y = mx + b ? Well, what if we had F = mC + b? So, F = 1.8C + b.

What about the constant b? When water freezes at C = 0 we have F = 32. In our equation, F = 1.8C + b, let C = 0 and F = 32 to get 32 = 1.8(0) + b. Meaning, 32 = 0 + b or b = 32.

We're done! The beautiful conversion equation between C and F is:

  • F = 1.8C + 32.

Example 1

Let's look at an example. Our friends in Boston would like to know what a Vancouver temperature of 15o C is in degrees Fahrenheit.

From F = 1.8C + 32 let C = 15. Then, F = 1.8(15) + 32 = 59. Therefore, in Boston we have 72o F while in Vancouver it's 59o F. Big difference! 72 - 59 = 13 degrees.

Example 2

Here's another example: our friends in Vancouver would like to know what the Boston temperature of 72o F is in Celsius.

From F = 1.8C + 32 , solve for C by subtracting 32 from both sides:

  • F - 32 = 1.8C + 32 - 32; which simplifies to
  • F - 32 = 1.8C. Then divide both sides by 1.8
  • (F - 32) / 1.8 = 1.8C / 1.8; which simplifies to
  • (F - 32) / 1.8 = C

So, C = (F - 32) / 1.8 = (72 - 32) / 1.8 ≅ 22.

Boston is at 22o C while Vancouver is at 15o C. Only a 7o C change. The difference in temperature sounds better in degrees Celsius.

Example 3

How about calculating the temperature in o F for another place in North America? How about Death Valley, CA,? Now here's a third example: the measured temperature in Death Valley is currently 35o C. What is this temperature in degrees Fahrenheit?

In degrees Fahrenheit this is F = 1.8C + 32 = 1.8(35) + 32 = 95.

Not bad, 95o F. However, on July 10, 1913, the hottest temperature ever recorded in the world was in Death Valley. This temperature was 134o F.

Example 4

Here's one more example: our friends in Canada can't relate to this 134o F. Let's convert to degrees Celsius.

C = (F - 32) / 1.8 = (134 - 32) / 1.8 ≅ 57o C. More than half way up the Celsius scale from freezing towards boiling. No wonder it's called Death Valley!

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Video Transcript

Solving Problems With Temperature

Planning a trip to Vancouver from Boston includes gathering lots of information. It helps to know local temperatures while deciding on the appropriate clothing to bring. Temperatures in Canada are in degrees Celsius while in the United States, the temperature is measured in degrees Fahrenheit.

With Internet resources, these conversions are easily done but have you ever wondered how to do them yourself? With one simple equation, the conversions with Celsius and Fahrenheit temperatures are easily made. Have you ever wondered where this equation came from? Then there's the temperature measure called the Kelvin. In this lesson, we will see how they are all related.

The Celsius-Fahrenheit Equation

The temperature in Boston this fine summer morning is 72o F while at the same time in Vancouver, the people are enjoying 15o C. To get to the same temperature scale, whether it's degrees Celsius or degrees Fahrenheit, means that these measurements have a relationship. We can convert from one to the other.

At sea level, water boils at 212o F and freezes at 32o F. That's a difference in temperatures of 212 - 32 = 180. You could say ΔF = 180. On the Celsius scale, water boils at 100o C and freezes at 0o C; a temperature difference ΔC = 100.

Let's think about a slope, m = ΔF / ΔC. The slope is ΔF / ΔC = 180/100 = 1.8.

Remember the equation of a line expressed as y = mx + b ? Well, what if we had F = mC + b? So, F = 1.8C + b.

What about the constant b? When water freezes at C = 0 we have F = 32. In our equation, F = 1.8C + b, let C = 0 and F = 32 to get 32 = 1.8(0) + b. Meaning, 32 = 0 + b or b = 32.

We're done! The beautiful conversion equation between C and F is:

  • F = 1.8C + 32.

Example 1

Let's look at an example. Our friends in Boston would like to know what a Vancouver temperature of 15o C is in degrees Fahrenheit.

From F = 1.8C + 32 let C = 15. Then, F = 1.8(15) + 32 = 59. Therefore, in Boston we have 72o F while in Vancouver it's 59o F. Big difference! 72 - 59 = 13 degrees.

