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Converting Fahrenheit to Celsius (and Vice Versa)

Converting Fahrenheit to Celsius (and Vice Versa)

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Fahrenheit is the temperature scale proposed in 1724 by, and named after, the physicist Daniel Gabriel Fahrenheit (1686–1736). Today, it is mostly used in the United States and a few other countries; the rest of the world uses Celsius. So what if you’re in a country that uses one and you want to convert it to the other? Here is how you do it.

What Is the Difference?

Fahrenheit

On the Fahrenheit scale, the freezing point of water is 32 degrees Fahrenheit (°F), and the boiling point is 212°F (at standard atmospheric pressure). There are 180 equal divisions between the freezing temperature of water and its boiling point. Each division is a Fahrenheit degree.

Celsius

On the Celsius scale, the freezing point of water is 0 degrees Celsius (°C), and the boiling point of water is 100°C (at standard atmospheric pressure). There are 100 equal divisions between the freezing temperature of water and its boiling point. Each division is a Celsius degree.

How to Convert

Each degree Fahrenheit equals of a degree Celsius:

Each degree Celsius equals of a degree Fahrenheit:

Fahrenheit to Celsius

Given the Fahrenheit reading, use the following formula to get the Celsius reading:

Celsius to Fahrenheit

Given the Celsius reading, use the following formula to get the Fahrenheit reading:

Practice Your Conversions

Here are some practice problems (and solutions) for converting from one temperature scale to another.

Sample Problem 1

When I lived in Russia, one of the coldest outside temperatures I experienced was −45°C. The coldest temperature I experienced in the United States (in Maryland) was +3°F. What is the difference in the coldest temperatures on the Fahrenheit scale?

Step 1: Change the Celsius temperature to Fahrenheit using the formula and substituting the value of −45°C:

We found that the coldest temperature I experienced in Russia was −49°F.

Step 2: To find the difference between the coldest temperatures in two countries, subtract the coldest temperature in Russia from the coldest temperature in the United States:

+3°F − (−49°F) = +3°F + 49°F = 52°F

Solution: The difference between the two coldest temperatures is 52°F.

Sample Problem 2

Find the temperature where both temperature scales converge.

Step 1: Since we want to equalize both temperature scales, we can write this mathematically as:

°C = °F

Step 2: Use the conversion formula:

Plug in the right side of the preceding equation into the right side of the equation in Step 1:

Isolate the variable:

Multiply both sides by 5:

5C − 9C = 5(32)

Collect like terms and multiply on the right side:

−4C = 160

Divide both sides by −4:

C = −40

We found that a temperature of −40°C = −40°F is the one at which both temperature scales converge.

Solution: −40°C = −40°F.

Sample Problem 3

Normal room temperature is 72°F. What is it on the Celsius scale?

Step 1: Change the Fahrenheit temperature to Celsius using the formula and substituting the value of 72°F:

We rounded the answer to the hundredths place.

Solution: Normal room temperature is 22.22°C.

Sample Problem 4

If the temperature drops 36°F, what is the corresponding drop on the Celsius scale?

Step 1: We know that each degree Fahrenheit equals of a degree Celsius, so we can state:

Step 2: We know how much 1 Fahrenheit degree is. To find how much 36°F is, we need to multiply the right side of the expression in Step 1 by 36:

Solution: A 36°F drop of temperature on the Fahrenheit scale means a 20°C temperature drop on the Celsius scale.

Sample Problem 5

If the temperature raises 45°C, what is the corresponding rise on the Fahrenheit scale?

Step 1: We know that each degree Celsius equals of a degree Fahrenheit, so we can state:

Step 2: Since we know how much 1 Celsius degree is, to find how much 45°C is, we need to multiply the right side of the expression in Step 1 by 45:

Solution: A 45°C rise in temperature on the Celsius scale means an 81°F rise on the Fahrenheit scale.

Now that you know how to convert from Celsius to Fahrenheit (and vice versa), you’ll never again wonder, “Just how cold is 3 degrees Celsius?”

From The Complete Idiot’s Guide to Algebra Word Problems by Izolda Fotiyeva, Ph.D.