Celsius to Fahrenheit explained — the formula and the intuition
F = C × 9/5 + 32. Here is why that formula is what it is.
The formula to convert Celsius to Fahrenheit is:
F = C \times \frac{9}{5} + 32
The two terms do separate jobs:
- 9/5 is the scale factor — Fahrenheit degrees are smaller. 1 °C spans 1.8 °F. (Celsius inherited the 0°/100° anchor from the freezing/boiling points of water at standard pressure; Fahrenheit inherited his scale from ice-water / human-body temperature.) - +32 is the offset — at the freezing point of water, Celsius says 0, Fahrenheit says 32.
To go the other way:
C = (F - 32) \times \frac{5}{9}
If you're a scientist, use kelvin. The kelvin scale has the same size as Celsius but starts at absolute zero (−273.15 °C). You can convert with:
K = C + 273.15
The reason the conversion has an offset and not just a scale is that temperature is an affine quantity: the zero points differ. Compare to mass, where "0 kg" actually means zero matter, and the conversion is just a multiplicative factor. (Hence "linear" units and "affine" units appear separately on this site.)