Temperature conversion

It's useful to take a minute and look at what's going on with these conversions. Why do we need more than just a ratio to do them? Let's start by taking a look at the two temperature scales below.

We find our conversion factor just like we would with any other units : by measuring the distance between two known points on each of our scales.   Freezing point and boiling point make good reference points. In Fahrenheit the distance is 212-32 = 180 degrees F°. In Celsius, the distance is 100-0 = 100 degrees C°.

 

 

 

 

That's were the conversion factor comes from. Me, I hate using fractions, so I use the decimal equivalent, 1.8 (look at the second factor above 18 / 10 = 1.8).  Note: if you use the reciprocal of 1.8 which equals 0.555555 be sure you use 3 decimal (0.555) places or you will get a rounding error in your calculations. Why would you want to use the the reciprocal 0.555? See the last paragraph.

One thing we notice about the two scales is that the Celsius units are bigger than the Fahrenheit units, in fact, they are 1.8 times bigger. For each unit in Celsius, I need 1.8 units in Fahrenheit. So for example, if I have 20 units Celsius, I'll need 20 X 1.8 units = 36 units in Fahrenheit. If you compare the two scales above, you'll see though that 20 C° sure doesn't correspond to 36 F°.  Why not?

The second thing we notice about the two scales :  they don't start in the same place relative to a common reference point, such as freezing. It's like if you used a ruler to measure something, but instead of starting at the beginning of the ruler you started at 1". If the object you're measuring was 6" you know it isn't really 6". It's 6"-1" or 5".

That's were the scalar of 32 comes from - it's the distance between the starting point of the two scales and a common reference point, in this case freezing.

Since Celsius starts at 0, but Fahrenheit starts at 32, to complete the example I started above, converting C° to F°, I'll need to add 32 to the 36 giving 68 F°.

[C° x 1.8] + 32 = F°

Converting from F° to C°, the first thing I have to do is subtract 32. This is exactly like starting the measurement at 1" only with Fahrenheit we're starting at 32.

[F° - 32] / 1.8 = C°

We divide because we need to end up with fewer Celsius units - remember they're bigger, so we'll need fewer of them to make up the same distance on the Fahrenheit  scale. This is where you might what to use the reciprocal.  It's easier & less error prone (I think) to multiply by 0.555 than to divide by 1.8

 

 

©1997-2002 Dale Sampson, RN