1643: Degrees

Explain xkcd: It's 'cause you're dumb.
Jump to: navigation, search
"Radians Fahrenheit or radians Celsius?" "Uh, sorry, gotta go!"
Title text: "Radians Fahrenheit or radians Celsius?" "Uh, sorry, gotta go!"


Cueball is being asked by a friend for the temperature. While he is checking his smartphone for the weather, he begins pondering what unit he should use when answering the question. (See below for Cueball's reasoning.)

In the US (where Cueball and Randall are from), the temperature scale used in daily life is Fahrenheit. However, most of the rest of the world uses Celsius in daily life, and even in the US it is commonly used for science. This is also why Randall has previously made the comic 526: Converting to Metric. There are also people who wish the US to change to the metric system, although some of them still wish to keep the Fahrenheit scale as mentioned in 1982: Evangelism

The Celsius scale is from the metric system. Though this system has been officially sanctioned for use in the US since 1866, it is not frequently used in daily American life (except for some things, like liter bottles of soda), although it is the preferred system for trade and commerce according to the Metric Conversion Act of 1975. The US remains the only industrialized country, and one of few countries period, that has not adopted the metric system as its official system of measurement. The unit degree Celsius or °C is an accepted derived unit from the International System of Units (SI units) used in science (which again is the modern form of the metric system). The SI unit of temperature is the kelvin, but this temperature scale is linearly related to the Celsius scale, which is why Celsius can be derived from it.
The Fahrenheit scale is from the US customary system and the (British) imperial system. The unit is degree Fahrenheit or °F, and the relation to the Celsius scale is not easy to find in a mental calculation. The relations are: [°F] = [°C]×9⁄5 + 32 or [°C] = ([°F] − 32)×5⁄9. (For this exact reason Randall has previously made a helpful table for these situations in 526: Converting to Metric.)

Unlike most areas of measurement, where the metric system is widely considered superior, there is considerable debate about the relative merits of Fahrenheit vs. Celsius. Cueball weighs up the benefits of both scales, but fails to find a solution he can live with, and since he feels he has to give his friend an answer now, he panics and gives the answer 0.173 radians.

Radian is the standard unit of angular measure, used in many areas of mathematics. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle. It has no units and is denoted with the superscript c, but more commonly rad, lest it be confused with angular degrees. One radian is an angle of approximately 57.3 degrees.
Angular degrees is a system used to measure angles in geometry, and although it too uses the symbol ° and the word "degrees", it has nothing to do with temperature measurements of any sort.

Thus, this answer is unhelpful and the joke is that traditionally both geometric angles and temperature are measured in "degrees", but there is no connection between the two.

Actually Cueball should have made a compromise and given the temperature on the Felsius scale (see 1923: Felsius).

The title text indicates that Cueball's friend still wants to know whether the answer is in radians Fahrenheit or radians Celsius, which, despite being a silly way to express temperature, would actually enable the friend to get some meaning out of the reply. But this just takes Cueball back to the problem he failed to solve in the first place of choosing one scale in preference to the other, so suddenly he announces has to go and runs off without ever clarifying what he meant. This result is probably because he is afraid of being a bad friend according to his very last point regarding Fahrenheit: Valuing unit standardization over being helpful possibly makes me a bad friend.

The answer Cueball gives of 0.173 radians corresponds to a geometric angle 9.91° (0.173 × 360°/). If this were "radians Celsius" it would be 9.91 °C corresponding to 49.8 °F and if it were "radians Fahrenheit" it would be 9.91 °F corresponding to -12.3 °C. Given the temperatures in Massachusetts (where Randall lives) when this comic came out, the day after Valentine's Day 2016, Cueball was probably giving his answer in radians Fahrenheit.

Cueball's reasoning[edit]

Degrees Celsius[edit]

