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Unlocking Fahrenheit to Celsius and Celsius to Fahrenheit Conversion: A Comprehensive Guide and Practice Lessons

Saturday, May 20th, 2023

Fahrenheit and Celsius

Temperature is a fundamental physical quantity that we encounter in our daily lives, from checking the weather forecast to setting our home thermostats. However, depending on location, scientific context, or practical considerations, the temperature can be measured using different units. Fahrenheit, Celsius, and Kelvin are the most commonly used temperature scales, with Kelvin mainly used in scientific applications. Being able to convert between these units is a valuable skill that can come in handy in real-life situations, and also serves as an excellent way to understand unit conversions in general.

Celsius to Fahrenheit Conversion

In the United States, it is natural to use Fahrenheit when referring to temperature. However, for most of the rest of the world, Celsius is the unit used. In everyday speech, we often use the term “degrees” instead of specifying Fahrenheit or Celsius. This can lead to confusion when traveling around the world.

We can use the following formula for converting Celsius to Fahrenheit.

\degree\text{F} = \frac{9}{5}\text{C} + 32

Let's understand how to apply the formula by working out the conversion of 38.5 celsius to fahrenheit problemstep by step.

Example

Example 1. What is 38.5 celsius in fahrenheit?

Answer:

Step 1: Substitute 38.5 c into the formula

We need to replace C by 38.5 in the following formula:

\degree\text{F} = \frac{9}{5}\text{C} + 32

\degree\text{F} = \frac{9}{5}\times 38.5 + 32

Step 2: Determine the temperature in Fahrenheit

Now we can simplify

\degree\text{F} = \frac{9}{5}\times 38.5 + 32

\degree\text{F} = 69.3 + 32

\degree\text{F} = 101.3

Hence, the temperature of 38.5 degrees Celsius is 101.3 degrees Fahrenheit.

Now that you know how to work with the formula let's try to extending this understanding to a practical scenario.

Question

Question 1.

Imagine you are planning a trip to Toronto, Canada, in the middle of October. You check the weather forecast and see that the temperature will be around 19 degrees Celsius. As someone who is used to the Fahrenheit scale, you want to know what to expect in terms of weather. Can you convert the 19 degrees celsius to fahrenheit to help you prepare for your trip?

Solution:

Step 1. Apply the conversion formula

We need to replace C by 19 in the following formula:

\degree\text{F} = \frac{9}{5}\text{C} + 32

\degree\text{F} = \frac{9}{5}\times 19 + 32

Step 2: Determine the temperature in Fahrenheit

Now we can simplify

\degree\text{F} = \frac{9}{5}\times 19 + 32

\degree\text{F} = 34.2 + 32

\degree\text{F} = 66.2

Hence, the temperature of 19 degrees Celsius is 66.2 degrees Fahrenheit.

Fahrenheit to Celsius Conversion

Once you know how to convert from celsius to Fahrenheit, it’s quite straightforward to go the other way around. We can start from the formula that was used to convert from celsius to fahrenheit and make the celsius parameter the subject. Below are the steps to derive the formula for converting from Fahrenheit (F) to Celsius (C):

\degree\text{F} = \frac{9}{5}\text{C} + 32

\degree\text{F} - 32 = \frac{9}{5}\text{C}

\degree\text{C} = \frac{5}{9}(\text{F} - 32)

Example

Example 2. When body temperature rises above 102.2 degrees Fahrenheit, it can be a sign of a serious infection. What is 102.2

\degree\text{F } \text{ in } \degree\text{C}

Practical example of converting fever 102.2 f to c

Solution:

Step 1. Apply the conversion formula

We need to replace F by 102.2 in the following formula:

\degree\text{C} = \frac{5}{9}(\text{F} - 32)

\degree\text{C} = \frac{5}{9}(102.2 - 32)

Step 2: Determine the temperature in Fahrenheit

Now we can simplify

\degree\text{C} = \frac{5}{9}(102.2 - 32)

\degree\text{C} = \frac{5}{9}(70.2)

\degree\text{C} = 39

Hence, according to the conversion formula we can say that a temperature higher than 39

\degree\text{C}

can be a sign of serious infection.

The rise and drop of temperature

In describing weather conditions it is quite common to mention the increase and decrease of temperature in degrees. However, it's essential to understand that the unit of measurement can significantly impact the magnitude of change. For instance, a 15-degree change in temperature can mean vastly different things depending on the unit used. Based on the conversion formula the change in Celsius,

\Delta\text{C}

, for a given change in Fahrenheit ,

\Delta\text{F}

, is given by :

\Delta\text{C} = \frac{5}{9}\times\Delta\text{F}

. This is an important conversion that everyone should be familiar with.

Question

Question 2.

If New York City is expected to experience a temperature rise of 27°F in the following week.
a) What is the equivalent increase in Celsius?
b) If the temperature in New York was 20

\degree\text{C}

, what would it be after the increase in Fahrenheit and Celsius?

Solution:

Step 1. Apply the conversion formula

Let's consider the rise in celsius to be

\Delta\text{C}

and

\Delta\text{F}

the rise in Fahrenheit

\Delta\text{C} = \frac{5}{9}\times\Delta\text{F}

Since

\Delta\text{F}

is 27, we get:

\Delta\text{C} = \frac{5}{9}\times 27

Hence,

\Delta\text{C} = 15\degree

Therefore, the expected rise in temperature in celsius is 15

\degree\text{C}

Step 2: Determine the temperature after the increase, in

\degree\text{F} \text{ and } \degree\text{C}

Since the temperature is 20

\degree\text{C}

initially, after an increase of 15

\degree\text{C}

the temperature will be 35

\degree\text{C}

We can now convert 35c to fahrenheit:

\degree\text{F} = \frac{9}{5}\times 35 + 32

\degree\text{F} = 63 + 32

\degree\text{F} = 95\degree

Hence, the temperature after the increase would be 35

\degree\text{C}

or 95

\degree\text{F}