Example 2

Here's another example: our friends in Vancouver would like to know what the Boston temperature of 72o F is in Celsius.

From F = 1.8C + 32 , solve for C by subtracting 32 from both sides:

  • F - 32 = 1.8C + 32 - 32; which simplifies to
  • F - 32 = 1.8C. Then divide both sides by 1.8
  • (F - 32) / 1.8 = 1.8C / 1.8; which simplifies to
  • (F - 32) / 1.8 = C

So, C = (F - 32) / 1.8 = (72 - 32) / 1.8 ≅ 22.

Boston is at 22o C while Vancouver is at 15o C. Only a 7o C change. The difference in temperature sounds better in degrees Celsius.

Example 3

How about calculating the temperature in o F for another place in North America? How about Death Valley, CA,? Now here's a third example: the measured temperature in Death Valley is currently 35o C. What is this temperature in degrees Fahrenheit?

In degrees Fahrenheit this is F = 1.8C + 32 = 1.8(35) + 32 = 95.

Not bad, 95o F. However, on July 10, 1913, the hottest temperature ever recorded in the world was in Death Valley. This temperature was 134o F.

Example 4

Here's one more example: our friends in Canada can't relate to this 134o F. Let's convert to degrees Celsius.

C = (F - 32) / 1.8 = (134 - 32) / 1.8 ≅ 57o C. More than half way up the Celsius scale from freezing towards boiling. No wonder it's called Death Valley!

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  • Activities
  • FAQs

Temperature Matching Game:

Reminders:

  • To convert Fahrenheit to Celsius, we use the formula F = 1.8C + 32.
  • To convert Celsius to Fahrenheit, we use the formula C = (F - 32) / 1.8.
  • To convert Kelvin to Celsius, we use the formula C = K - 273.15.
  • To covert Celsius to Kelvin, we use the formula K = C + 273.15.

Materials Needed:

  • Notecards with temperatures on them, such that each notecard with a Fahrenheit temperature on it has a corresponding notecard in the bunch with an equivalent temperature in Celsius and a corresponding notecard in the bunch with an equivalent temperature in Kelvin. The number of notecards needed will be the largest number that is divisible by 3, but less than or equal to the number of students in the class. This is because corresponding notecards will be in groups of 3.

How to Play One Round:

  1. Have each student in the class draw a card from the group of notecards. If the number of students in the class is not divisible by 3, they can take turns being the judges while they sit around out of the game. Otherwise, the teacher can be the judge.
  2. Each student must find the two students that have cards with temperatures that are equivalent to theirs.
  3. The three students that find their matching group first win the round. The judge will decide on who was first if there are any close outcomes.

Discussion Questions:

  1. Suppose Mary got the notecard with 15° Celsius on it. What will be on the cards of the others in her matching group?
  2. Suppose Joy got the notecard with 318.15° Kelvin on it, and Mike got the notecard with 40° Celsius on it. Will Joy and Mike be in the same matching group? Why or why not?

Answers:

  1. 15° Celsius is equivalent to 59° Fahrenheit and 288.15° Kelvin, so these will be the values on the cards of the others in Mary's matching group.
  2. No, because 318.15° Kelvin is equivalent to 45° Celsius, not 40° Celsius, so their cards are not equivalent. Hence, they won't be in the same matching group.

What are the temperature conversion formulas?

To convert from Fahrenheit to Celsius:

T (°C) = ( T (°F) - 32 )/1.8

To convert from Celsius to Fahrenheit:

T (°F) = ( 1.8 * T (°C) ) + 32

What is the Celsius value for 98.6 F?

Using the following formula to convert the temperature from Fahrenheit to Celsius:

T (°C) = ( T (°F) - 32 )/1.8

= (98.6°F - 32)/1.8 = 37°C

What does 40 Celsius mean in Fahrenheit?

Convert from Celsius to Fahrenheit:

T (°F) = ( 1.8 * T (°C) ) + 32

T (°F) = ( 1.8 * 40 (°C) ) + 32 = 104 °F

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