How to Convert Temperature (F<-->C) Quickly in Your Head

 

These are the "exact" equations for converting between Fahrenheit and Celsius:

C = ( F - 32 ) x 5/9
F = C x 9/5 + 32

https://en.wikipedia.org/wiki/Conversion_of_units_of_temperature#Celsius_.28centigrade.29

But what if you see temperatures on TV, and just want to convert it in your head to get a feel for how hot or cold it is, without unlocking your phone to use a calculator?

 

Easy.  Use equations that are easier to do in your head, but that also give you answers close enough to be useful for our purposes.  As long as you're not doing chemistry calculations requiring mission-critical accuracy, you should be fine.

I finally figured out a way while waiting on the subway:

C = (F-30)/2

F = Cx2+30

These are what I'll call

"Rapid equations":

C = ( F - 30 ) / 2 --> and round
F = C x 2 + 30 --> and round

I'm guessing a few degrees off doesn't make that much difference in how hot/cold it feels for you, so you can round to the nearest 10 degrees.

If you want more accuracy, going into the 1's places or decimals, add the

"refiners":

C = (F-30) /2 + F/2 /10 + 1
F = Cx2 +30 - Cx2 /10 + 2

These can also be written as:

C = (F-30) /2 + F/20 + 1
F = Cx2 +30 - Cx0.2 + 2

If you want a way to remember the "rapid equations", take the first letter of each relevant math operation, and create some

mnemonics (memory aids) :

"farmed cow":

FMDRC, which means:
F --> Minus, Divide, Round --> C

"C = F M D R"

C = (F Minus 30) Divide by 2 and Round to one significant digit.

C = ( F - 30 ) / 2 --> round

"caterpillar fly":

CTPRF, which means:

C --> Times, Plus, Round --> F

" F = C T P R"

F = (C Times 2) Plus 30 and Round to one significant digit.

F = C x 2 + 30 --> round

2 is involved in multiplying/dividing, and
30 is involved in adding/subtracting.

Or you can make up your own way to remember the formulas, but they're pretty simple.  Just two steps.

Practice:

Check if you can do these in your head:

100 C  ~  200 F (or 212 F)
20 C  ~  70 F  (or 68 F)
10 C  ~  50 F
0 C  ~ 30 F (or 32 F)
-10 C  ~  10 F (or 14 F)

Now you can tell your American friends how cold (or hot) this winter felt.

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Why does this all work?


Algebra and rounding.

It goes back to the original "exact" equations:

C = ( F - 32 ) x 5/9
F = C x 9/5 + 32

These can be re-written as:

C = ( F - 32 ) x 0.55555
F = C x 1.8 + 32

And these can be re-written as:

C = ( F - 32 ) x (1/2 + 1/20 + 1/200 + 1/20000 + ...)
F = C x (2 - 0.2) + 32

Or:

C = ( F - 30 - 2 ) x (1/2 + 1/20 + 1/200 + 1/20000 + ...)
F = C x (2 - 0.2) + 30 + 2

And if we trade off a little accuracy, we can get rid of the less significant multipliers:


C = ( F - 30 - 2 ) x (1/2 + 1/20 + 1/200 + 1/20000 + ...)
F = C x (2 - 0.2) + 30 + 2

And from there you can keep going using the simplifying assumptions of significant digits and eventually you can get to the same place as the "rapid equations".


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