Why temperature conversion needs an offset, not just a scale factor
Most unit conversions (length, weight, volume) are a pure multiplication because both units start counting from the same zero — 0 meters is 0 feet, 0 kilograms is 0 pounds. Temperature scales don't share a common zero: 0°C (water's freezing point) is 32°F, and 0 Kelvin (absolute zero, the coldest physically possible temperature) is −273.15°C. Any conversion has to shift for this offset in addition to rescaling for the different degree sizes.
The three key reference points
0°C converts to exactly 32°F and 273.15 K. 100°C (water's boiling point at sea level) converts to exactly 212°F. Normal human body temperature, 37°C, converts to 98.6°F — a number many people memorize without realizing it's a direct Celsius-to-Fahrenheit conversion of a single reference point.
The one point where Celsius and Fahrenheit agree
Because Celsius and Fahrenheit have different zero points AND different degree sizes, their scales cross at exactly one value: −40°C converts to exactly −40°F. Below or above that single crossing point, the two scales diverge again in the other direction — it's a genuine one-time coincidence of the specific offset and scale factor between the two systems, not a repeating pattern.
Why Kelvin has no negative numbers
Kelvin is an absolute scale — its zero point is absolute zero, the theoretical lower limit of temperature, where classical thermal motion stops entirely. Because of this, Kelvin never has negative values in physical use, unlike Celsius and Fahrenheit, which can go arbitrarily negative in ordinary weather or lab contexts. Kelvin uses the same degree size as Celsius (a 1-degree change is identical in both), so converting between them is pure addition/subtraction (+273.15) with no rescaling — the only pair of these three scales where that's true.
Why this matters for calculations, not just conversions
Confusing an offset-based conversion for a pure-multiplication one produces wildly wrong results — doubling a Celsius temperature does not double the equivalent Fahrenheit temperature (20°C is 68°F, but 40°C is 104°F, not 136°F). Any calculation involving temperature differences or ratios needs to account for which scale is being used and whether the offset matters for that specific calculation — a temperature difference in Celsius and Kelvin is numerically identical (since both share the same degree size), but a temperature difference in Fahrenheit is not directly comparable without conversion.