# Derive the formula for Celsius to Fahrenheit?

Jul 11, 2017

Compare the number of degrees from the freezing point of water to its boiling point on each scale to find a ratio and add in the differences between the freezing points.

#### Explanation:

The Fahrenheit freezing point of water is ${32}^{\circ} \text{F}$ and its boiling point is ${212}^{\circ} \text{F}$.

${212}^{\circ} \text{F" -32^@"F" = 180^@"F}$ between the freezing point and boiling point of water.

The Celsius freezing point of water is ${0}^{\circ} \text{C}$ and its boiling point is ${100}^{\circ} \text{C}$.

${100}^{\circ} \text{C" -0^@"C" = 100^@"C}$ between water's freezing and boiling points.

This results in a ratio for C to F of $\frac{100}{180}$ or $\frac{5}{9}$, and
this results in a ratio for F to C of $\frac{180}{100}$ or $\frac{9}{5}$.

Then ${32}^{\circ} \text{F}$ equal ${0}^{\circ} \text{C}$, so

The formula for $\text{^@"C}$ to $\text{^@"F}$ is

( ""^@"C" xx 9/5 )+ 32 = ""^@"F"