For the quick answer, here are the two formulas so you can go and do it.
C = (F – 32)*5/9
F = (C*9/5) + 32
F = degrees Fahrenheit
C = degrees Celsius
* = multiply
/ = divide
() = do this first
If you wanted to actually derive the formula for converting one to the other, here’s how.
Because both scales are linear, the conversion between them will also be linear. To define a line, you need exactly two known points. Typically, people choose to use the freezing and boiling points of water, as these are the two points used to define both of the temperature scales.
At freezing, F = 32, C = 0
At boiling, F = 212, C = 100
If you want to write these as graphical coordinates (C,F) then we have (0,32) and (100,212).
The equation of a line is y = m*x +b
The slope of a line (m) is “change along the y-axis”/”change along the x-axis”. For us, F is y, and C is x.
slope (m) = (212-32)/(100-0) = 180/100 = 9/5
A line also needs a y-intercept (b).
Find the y-intercept (b) by plugging in y, m, and x for either the boiling or freezing point. I’ll use the boiling point.
y = m*x + b
F = m*C + b
212 = (9/5) * 100 + b
212 = (1.8) * 100 + b
212 = 180 + b
212 – 180 = 180 – 180 + b
32 = b
putting b = 32 into our equation gives:
F = 9/5 * C + 32 which matches our original equation, written as F = (C*9/5) + 32
To find the equation for Celsius, just use algebra to rearrange this equation.
F = 9/5 * C + 32
F – 32 = 9/5 * C + 32 – 32
F – 32 = 9/5 * C
(F – 32) * 5/9 = 9/5 * 5/9 * C
(F – 32) * 5/9 = C
or
C = (F – 32)*5/9