International standard
Degrees Celsius is derived unit in the SI system of units used to measure temperature in most countries today. Using the SI system would allow Cueball to be easily understood in most countries and is by far the most recognized system, but it is not the most commonly used in the United States, his presumed location in the comic.
Helps reduce America's weird isolationism
The United States uses its own set of units, including degrees Fahrenheit, called the United States customary system (similar but not equal to the imperial system), in contrast to most of the rest of the world, which uses the SI system. The US's system of units is therefore considered "weird" as it makes the US different from most of the world, but previous efforts to convert the US to the SI system have failed. Cueball evidently believes that by using SI units, he will help to eventually convert the US to the SI system, bringing considerable trade and tourism benefits and reducing confusion when dealing with foreigners.
Nice how "negative" means below freezing
On the Celsius scale, the freezing point of water at standard atmospheric pressure (101.325 kilopascals) is very close to 0 °C, and any temperature below that is below the freezing point. The Fahrenheit scale uses different points of reference (using a water/ammonium chloride chemical reaction for the lower calibration, while the upper calibration is set such that water freezing and water boiling are 180 degrees apart), and as a result the freezing point of water is a less memorable 32 °F.
Physics major loyalty
Cueball is apparently a physics major, like Randall, and SI units are more commonly used for scientific work (as the kelvin scale is sometimes used in physics and other sciences), even in the US. By using the Celsius scale in casual conversation, he would show his loyalty to the system used by actual physicists.
Easier to spell
"Celsius" is generally considered to be an easier word to spell than the German surname "Fahrenheit" (at least this is the case for Cueball, but not necessarily for those who more commonly use Fahrenheit than Celsius). In this case the word is being spoken and the point is not immediately relevant, but part of the joke is that Cueball is overthinking things and worrying about the general use of the word when an answer is needed in this specific case.
We lost a Mars probe over this crap
The Mars Climate Orbiter disintegrated in Mars' atmosphere because Lockheed used US customary units instead of the contractually specified metric units. Note that this had nothing to do with temperature scales, but was the use of the unit pound-seconds where newton-seconds should have been used. This was a great and tragic loss for science in general, Mars exploration in particular, and thus also for Randall who has shown deep interest in any kind of space exploration, especially regarding Mars (mentioning many Mars probes in his comics so far).

Degrees Fahrenheit[edit]

0 °F to 100 °F good match for temperature range in which most humans live
In the context of air temperature, 0 °F and 100 °F correspond to "just about as cold as it gets" and "just about as hot as it gets" in temperate zones, thereby making Fahrenheit a useful temperature scale for weather reporting where most people live. By contrast, in Celsius a range of common temperatures in temperate zones is -20 °C to 40 °C, which is a less intuitive range for those used to the Fahrenheit scale.
Rounds more usefully (70's, 90's)
An argument sometimes heard for the continued use of Fahrenheit temperatures is that each 10 degrees change is meaningful in how we feel the temperature. Thus, it is convenient to talk about the temperature being in the 70's today, or in the 90's, etc. Since the Celsius degrees are almost twice as large, a similar statement about the temperature being in the 20's or 30's is not as useful, unless more precision is added by using phrases like low 20's or high 30's. However, this seems likely to be more a matter of which scale you are used to using than anything inherent in one scale or the other.
Unit-aware computing makes imperial less annoying
If you need to constantly convert between imperial and SI measurements in your head, or even between different imperial units (e.g., ounces and pounds), it gets annoying and is a strong argument for everyone using metric measurements all the time. But when it is easy to get the temperature - or any other measurement - reported in whatever units you want just by selecting the units you want your computer to report, then the annoyance is minimized, and the arguments for why we should stop using a familiar scale are weakened. Note that Cueball is looking at his smart-phone to get the current temperature.
As many Americans, Randall is confusing the United States customary system with the imperial system used in most of the rest of the English speaking world. In both systems temperature is measured in degrees Fahrenheit.
SI prefixes are less relevant for temperatures
One of the nice things about SI measurements is how the same basic unit scales by factors of 10 with common prefixes - e.g., kilometer, millimeter, kilogram, milligram, etc. Imperial measurements don't have this feature - you don't talk about long distances as kiloinches or small weights as millipounds. But, we generally don't use multiple units for atmospheric temperature (millidegrees or kilodegrees), so this argument for using SI measurements for length, mass, volume, etc., isn't as applicable for temperature scales.
Fahrenheit is likely more clear in this context
Cueball apparently knows that the inquirer is most likely to assume the answer will be in degrees Fahrenheit, so giving the answer that way would be the least likely to be misinterpreted. If he surprisingly gives an answer in Celsius, without explicitly stating he is reporting the temperature in Celsius, then that could be confusing.
Valuing unit standardization over being helpful possibly makes me a bad friend
The final thing Cueball considers is to question why he would give an answer that attaches more value to promoting standardization of units when all his friend wants to know is whether it is cold or warm outside. Wouldn't it be more friendly to just answer the question the way his friend will find most convenient? This is probably the reason he ends up not giving any real answer, as giving the answer in Celsius would make him a bad friend. Giving the answer in panic in radians makes him a weird friend, which might or might not be preferable to being a bad friend.


