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 F-to-C and C-to-F)

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 visualizing-and-memory.

A convenient starting point for 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 in terms of the freezing point of water, at  0° C  =  32° F .

A Mathematical Equation for Converting Celsius & Fahrenheit:
To convert between temperatures in °C and °F, calculate how
many degrees the temp is above (or below) freezing water,
and then add (or subtract) this from either 0°C or 32° F, so
temperature in °C  =  0  +  (5/9)(32 - °F)
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 temperatures at intervals of 5° C and 9° F, as shown below where
(to understand-and-remember more 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
 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 interpolate between these 5-and-9 temperatures, you can
estimate that temperature 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":
°C °F °F  °F   °C 
10  50 +  0/5 50.00  50  10
11  50 +  9/5  51.80  52  11
12  50 + 18/5  53.60  54  12
13  50 + 27/5 55.40  55  13
14  50 + 36/5 57.20  57  14
15  50 + 45/5 59.00  59  15
When rounded to the nearest degree, notice that
each interval (except the middle) is 2, for 22122.
10   11   12 13   14   15  
50   52   54 55   57   59  
+2
+2
+1
+2
+2
the differences are 2 2 1 2 2

Or, to estimate temperatures in the reverse direction, notice
the pattern of paired temperatures  ( 10  11-11  12-12  13-13  14-14  15 ) for all of the
in-between Celsius temperatures, but not for temperatures that are multiples of 5, such as 10 and 15.
°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