## Tuesday, July 03, 2012

You may remember the complicated Fahrenheit-to-Celsius and Celsius-to-Fahrenheit conversion formulas. Or you may not remember them, but you may remember the fact that they are complicated, and involve 5/9 and 9/5, and adding or subtracting 32. But do you add (or is it subtract?) first, and then multiply, or do you multiply first, and by which factor?

Worry no longer, my friends! There is a much easier way to do it. The only formula you will need is the following:
T1 = (T2+40)*factor - 40.
The end.

This formula works for both temperature scales (so {T1,T2} = {F,C} or {C,F}). The only thing you need to remember is whether factor is 5/9 or 9/5. But that is not so hard: there are more degrees between freezing and boiling in Fahrenheit than Celsius, so when you convert to Fahrenheit, you need to use the bigger number, 9/5. Likewise, when converting to Celsius, use 5/9.

Does it really work? Yes! Let's do some examples.

Body temperature is 37 C or 98.6 F. Can we convert to those numbers? Let's start with C to F:
F = (C+40)*9/5 - 40
F = (37+40)*9/5 - 40 = 77*9/5 - 40 = 138.6 - 40 = 98.6
Now what about F to C?
C = (F+40)*5/9 - 40
C = (98.6+40)*5/9 - 40 = 138.6*5/9 - 40 = 77 - 40 = 37
You can derive the traditional formulas for temperature conversion from this simple one.
F = (C+40)*9/5 - 40 = 9/5*C + 40*9/5 - 40 = 9/5*C + 72 - 40 = 9/5*C + 32
C = (F+40)*5/9 - 40 = 5/9*(F+40 - 9/5*40) = 5/9*(F + 40 - 72) = 5/9*(F - 32)
As easy as this formula is, it's still non-trivial to do in your head. So my sister Rachel told me an easy thing to remember about Celsius temperature ranges when it comes to the weather:

• 40+ C: extremely hot (=104+ F)
• 30-39 C: very hot (=86-102 F)
• 20-29 C: comfortable-hot (=68-84 F)
• 10-19 C: cool-comfortable (=50-66 F)
• 0-10 C: chilly (=32-42 F)
So the ideal you'd be most comfortable in is the range around 20-25 Celsius (68-77 F). From there you can see how much the temperature deviates from the ideal. (In Perth, once every couple of years it dips down to freezing, so I did not go any lower on the scale.)

#### 1 comment:

Anne said...

The salute of tens is so helpful! Thanks!