Figuring It Out by Degrees

Most of the rest of the world reckons temperature on the Celsius or centigrade scale, and Celsius is even seen occasionally in this country on electric time-and-temperature signs outside banks.

But the usual method for converting from Fahrenheit to Celsius is cumbersome, difficult to remember and hard to do in your head. In degreeof difficulty among algorithms, it is second only to extracting a square root with pencil and paper.

It turns out that there is a better, easier way to do it that is rarely taught, though it should be.

The almanac gives the standard method. “To convert Fahrenheit to Celsius,” it says, “subtract 32 and multiply by 5/9. To convert Celsius to Fahrenheit, multiply by 9/5 and add 32.”

The first problem with this method for converting temperature scales is that it is really two methods, and some people (us included) can never remember which is which. To go from Fahrenheit to Celsius, you subtract first and then multiply. To go from Celsius to Fahrenheit, you multiply first and then add. What’s more, in one case you have to subtract, and in the other case you have to add.

If you do the steps in the wrong order, or if you add when you’re supposed to subtract, or the other way around, you get the wrong answer.

Here’s the better way to do it:

Regardless of whether you’re going from Fahrenheit to Celsius or Celsius to Fahrenheit, add 40 to the temperature.

If you’re going from Fahrenheit to Celsius, multiply by 5/9. (That’s easy to remember because the Celsius numbers are smaller. The boiling point of water is 212 degrees Fahrenheit but only 100 degrees Celsius.)

If you’re going from Celsius to Fahrenheit, multiply by 9/5. (That’s also easy to remember, for the same reason. Fahrenheit numbers are larger.)

Then subtract 40.

The number that’s left is the answer. And that’s all there is to it. This method works in either direction for any number.

For example: To convert 212 degrees Fahrenheit to Celsius, add 40, giving 252. Multiply by 5/9, giving 140. Subtract 40, leaving 100. So 212 degrees Fahrenheit is 100 degrees Celsius, which is correct.

If you want to convert 0 degrees Celsius to Fahrenheit, add 40, giving 40. Multiply by 9/5, giving 72. Subtract 40, leaving 32. So 0 degrees Celsius, the freezing point of water, is 32 degrees Fahrenheit, which is also correct.

Why does this method work? The Fahrenheit and Celsius scales cross at -40 degrees. That is, both scales are the same at -40. By adding 40 to start, this point of equality is shifted to 0. Then the multiplication can be carried out directly, without having to add or subtract anything before or after. Finally, subtracting 40 shifts the two scales back to their correct positions.

The real question is, why is this method a secret? It’s much superior to the standard method, which nonetheless continues to be the standard method. Nor is the regular method conceptually easier than the add-40-subtract-40 method of doing it. Adding or subtracting 32 isn’t any more enlightening to students about what is going on than adding and subtracting 40.

Textbook publishers and teachers should switch. If there’s a better way to do something, why not do it?