Fahrenheit to Celsius (F to C)

Fahrenheit to Celsius is C = (F - 32) x 5/9. Written the way it computes, that is 5/9 times the Fahrenheit figure minus 17.777778, and the two parts do different jobs: the 5/9 accounts for the two scales having different degree sizes, and the 17.777778 accounts for them having different zero points.

That second term is what makes temperature different from every other conversion. Length, mass and volume units all share a zero (zero centimeters is zero inches), so converting one is a single multiplication. Fahrenheit and Celsius do not, so the conversion is affine rather than scalar and needs an offset as well as a ratio. It is the reason a temperature and a temperature difference convert by different rules: a rise of one degree Fahrenheit is a rise of 0.5556 degrees Celsius, because an interval scales with the ratio and takes no offset at all.

Worked through at a value people look up: 70 °F x 5/9 - 17.777778 = 21.1111 °C.

Going back, Celsius to Fahrenheit is 9/5 times the Celsius figure plus 32. Note what does not happen here: with a scalar conversion the two factors are reciprocals and knowing one gives you the other, but an affine conversion has two constants and the reverse offset is not the negative of the forward one unless the slope is 1.

For mental arithmetic: Subtract 30 and halve. 70 F gives 20 against a true 21.1, which is close enough to decide what to wear.

Most of the demand for this direction is a recipe. An American recipe says 350 F and a European oven dial is marked in Celsius, and 350 F is 176.67 C, a number no oven has. The convention is to round to the nearest 10, so 350 F is set as 180 C, 400 F as 200 C and 425 F as 220 C. That rounding is deliberate and harmless for baking, where oven thermostats swing by more than the error, but it is worth knowing that the printed equivalence is a convenience rather than the conversion. The other large cluster is body temperature: 98.6 F is 37 C exactly, and that figure is itself a conversion of a 19th-century Celsius measurement, which is why it looks suspiciously precise.

On precision: the 9/5 and the 32 are both exact, so the conversion introduces no error of its own. What it cannot do is add precision the input never had. A weather reading of 70 °F is good to about a degree, and reporting 21.111111 °C from it implies a thermometer nobody owns. The converter scales its decimals to the magnitude of the input for that reason.