Converting Celsius and Fahrenheit: a simple trick

When comparing the Metric system, which includes Celsius, to the Imperial system, which includes Fahrenheit, there is little debate over which is better for scientific measurements. (hint: The International System of Units are Metric.)

However, most of us grew up understanding our surroundings in terms of one, but not the other. For example, if you grew up in the US, Liberia, or Myanmar, then you probably think of the weight of an object in pounds, someone’s height in feet and inches, and the outside temperature in Fahrenheit (abbreviated as F). If you grew up somewhere else, then you might think of the weight of an object in kilograms, someone’s height in meters, and the outside temperature in Celsius (abbreviated as C).

If you know someone that uses the system you aren’t used to, wouldn’t it be nice to better understand each other when talking about temperature?

In this post, I will share a simple math trick to help you estimate the conversion between Celsius and Fahrenheit. It does not do the exact conversion (F = 1.8C + 32), but it’s close enough to be useful for any temperature that might come up when talking about the weather. After sharing, I will explain how and why it works.

The Trick

To go from C to F: Double it and add 30

To go from F to C: Take away 30 and halve it

Yep, it’s that simple.

♪ Reminder: This trick uses an estimated conversion. The actual conversion is discussed later on.

Examples:

C to F

25° C ⇒ double 25 to get 50, then add 30 to get ⇒ 80° F
5° C ⇒ double 5 to get 10, then add 30 to get ⇒ 40° F
-15° C ⇒ double -15 to get -30, then add 30 to get ⇒ 0° F

F to C

80° F ⇒ subtract 30 from 80 to get 50, then halve 50 to get ⇒ 25° C
40° F ⇒ subtract 30 from 40 to get 10, then halve 10 to get ⇒ 5° C
0° F ⇒ subtract 30 from 30 to get -30, then halve -30 to get ⇒ -15° C

These are nice numbers that double and halve easily, but the trick works with any number:

18° C ⇒ double 18 to get 36, then add 30 to get ⇒ 66° F
66° F ⇒ subtract 30 from 66 to get 36, then halve 36 to get ⇒ 18° C

That is it! If you can double or halve numbers 2-digit numbers, and add/subtract 30 to/from a number, then you can use this trick! If you can’t, then this will be good practice.

What to Remember

If you were born into the Imperial (Fahrenheit) system, the next time your Metric (Celsius) friend says: “It’s nice out, it’s 22!” Double it and add 30. You can quickly know that it is indeed nice weather (temperature as C), and not below freezing (misinterpreting temperature as F). (Try it!)

Or if you are a Metric person, and your Imperial buddy says: “It’s freezing today, it’s 34!” Take away 30 and halve it, and you will understand that it is in fact close to freezing (temperature as F), and not too hot to go outside (misinterpreting temperature as C). (Try it!)

I grew up with Fahrenheit and learned this trick many years ago, and have always found it useful. I only really need to remember how to convert C to F, since I already understand what temperatures in F mean. So if you are like me, and are familiar with temperature in Fahrenheit, just remember how to get C to F: Double it and add 30.

If you are more familiar with Celsius, you more often only need to convert F to C. So just remember: Take away 30 and halve it.

If you just wanted to learn the trick, then you can stop reading now. If you are curious to see how it works, then read on.

How it works

I mentioned above that the trick estimates the conversion. The actual conversion is very similar, but the numbers are not as simple to work with:

To go from C to F: Multiply by 1.8 and add 32

To go from F to C: Subtract 32 and divide by 1.8

If you can do this conversion quickly in your head (multiplying by 1.8 is the same as multiplying by 9 and dividing by 5, since 1.8 = 9/5), more power to you! If you can’t, that’s OK, because using the estimated conversion, which makes use of more user-friendly math, is good enough. Let’s see why…

The actual conversion is a linear function, just like the estimated conversion. (Remember y = mx + b from Algebra class?) This means that if all of the C and F value pairs are drawn on a graph, then a straight line will be produced.

The following graph shows how close the actual conversion line is to the estimated conversion line.

♪ Side Note: This graph uses C as the x-axis and F as y-axis, which represents the formula for C to F, but the proximity of the lines would be recognized either way.

The estimated conversion formula makes the math “close enough” by replacing the linear function constants with more simple numbers: 1.8 with 2 (the m), and 32 with 30 (the b). It turns out that by slightly rounding 1.8 up to 2, and then compensating 32 down to 30, a very accurate model is produced for the range of values we care about.

But what exactly is meant by “close enough” when talking about the weather? Notice how close together the lines are near the center of the graph, which happens to be the more natural range for the temperatures we experience on Earth. In fact, at 10° C or 50° F, the estimated formula produces the exact same values as the actual formula, and the lines intersect. However, the further the temperature is (in either direction) from this intersection, the worse the estimate becomes.

The following table shows what the errors (in degrees Fahrenheit) are between the estimated conversion and the actual temperature from -40° C and -40° F to 50° C and 122° F.

This table shows how accurate the estimated conversion is for the range of temperatures that are most often used when talking about the weather. In this range, the difference of the estimated values and the actual values are off by no more than a couple of degrees for both scales. That’s a pretty good model!

♪ Side Note: The system of equations can be solved to see where the estimated conversion value is exactly the same as the actual conversion value:

F = 1.8C + 32
F = 2C + 30
2C + 30 = 1.8C + 32
0.2C + 30 = 32
0.2C = 2
C = 10

F = 1.8 * 10 + 32
F = 2 * 10 + 30
F = 50

Closing Remarks

After exploring the actual conversion formula, and understanding that it is a linear function, I wondered why Daniel Gabriel Fahrenheit decided that 1.8 and 32 should be m and b in y = mx + b. Why not y = 2x + 30? Or why not skip the new unit altogether (y = x)? The Kelvin scale, for example, has a simple and purposeful conversion formula: K = C + 273. It helps us understand temperature in the context of absolute zero. But what is Fahrenheit helping with? If you are also curious, the wikipedia article has some interesting tidbits.

I think this trick is pretty easy to remember, and I appreciate how close the results are to the real values. Also, it only takes a little bit of mental math. Try it out the next time you have a chance.

Thanks and happy temperature converting!

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