Converting Between Fahrenheit and Celsius Temperatures

Have you ever been in a foreign country and heard the weather forecast? If the forecast is for \(22\text{°C}.\) What does that mean?

The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit, written \(\text{°F}.\) The metric system uses degrees Celsius, written \(\text{°C}.\) The figure below shows the relationship between the two systems.

On the left side of the figure is a thermometer marked in degrees Celsius. The bottom of the thermometer begins with negative 20 degrees Celsius and ranges up to 100 degrees Celsius. There are tick marks on the thermometer every 5 degrees with every 10 degrees labeled. On the right side is a thermometer marked in degrees Fahrenheit. The bottom of the thermometer begins with negative 10 degrees Fahrenheit and ranges up to 212 degrees Fahrenheit. There are tick marks on the thermometer every 2 degrees with every 10 degrees labeled. Between the thermometers there is an arrow pointing on the left to 0 degrees Celsius and on the right to 32 degrees Fahrenheit. This is the temperature at which water freezes. Another arrow points on the left to 37 degrees Celsius and on the right to 98.6 degrees Fahrenheit. This is normal body temperature. A third arrow points on the left to 100 degrees Celsius and on the right to 212 degrees Fahrenheit. This is the temperature at which water boils.

A temperature of \(37\text{°C}\) is equivalent to \(98.6\text{°F}.\)

If we know the temperature in one system, we can use a formula to convert it to the other system.

Definition: Temperature Conversion

To convert from Fahrenheit temperature, \(\text{F},\) to Celsius temperature, \(\text{C},\) use the formula

\(C=\frac{5}{9}\left(F-32\right)\)

To convert from Celsius temperature, \(\text{C},\) to Fahrenheit temperature, \(\text{F},\) use the formula

\(F=\frac{9}{5}C+32\)

Optional Video: Convert from Celsius to Fahrenheit

Example

Convert \(50\text{°F}\) into degrees Celsius.

Solution

We will substitute \(50\text{°F}\) into the formula to find \(\text{C}.\)

Use the formula for converting °F to °C	\(C=\frac{5}{9}\left(F-32\right)\)

Simplify in parentheses.	\(C=\frac{5}{9}\left(18\right)\)
Multiply.	\(C=10\)
	A temperature of 50°F is equivalent to 10°C.

Example

The weather forecast for Paris predicts a high of \(20\text{°C.}\) Convert the temperature into degrees Fahrenheit.

Solution

We will substitute \(20\text{°C}\) into the formula to find \(\text{F}.\)

Use the formula for converting °F to °C	\(F=\frac{9}{5}C+32\)

Multiply.	\(F=36+32\)
Add.	\(F=68\)
	So 20°C is equivalent to 68°F.

Optional Video: Convert from Fahrenheit to Celsius

This lesson is part of:

Properties of Real Numbers

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