Temperature Conversions & Temperature Scales:

Celsius (Centigrade) and Fahrenheit
Converting F-to-C, C-to-F

by Craig Rusbult, Ph.D.

If you just want a simple numerical answer, use
A Converter-Calculator (for C-to-F and F-to-C)

But if you want to UNDERSTAND the two scales,
and two ways to convert from F to C, and C to F, by
using a mathematical equation or (usually it's more
practical in everyday life) visualizing-and-memory.

 
A convenient starting point for understanding the
temperature scales (and temp-conversions) is to
compare the boiling and freezing points of water:

BOILING POINT of water is 100° C 212° F
difference in degrees = 100 C° 180 F°
FREEZING POINT of water is   0° C  32° F

As you can see by comparing numbers in the table above,
degrees differ in SIZE:  100 C° = 180 F°,  so  5 C° = 9 F°
(a Celsius-degree is larger than a Fahrenheit-degree, and
there are 100 C-degrees between freezing and boiling, so
the Celsius scale originally was called the Centigrade scale)

The two scales also differ in STARTING POINTS: 
I find it useful to "think about the two starting points" by
comparing the freezing points of water, at  0° C  =  32° F .

Notice the difference between the meaning of " ° " when its
indicating a temperature (0° C, or 32° F) and when it shows
the size of a degree, as in "5 C° = 9 F°".  Almost always it's
used to indicate a temperature, e.g. 0° or 32°,  100° or 212°.
Also, the placement of symbols (before or after) matches our
language:  we pronounce "32° F" as "32 degrees Fahrenheit"
but pronounce "9 F°" as "9 Fahrenheit-degrees".

A Mathematical Equation for Converting Celsius & Fahrenheit:
To convert between temperatures in °C and °F, we first calculate
how many degrees the temp is above (or below) freezing water –
this is (32 - °F) or (0 - °C),  then convert F°-into-C° or C°-into-F°,
using "5 C° = 9 F" and then add this number (which usually is
positive but could be negative) to either 0°C or 32° F, so
Celsius-temperature in °C       =   0   +  (5/9)(32 - °F)
Fahrenheit-temperature in °F  =  32  +  (9/5)(0 - °C)

 
Visualize-and-Memorize
to convert between Celsius and Fahrenheit:
You can use the formulas above to convert by math-calculating,
but for practical everyday conversions I think it's more useful to
memorize matching temperatures at intervals of 5° C and 9° F,
shown in the table below where (to understand-and-remember
easily) you can begin at 0/32 and move upward or downward:
  °C     °F  
  etc   etc
  40  104
  35   95
  30   86
  25   77
  20   68
  15   59
  10   50
   5   41
   0   32
 - 5   23
 -10   14
 -15    5
 -20  - 4
 -25  -13
 -30  -22
 -35  -31
 -40  -40
 -45  -49
 etc  etc
As shown by "etc" at the top and bottom, this 5-and-9 pattern
continues above and below the temperature range in the table. 

To quickly estimate T's between these 5°-and-9° T's, use
the rough estimate that T changes by 1 C° for every 2 F°.
And for more precision, use the easy calculations below;
to make the math more intuitive and easy to remember,
we'll start at 10-and-50 where both temps end in a "0".
Here are some concrete examples, to help you become
comfortable with using this strategy-for-estimating:
 °C  °F (actual) °F (actual)  
 estimates { from C to F } 
    °C 
 { from F to C } 
 10  50 +  0/5  50.00    10 is 50     10  51 or 50 is 10
 11  50 +  9/5   51.80, and     11 is 52, up 2 more, up 2 total    11  51 or 52 is 11 
 12  50 + 18/5   53.60, and    12 is 54, up 2 more, up 4 total     12  53 or 54 is 12 
 13  50 + 27/5  55.40, and    13 is 55, up 1 more, up 5 total    13  55 or 56 is 13
 14  50 + 36/5  57.20, and    14 is 57, up 2 more, up 7 total    14  57 or 58 is 14
 15  50 + 45/5  59.00, and    15 is 59, up 2 more, up 9 total    15  51 or 59 is 15
To produce a memory-helping principle,
notice that this table contains these patterns:
For C-to-F, when rounded to the nearest degree,
    each interval (except the middle) is 2, so 22122,
    and the total up-change (from 50) is 2, 4, 5, 7, 9.
And for F-to-C, each C-Number (in between) has
    two F-Numbers (51 52 - 53 54 - 55 56 - 57 58)
    that, when rounded, will give this C-Number,
    i.e. 51 and 52 both round to 11, and so on.
10   11   12 13   14   15  
50 51 52 53 54 55 56 57 58 59  
    +2   +2 +1   +2   +2  
    +2   +4 +5   +7   +9  


Or, in a table (below) that shows only the F-to-C conversions,
to get "rounded to nearest degree" temperatures in the reverse direction, notice
the pattern of paired temperatures  ( 50  51-52  53-54  55-56  57-58  59 ) for all
in-between Celsius temperatures, but not for multiples of 5, like 10 and 15.
10 11 11 12 12 13 13 14 14 15
50 51 52 53 54 55 56 57 58 59

°F  °C +  C°   °C  °C  °F 
50  10 +  0/9  10.00  10   50
51  10 +  5/9 10.56  11  51
52  10 + 10/9 11.11  11  52
53  10 + 15/9  11.67  12  53
54  10 + 20/9 12.22  12  54
55  10 + 25/9 12.78  13  55
56  10 + 30/9 13.33  13  56
57  10 + 35/9 13.89  14  57
58  10 + 40/9 14.44  14  58
59  10 + 45/9 15.00  15  59
 


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