Conversion between Celsius and Fahrenheit?

Question

I understand the equations to convert one to the other, but now that I am thinking more about it I have a question.

It's easy to see when you convert from C to F, you have to take the temperature in C and multiply it by 9/5 (this adjusts the scale range and makes it bigger since C only goes from 0 to 100 for freezing point of water through boiling point) and then you add 32 (to adjust for the starting point since since F starts at 32).

And of course when you do it the other way, it is just the inverse. That is why you take your temperature in F and then subtract 32 first and then multiply by 5/9.

Okay maybe I am looking into this too deeply and confusing myself but if someone in the beginning started thinking about F first and how to convert to C, wouldn't he have thought: hey I should take the Fahrenheit scale and multiply it by 5/9 and then subtract 32 to adjust for the starting point.

But we know that we subtract 32 first and then multiply by 5/9 when converting from F to C (because the equation for converting C to F is known and you just do solve for C when makes you do the inverse.

I hope you guys understand my question. Basically when you take the logic "I need to take my temperature in C and multiply by 9/5 and then add 32 to get temp in F" works, how come the logic coming from F to C doesn't work: "I need to take my F and times it by 5/9 and then subtract C."

Sorry if this is confusing.

Answer 1

Yeah this is an order of operations question. To get the math to work out right, you need to do the subtraction first. As to why the equation works out that way, here is the answer:



5/9 is the scaling factor, as you imply. Now before you multiply by that scaling factor to convert between the two temperature types, you need to have the same starting point, otherwise you get the wrong answer. Think of it this way- if you multiply 5/9 by 9 then subtract 2, you get 5 - 2 = 3. But if you multiply 5/9 by 18 then subtract 2, you get 10 - 2 = 8. Now notice that 18 is only twice times 9, but when I do the operations, the answers differ by much more than twice. I hope that makes sense. The subtraction by 32 allows you to compare the two from the same starting point and then scale between them.. if you tried to do it the other way around, you wouldn't be comparing apples to apples.



Hope this helps



EDIT: Ok, sorry for being unclear. Let's look at it from a purely mathematical standpoint. We want to find a conversion equation between the two scales, so we need two equivalent points. This makes sense- if we want to compare the two scales, we'd better have an equation that has points that match up with each other. As an aside, we can do this because both scales are linear, so the conversion scale between the two is linear as well. The obvious points anyway are the boiling points and freezing points of water. Write the points in an ordered pair in this form: (celsius, fahrenheit). So our two points are:



(0, 32) and (100, 212)



Using those two points we can find the equation of the line that connects them, in the form y = mx + b. First the slope, m:



(212 - 32) / (100 - 0) = 1.8 = 9/5



Here is where the 9/5 comes from. Then we need the y intercept, b, so let's do that, using the (0, 32) point:



32 = 9/5 * 0 + b



b = 32



There is where the factor of 32 comes in. Now we have the equation:



y = 9/5*x + 32



Where we have defined y as F and x as C. So let's just write it finally as:



Tf = 9/5*Tc + 32



The subtraction and addition of the 32 and in what order just comes as a consequence of solving for the other variable algebraically.



Hope this helps.

Answer 2

I understand that Fahrenheit, for whom the scale is named, used non-standard, non-absolute reference points (e.g. human body temperature) and also made some rounding and measurement errors when trying to create individual thermometers he made by hand. His scale split the difference between 3 points and strangely, the freezing point of water wasn't one of them. He wanted 180 increments : 90° on each side of what he thought was the standard human body temperature.



The boiling point of water we know is actually 212° , not 200° , not 180°-- so Fahrenheit's scale which was used mainly for medical purposes had already been accepted into wide use before the construction errors were known. The sanitized story of how it was developed is in the link below.



To your question: the ratio of Celsius° to Fahrenheit° is a fixed relationship but the "scale" has different starting points. So conversion is matter of fact, adjusting ratios to derive equivalent degrees--except for one small problem; that starting point problem. It would have ended there except that Fahrenheit chose the freezing solid of brine as his scale's zero point and not the temperature of freshwater initial formation ice of surface ice like on Celsius' scale. This subjectivity did not address things like latent heat which we understand more precisely today.



We cannot accurately convert the temperatures without adjusting for the scale zero point. This has to be done on the F side. The zero point C is already water's freezing point so it is the Fahrenheit portion which has to be set to 32° when the temperature. Had Celsius set his zero point at 10° we would have to subtract 10 before conversion, convert and add back 32 and vice versa-- all to keep the zero point the same zero point across the board.

Answer 3

Celsius to Fahrenheit: °F = (°C × 1.8) + 32

Fahrenheit to Celsius: °C = (°F − 32) /1.8

Answer 4

Just use Fahrenheit, OK?

Answer 5

Give me the table of conversion