# Listen to Those Rails A-Thrumming All Aboard

May 24, 2014

To convert from Fahrenheit to Celsius and back again is often a pain in the neck. Do you multiply by 5/9 first, and then subtract 32? The other way around? Add 32? How does it go, again?

Most people know that water freezes at 32˚F / 0˚C, and boils at 212˚F / 100˚C (at standard pressure).Why was 212˚F chosen as the boiling point? Well, freezing and boiling are in some sense opposite, and they are separated by 180˚…

This information is enough to convert. But most people don’t want to solve two equations in two unknowns on the fly. So people make up rules of thumb.

A rule of thumb that isn’t so bad at temperatures near freezing is that each degree Fahrenheit is half a degree Celsius. It is only off by 1 part in 18 so that it’s off by only 1˚C at 50˚F. But the error gets worse as you get further from freezing.

Luckily, I know another rule of thumb that stays within 1˚C of the true value. It has to do with the 6 train, also called the Lexington Avenue local train, in New York City. The rule is this: the stop at 33rd street is 0˚C, each stop (thought of as ˚F) farther up town is another 5˚C.

That is:

Stop Exact Conversion Rule of thumb
[Street or ˚F] [˚C] [˚C]
33rd 0.555 0
42nd 5.555 5
51st 10.555 10
59th 15 15
68th 20 20
77th 25 25
86th 30 30
96th 35.555 35
103rd 39.444 40

which is good to 5/9˚C all the way through 103rd street. After that, it sort of… goes off the rails.

May 24, 2014