Mental math: how to convert Celsius to Fahrenheit

A lot of people know the formula for converting Celsius to Fahrenheit: multiply by 1.8 and add 32. Unfortunately this is somewhat annoying for mental-arithmetic purposes, because 1.8 is somewhat unwieldy. A few people suggest the rule of doubling the Celsius temperature, then adding thirty:
here, here, here. This is exactly correct at 10 Celsius / 50 Fahrenheit, and is off by one Fahrenheit degree for each five Celsius degrees . For example, it converts -20 C to -10 F (should be -4 F) and 40 C to 110 F (should be 104 F). So for weather-conversion purposes this is actually quite good, as 50 is right around the center of the “typical” weather range of 0 to 100. (I’m showing my roots here.)

For culinary purposes, I’ve seen the suggestion of doubling the Celsius temperature to get the Fahrenheit temperature. Solving the equation 1.8C + 32 = 2C gives C = 160, and 160 Celsius = 320 Fahrenheit, which is a fairly typical oven temperature.

As it turns out, in order to convert Celsius to Fahrenheit I don’t actually do the whole multiplying by 1.8 trick. Instead, I know what multiples of 5 degrees Celsius are in Fahrenheit:

C 0 5 10 15 20 25 30 35 40
F 32 41 50 59 68 77 86 95 104

I didn’t consciously memorize these. I knew the pair (0, 32) like everyone does (it’s the freezing point of water); (20, 68) is pretty common as room temperature. To get the others, note that the Fahrenheit temperatures go in steps of 9.

So to convert Celsius to Fahrenheit: say it’s 37 degrees Celsius. That’s near 35, so the Fahrenheit temperature must be near 95. But how far? Well, it’s two degrees Celsius warmer, or about four degrees Fahrenheit warmer; figure 1 Celsius degree is 2 Fahrenheit degrees. So 37 Celsius is 95 + 4 = 99 Fahrenheit. The truth is 98.6, which isn’t body temperature anyway. (You know that the whole 98.6 body temperature is an overly precise conversion of 37 Celsius, right? If not, now you do.)

Or right at this moment it’s 18 degrees Celsius in San Francisco. 20 Celsius is 68 Fahrenheit; it’s two degrees Celsius cooler than that, or about four degrees Fahrenheit. So 18 Celsius = 68 – 4 = 64 Fahrenheit.

In general, to convert Celsius to Fahrenheit, the method is as follows:

  • first, take the closest Celsius temperature from the first row of the table. Get a rough conversion into Fahrenheit from the second row.
  • for each degree Celsius you are above or below this approximation, add or subtract two Fahrenheit degrees from your rough conversion

The second step contributes an error of (2 – 1.8) = 0.2 degrees Fahrenheit for each Celsius degree of error — but no matter the starting Celsius temperature, one of the table entries is within two degrees of it, so we get an error of at most 0.4 degrees. If we’re rounding to the nearest integer anyway, who cares?

A simpler version is to only use every other column of the table; then you may end up with errors of as much as a whole degree.

(I didn’t realize this was what I was doing until I realized a few days ago that I could do these conversions in my head, and found myself trying to explain what I was doing. It would be harder between 0 and 32 F, because Celsius and Fahrenheit have opposite signs there, but I live somewhere now where it never gets below freezing.)

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Weekly links for September 2

What does the cone of uncertainty for hurricanes actually mean?

Is soccer sabremetrics coming?

Are we reaching a saturation point for scientists?

Google earth fractals

From xkcd, what if everybody only had one soulmate?

Skip Garibaldi wrote in Mathematics Magazine, in 2008, Somewhat more than governors need to know about trigonometry.

Jeremy Kun, K-Nearest-Neighbors and Handwritten Digit Classification.

The Dot and the Line: A romance in lower mathematics, an animated short film after the book of the same name by Norton Juster

Vi Hart doodles conic sections, cardioids, and so on. (Embedded in this is an interesting commentary on matheamtics education.)

Prime factorization sweater.