On Converting Celsius to Fahrenheit and Back

I pride myself on being able to carry out calculations in my head that cause most people to go for the calculator. Need to calculate a 15% tip? Divide the total bill by 10, and then divide by 2, and then add the results. Easy. Sometimes while exercising on a bike I try to factor four or five digit numbers in my head. Or try to remember how Conway’s Doomsday Algorithm allows you to compute the day of the week for arbitrary dates. It’s just a way to exercise the mind.

Another calculation that frequently (well, not that frequently, but still) comes up is to convert temperatures between Celsius and Fahrenheit. The way that I remember this is that zero C is 32 F, so to convert Celsius to Fahrenheit, you multiply C by 9/5 and then add 32. Of course, to do the reverse, you have to do the subtraction first (F-32) and then multiply by 5/9. They aren’t hard to remember, but I was shocked to find there is a nicer way that avoids the assymetry.

The Citizen Scientist has a cute article that shows the easier way. The fact you have to remember is that -40C is the same temperature as -40F. How does that help? Well, to convert from C to F, you

  1. Add 40 to C
  2. Multiply by 9/5
  3. Subtract 40

To convert from F to C, you:

  1. Add 40 to F
  2. Multiply by 5/9
  3. Subtract 40

So, a balmy 86F is 30C. 15C is 59F. Neat!

Having difficulty multiplying by 9/5 or 5/9? You could just use 2 and 1/2 if you’d rather, it introduces about a 10% error, which might be close enough. (You’d get 23C and 50F above). You can get closer if you subtract 10% when you multiply by 2, and add 10% when you multiply by 1/2, but frankly, I think that reintroduces the problems of assymetry that this revamp gives you. Probably easier (and more accurate) just to work on multiplying and dividing by 9 and 5.
Anyway, cool article.

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3 thoughts on “On Converting Celsius to Fahrenheit and Back”

  1. Here’s another strategy to add to the list. The key point is that multiplying by 9/5 is the same as multiplying by (2 – 0.2)

    F = C * 9/5 + 32
    F = C * (1.8) + 32
    F = C * (2 – 0.2) + 32

    It’s easy to multiply by 2 and immediately subtract a tenth.

    20 C is?

    Start with: 20
    Double it: 40
    Subract 1/10th: 40 – 4 = 36
    Add 32: 68

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