How was the mathematical equation for converting Fahrenheit to Celsius scale determined?

Answer 1

The equations to convert Fahrenheit and Celsius are based on the definitions of their common temperatures, and on the confusing fact that a "degree" on one scale is not equal to a "degree" on the other scale!

A Celsius (centigrade) degree is 1/100 of the difference between the measured freezing and boiling points of water -- 0° and 100° respectively.

A Fahrenheit degree is 1/180 of the difference between the measured freezing and boiling points of water -- 32° and 212 ° respectively.

So the conversion involves adjusting the temperatures for size of degree and for the "offset" from zero on the Fahrenheit scale. The two conversions are:

C = (F-32) x 5/9

Once the starting point is the same numerically (F-32), then the multiplier 5/9 changes the size of the smaller Fahrenheit degrees to the 1.8 times larger Celsius degrees.

F = (9/5 x C) + 32

Once the number of smaller Fahrenheit degrees above freezing is found (9/5 C), the temperature is adjusted by 32 upward to account for the higher starting point of Fahrenheit.