Mathematics » Properties of Real Numbers » Systems of Measurement

# Converting Between Fahrenheit and Celsius Temperatures

## 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.

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

$$F=\frac{9}{5}C+32$$

## 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.