Why the scales cross at −40
Celsius and Fahrenheit assign different numbers to the same physical temperatures because they use different reference points and different-sized steps. On the Celsius scale, water freezes at 0°C and boils at 100°C under standard atmospheric pressure. On Fahrenheit, those points are 32°F and 212°F. The gap between freezing and boiling is therefore 100 Celsius degrees but 180 Fahrenheit degrees, so each Celsius degree spans 1.8 Fahrenheit degrees.
A conversion has to account for both that change in step size and the 32-degree offset at water’s freezing point. In formula form, °F = (9/5 × °C) + 32. The scales agree where that formula returns the same number it started with: solving °F = °C gives −40.
Why the shared number is negative
At 0°C, Fahrenheit reads 32°, so the Fahrenheit scale starts this comparison 32 numbers higher. To make the readings converge, the temperature must fall below zero on both scales. But because Fahrenheit degrees are smaller, its reading drops faster for each Celsius degree of cooling. At −40, that faster drop exactly cancels the initial offset.
This is a crossing point, not a special change in the physical behavior of cold. The air at −40°C is the same temperature as air at −40°F; only the labels differ. The memorable part is that the usual conversion arithmetic disappears: when the two scales meet, either number can be read directly as the other.
