# Fahrenheit and Celsius

I’m currently recommending Ratio by Michael Ruhlman to anyone who’ll listen - it’s a cookbook that teaches you how to cook, not just how to make things. Its one fault, though: it gives temperatures in degrees Fahrenheit. It’s not technically true that Fahrenheit picked 100º to be the temperature of his wife’s armpit, but I can’t imagine it’s any less bizarre than what really happened.

In any case, I lived in the US for several years, and got pretty good at converting temperatures over the relatively large swings of the Montana weather - from -30ºC in the depths of the winter to over 40ºC in the summer. However, that doesn’t help when you’re baking bread.

There’s a formula, of course, and it’s not even that hard a conversion (for sensible numbers): $C = \frac{F-32}{1.8}$. But when you’re up around 425ºF, it’s a bit of a faff. I want a quicker way.

(Yes, sensei, of course I *can* do it. Take away 32 to get 393. Divide by 9 to get 44 less a third. Multiply by 5 to get 220 less five thirds, call it 218ºC).

That’s pretty close to “halve it”, isn’t it? It’s only off by about six degrees, which (given the age of our oven) is probably within operational parameters. But the Ninja isn’t going to let me get away with that in general: they will want at least a corrected estimate.

### Where does doubling work?

Suppose $F = 2C$. Then $C = \frac{2C - 32}{1.8}$, or $0.9C = C - 16$. This gives $C=160$ and $F=320$ as the temperature where the ratio works exactly. As you move away from 320ºF, the error will vary linearly. What I want is a rule that says “see how far you are away from 320ºF and add or take a multiple of that.”

I know that 32ºF is 0ºC, so the halving rule gives me a Celsius temperature 16º too high - so if I’m 288ºF below 320ºF, my correction is -16ºC.

Happily, 288 is 18 × 16, so every 18 degrees I move (down/up) from 320, I need to adjust my halving estimate (down/up) by one degree.

In the case I had, I was 105ºF above 320ºF, which is just short of 6 × 18, so I need to adjust my estimate of 212.5 up by a little short of 6 degrees. It works!

A more extreme case: I know that -40ºF and -40ºC are the same temperature. That’s 360ºF below 320ºF, so I’ll need to adjust my halving estimate down by 20ºC. Halving gives -20ºC, and the correction gives -40ºC.

### Going the other way

If, for some unfathomable reason, you need to convert Celsius to Fahrenheit, it’s a bit more awkward AS GOD INTENDED.

However, the correction you would need here is to take of a fifth of the difference above 160ºC. Given 200ºC, you would double (400) and take off a fifth of 40 (8) to get 392ºF. Given 40ºC, you would double (80) and add on fifth of 120 (24) to get 104º.

Have you got other nice conversion recipes? Let me know about them below!