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Why is it so simple to convert between °F and °C?

edro

edro

Lifer
The calculation is so simple.
Does it have to do with how each scale was founded?
Or is it just a well accepted approximation?

F->C
(F-32)/(9/5)

C->F
(C*(9/5))+32

What is magical about 9/5? 1.8? 180%?

Google just keeps telling me ways to calculate it.
I want to know why the formula is so perfect.
 
edro said:
The calculation is so simple.
Does it have to do with how each scale was founded?
Or is it just a well accepted approximation?

F->C
(F-32)/(9/5)

C->F
(C*(9/5))+32

What is magical about 9/5? 1.8? 180%?

Google just keeps telling me ways to calculate it.
I want to know why the formula is so perfect.
Click to expand...
The ratio of the size of a degree in each scale (9/5) and the offset of 0 in each scale (32)
 
I used to think it was overcomplicated. 0ºC=32ºF, right? So to convert C to F, just add 32 to the C number.

But it doesn't work that way.
 
Both scales are linear (the graduations are evenly spaced.) Thus, I can arbitrarily determine my own scale for a thermometer:

0 degrees bear is the temperature of bear shit I found in the woods on a Saturday in late November. 100 degrees bear is what I mark the rectal temperature of the bear on my thermometer. That is, pop that thermometer out, draw a line where the mercury (or dyed alcohol) is, and call that line 100.

On your Fahrenheit scale, my 0 is your 40 degrees. My 100 degrees is your 90 degrees. So, my scale goes up 100 degrees, while your scale only goes up 50 degrees. That is, a change of 2 degrees on my scale corresponds to a change of 1 degree on your scale. Now, to do a conversion, we merely have to do a slight shift.

Let's say that you measure something to be 50 degrees F. You want to convert it to Bears. You note that it's 10 degrees above the F temperature that corresponds to the 0 on my scale. [In other words, 50 - 40 = 10]. And, you know that 1 of your degrees F is equal to 2 of my degrees B. So, 10*2 = 20.

The formula, thus, looks like this:
B=2(F-40)

Or, to convert the other way, let's say I measure a temperature of 60 degrees Bear. I'd know that each of my degrees was 2 of your degrees. So, I'm 30 of your degrees above my zero. My zero is 40 of your degrees. That makes it 70 of your degrees.
F= (1/2)B + 40


0C corresponds to 32F
100C corresponds to 212F
So a change of 100 degrees C = a change of 180 degrees F
100/180 = 5/9
180/100 = 9/5
And, I think you can figure out why you add or subtract the 32 now.
 
dank69 said:
The ratio of the size of a degree in each scale (9/5) and the offset of 0 in each scale (32)
Click to expand...
This. There's no magic, someone smart just said "Well, There's two points, the boiling point of water and the freezing point of water, and I think that should be divided into 100. Yeah, that works."

And that's how centigrade was developed. Fahrenheit I think was just drunk.

As for Kelvin, well, Lord Kelvin said, "You know, Celsius was on to something, and I don't think I wanna make a whole new scale, so let's use his degrees but make the zero REALLY FUCKING ZERO. Like, can't get any colder bitch!" So he did a bunch of math and physics experiments and found out that absolute motherfucking zero corresponded to 273.18something or other was as cold as shit could possibly, ever get, in the vacuum of space or inside the brains of half the neffers here (cough M3 cough).

And they thus called him Lord Kelvin.
 
Mixolydian said:
I used to think it was overcomplicated. 0ºC=32ºF, right? So to convert C to F, just add 32 to the C number.

But it doesn't work that way.
Click to expand...

but 100C = 212F.

OP they are both measuring the same thing just in different increments. It's the same reason why it's a simple ratio to switch between lb and kg or ft and meters.

(212-32)= 180
180/100 = 9/5
 
It's almost like that slope intercept thing we learned in school.

Y=mX+b

If only I had a graphing calculator...or even graphing paper. I just realized I have no graphing paper. How did this happen?
 
Great comments and insight.

I know they are the same thing and both are linear... but why is it a simple 1.8 ratio?
Why not 1.8135?

Maybe I need to see who came up with the scale first and why the second scale was "needed".

I guess the same applies to Feet and Meters.
Why exactly 2.54 and not 2.546781?
 
The international inch is defined in terms of the metric (!) system of units to be exactly (!) 25.4 mm. This definition was agreed upon by the U.S. and them British Commonwealth in 1958. Prior to that, the U.S. and Canada each had their own, slightly different definition of the inch in terms of metric units, while the U.K. and other Commonwealth countries defined the inch in terms of the Imperial Standard Yard. The U.S. continued to use its previous national definition of the inch for surveying purposes. This inch, known as the U.S. survey inch is defined so that 1 metre is exactly 39.37 survey inches. 1 survey inch equals approximately 25.40000508 mm, or 1.000002 international inches.
Click to expand...

Ah... great nations agreed on it! ISO must have decided on C and F too.
 
There's another way to calculate the temperature conversion. The two equations are really really simple but I can't remember them it's been too long.

I'm working on it.

The equations you posted are unnecessarily complicated. I'll remember. Gimme a bit...
 
It's even easier to convert between °C and °K. 🙂

PS. A small PSA: 20°C is not twice the temperature of 10°C in any meaningful way.
 
DrPizza said:
Both scales are linear (the graduations are evenly spaced.) Thus, I can arbitrarily determine my own scale for a thermometer:

0 degrees bear is the temperature of bear shit I found in the woods on a Saturday in late November. 100 degrees bear is what I mark the rectal temperature of the bear on my thermometer. That is, pop that thermometer out, draw a line where the mercury (or dyed alcohol) is, and call that line 100.

On your Fahrenheit scale, my 0 is your 40 degrees. My 100 degrees is your 90 degrees. So, my scale goes up 100 degrees, while your scale only goes up 50 degrees. That is, a change of 2 degrees on my scale corresponds to a change of 1 degree on your scale. Now, to do a conversion, we merely have to do a slight shift.

Let's say that you measure something to be 50 degrees F. You want to convert it to Bears. You note that it's 10 degrees above the F temperature that corresponds to the 0 on my scale. [In other words, 50 - 40 = 10]. And, you know that 1 of your degrees F is equal to 2 of my degrees B. So, 10*2 = 20.

The formula, thus, looks like this:
B=2(F-40)

Or, to convert the other way, let's say I measure a temperature of 60 degrees Bear. I'd know that each of my degrees was 2 of your degrees. So, I'm 30 of your degrees above my zero. My zero is 40 of your degrees. That makes it 70 of your degrees.
F= (1/2)B + 40


0C corresponds to 32F
100C corresponds to 212F
So a change of 100 degrees C = a change of 180 degrees F
100/180 = 5/9
180/100 = 9/5
And, I think you can figure out why you add or subtract the 32 now.
Click to expand...

DrPizza said:
Yes, but it's -160 Bears. And that sounds a lot colder than -40, so I propose we switch to my new units of temperature measurement.
Click to expand...

That's an awesome final exam problem for an ?Algebra 2? class. I gave problems like that to my intro to MATLAB class (example isn't as fun, no bear poop involved) and I got a bunch of complaints: This isn't a math class, it's MATLAB!
 
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