[Cueball is looking at his smartphone while a friend calls to him from off-panel. Cueball is thinking as indicated with a thought bubble.]
Off-screen voice: Hey, what's the temperature outside?
Cueball (thinking): Should I give it in °F or °C?
[Zoom in on Cueballs head with a list of reason to use Celsius above him:]
Degrees Celsius
  • International standard
  • Helps reduce America's weird isolationism
  • Nice how "negative" means below freezing
  • Physics major loyalty
  • Easier to spell
  • We lost a Mars probe over this crap
[Same view of Cueballs head, but wider frame to accommodate a broader a list of reason to use Fahrenheit:]
Degrees Fahrenheit
  • 0°F to 100°F good match for temperature range in which most humans live
  • Rounds more usefully (70's, 90's)
  • Unit-aware computing makes imperial less annoying
  • SI prefixes are less relevant for temperatures
  • Fahrenheit is likely more clear in this context
  • Valuing unit standardization over being helpful possibly makes me a bad friend
[Cueball is holding his smartphone down while thinking as indicated with another thought bubble floating at the top. He then speaks and gets a reply from his off-panel friend.]
Cueball (thinking): Crap, gotta pick something. Uhh...
Cueball: ...0.173 radians.
Off-screen voice: I'll just go check myself


  • At -0.698 radians (-40 degrees) it would not have mattered whether it was radians Celsius or radians Fahrenheit as the two scales are equal at this point: -40 °F is the same temperature as -40 °C.

comment.png add a comment! ⋅ comment.png add a topic (use sparingly)! ⋅ Icons-mini-action refresh blue.gif refresh comments!


Rankine is a good compromise. 14:11, 15 February 2016 (UTC)

0.173 rad = 10°. Now it could be 10°C (50°F) or 10°F (-12°C).-- 14:14, 15 February 2016 (UTC)

It should probably be noted that since 0.173 radians is equal to around 9.91 degrees, the temperature that Cueball gave is likely in 'radians Celsius', since 9.91 degrees Farenheit would be an unlikely temperature to occur, unless they're somewhere like Canada or northern Russia -- 14:17, 15 February 2016 (UTC)

It would appear that that's already been noted since I started writing that comment. Ignore me. -- 14:18, 15 February 2016 (UTC)
It would appear you're not in New England. Temperature last night -14°F = -26°C = -0.244 rad F = -0.556 rad C. But others have noted this as well. Bob Stein - VisiBone (talk) 23:41, 15 February 2016 (UTC)
Even Manhattan, New York reached -0.9°F on Sunday, the first time it's been below 0°F there in a generation. We came within 1 part in 269 of tying the 2006 record for biggest snowstorm 3 weeks before this, broke the record for latest frost by 12 days with bitter cold 3 weeks before that, had cherry blossoms suicidally bloom on Christmas 10 days before that (because they thought it's spring) and that whole month was twice as many degrees above normal as the previous record warmest December. We also broke the record for warmest November and September a few months ago. This is called global weirding. (the more accurate name for global warming) 04:28, 16 February 2016 (UTC)

Guys, we moved away from the Réaumur-scale: You can do the same for the Fahrenheit :-). --DaB. (talk) 14:20, 15 February 2016 (UTC)

And we all moved away from the Rømer scale (what Reumer and Fahrenheit were both based on), 0F is 0Rø, 100C/80Reu is 80Rø). We even moved from the 100C-0C to 0C-100C since Celsius was a (half) crazy Swedish scientist who thought Reumer made sense if it was based on 100 instead of 80, and 100 was the freezing point (everybody ignores the second part of his scale). 17:07, 15 February 2016 (UTC)
Rømer was Danish -- Calling him Sweedish is an insult -- kind if the same insult as calling Cruz Canadian Spongebog (talk) 17:14, 15 February 2016 (UTC)
Then it was great that it was Celsius who was called a crazy Swedish scientist above, (and he was Swedish). Rømer is luckily more known for making the first quantitative measurements of the speed of light and not for his failed temperature scale. (I'm from Denmark and like the light part: He measured the hesitation of light ;-) --Kynde (talk) 21:31, 15 February 2016 (UTC)

I'm pretty sure the only people who could possibly find "Fahrenheit" easier to spell than "Celsius" are those whose first written language was German. Promethean (talk) 01:31, 17 February 2016 (UTC)

Considering how cold New England is today, I'm pretty sure it's Fahrenheit. (talk) (please sign your comments with ~~~~)

