Question

How do you convert Fahrenheit ($°F$) to Celsius ($°$$C$)?

Answer 1

Step 1: Calculate the differences and ratio

We know that,

The boiling point and freezing point of water in Celcius is $100°C$ and $0°C$.

Hence, their difference is $\left(100-0\right)°C$.

Again, the boiling point and freezing point of water in Fahrenheit is $212°F$ and $32°F$.

Hence, their difference is $\left(212-32\right)°F=180°F$.

The ratio between the difference between boiling point and freezing point in Fahrenheit to Celcius is

$\frac{180}{100}=\frac{9}{5}$

$0°C$ is equivalent to $32°F$.

Step 2: Establish the relation

Therefore, the relation between $°C$ and $°F$ is

$\frac{9}{5}°C+32=°F$

$\Rightarrow$ $\frac{9}{5}°C=°F-32$

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

Hence, Fahrenheit ($°F$) can be converted to Celsius ($°$$C$) using the relation $°C=\frac{5}{9}\left(°F-32\right)$.