Temperature is given in F. Look at which month it is. And how this is a darn cold winter (at least in Canada). 14:32, 15 February 2016 (UTC)

its currently 10F in the Boston area where Randall lives.
For people from the future, see this historical data page for the day the comic was released -- 19:00, 15 February 2016 (UTC)

What's with the "We lost a Mars probe over this" remark? 14:33, 15 February 2016 (UTC)

One of the Mars probes crashed into Mars because one of the NASA contractors was using US Customary units instead of SI units. Blaisepascal (talk) 14:39, 15 February 2016 (UTC)
Is there a reference for this ?? Spongebog (talk) 17:17, 15 February 2016 (UTC)
It was the Mars Climate Orbiter, it crashed in 1999 because software supplied by Lockheed Martin produced results in US customary units even though the specs called for metrics units. https://en.wikipedia.org/wiki/Mars_Climate_Orbiter Martin (talk) 22:04, 15 February 2016 (UTC)
The mars probe remark is in reference to a mistake in switching navigational numbers from American standard to metric (namely in that they didn't) which caused the probe to slam into the surface of mars. If I remember correctly that is. 14:43, 15 February 2016 (UTC)
I remember when this happened, thinking "OK, Lockheed, time to get out your checkbook and cough up the entire cost of that probe and launch," though I expect their bought-and-paid-for pet legislators made sure that didn't happen. Miamiclay (talk) 21:23, 16 February 2016 (UTC)

I used to think that physicists prefer Kelvin, which is of course sort of based on Celsius. Jkrstrt (talk) 15:28, 15 February 2016 (UTC)

If he used Radians Fahrenheit, then 1 would be very close to earth's historical mean temperature for the period 1951 to 1980. 16:19, 15 February 2016 (UTC)

That sounds like it could almost be useful.... What is the temperature on the surface on the sun in Radians ? Spongebog (talk) 17:20, 15 February 2016 (UTC)
96.08 radians Celsius, or 173.5 radians Fahrenheit. -- 19:00, 15 February 2016 (UTC)

"Easier to spell"? When editing, I had to correct myself from "Celcius" to "Celsius". I never get Fahrenheit wrong! Cosmogoblin (talk) 20:55, 15 February 2016 (UTC)

Can someone explain to me why Fahrenheit's scale is so much more popular across the Atlantic than in his home city country continent? 21:37, 15 February 2016 (UTC)

Same reason that the British used it. It was there. Unlike the Brits the US just never got around to change it Spongebog (talk) 02:18, 16 February 2016 (UTC)
As a Brit. I love it that the US was at one point the last bastion of the BTU (British Thermal Unit), I still see 17th century measures in some farming contexts - bushels though I think we both still agree that "Acres" are a much better measure area than the soul-destroying "hectare". :) 08:22, 16 February 2016 (UTC)

Not being an instinctive science type, and on a tiny screen, I initially read the comic as "51 prefixes," and thought to myself "I could probably get from peta- to pico- in my head, but there are really 51 of those?" Miamiclay (talk) 02:46, 16 February 2016 (UTC)

Maybe one should include the explanation why both angles and temperature use the term "degree". "Degree" in measurement means, that the definition comes from a partition of a known interval. For angles, that is "a full circle is 360 degrees" and for temperature in Celsius that is "100°C is the range from freezing to boiling water". That is historical, because modern SI units are defined in terms of partitions as well. 10:23, 16 February 2016 (UTC)

I'm not a linguist, but I think that it to a certain degree (!) just means "partial", "part" or "step" -- I can agree with you partially by which I will agree with you to a degree -- any scale can in a similar degree be broken up where each part is a degree closer to the full outcome -- so in Temperature a degree is a step toward boiling, and your Masters degree is a step beyond your Bachelor towards your Doctoral degree -- in short it is to some degree just a duhdah word representing nothing but makes it easier to form a sentence around an abstract concept 20:28, 16 February 2016 (UTC)

talking about weird us customs/units i think the way trailers and such specify release dates by season is terrible. 1. there are 2 hemispheres 2. internationally seasons may vary and it is rarely specified if its north or south seasons 06:37, 17 February 2016 (UTC)

Personally, I like to give temperature in meV/particle Edo (talk) 14:29, 17 February 2016 (UTC)

Do you mean MeV per non-frozen degree of freedom? The nitrogen in room-temperature air carries five-sixths the MeV/atom as argon in the same air at the same temperature. 00:21, 18 February 2016 (UTC)

Haha, "degree of correlation". Nice. 10:34, 27 December 2016 (UTC)