degree Fahrenheit
Temperatureexact by definition
The degree Fahrenheit is the customary temperature unit of the United States, related to the kelvin by T/K = (t/°F + 459.67) × 5/9. The 5/9 factor and the 459.67 offset are both exact by definition, since Fahrenheit has been defined off the kelvin since the middle of the twentieth century rather than off any physical fixed point. A Fahrenheit degree is exactly five-ninths the size of a Celsius degree, so the Fahrenheit scale has 180 divisions between the freezing and boiling points of water where Celsius has 100.
Watch out: Converting a temperature and converting a temperature change are different operations. 10 °C is 50 °F, but a rise of 10 Celsius degrees is a rise of 18 Fahrenheit degrees. Use this unit type only for a temperature reading, and the temperature-difference type for a delta-T.
| 1 °F | -17.222222 °C (offset scale) |
Daniel Gabriel Fahrenheit set out his scale in 1724 using a zero at the temperature of a brine of ice, water and ammonium chloride, which was the coldest reproducible bath he could make, and a value near 96 for human body temperature. Later the scale was redefined on the freezing and boiling points of water at 32 and 212, which is where the awkward-looking 180-degree span comes from.
About the degree fahrenheit
Fahrenheit is the scale that looks arbitrary and mostly is, but it is arbitrary in a way that suited its purpose. Daniel Gabriel Fahrenheit was a glassblower and instrument maker in the Dutch Republic, and his problem was reproducibility: he needed fixed points that any other maker could recreate. A saturated brine of ice, water and ammonium chloride gave a stable low point he called zero, and something close to human body temperature gave the upper anchor near 96. Those numbers were chosen partly because the interval between them divides neatly by two over and over, which matters when you are marking a glass tube by hand rather than by calculation.
The modern definition threw all of that away and defined the scale off the kelvin instead, exactly: \(T_K = (t_F + 459.67) \times 5/9\). Both numbers in that expression are definitions, not measurements. Working the other way, \(t_F = t_C \times 9/5 + 32\). The 9/5 is the ratio of degree sizes and the 32 is where the ice point landed on Fahrenheit's original marks.
The one genuine advantage of the scale is resolution in the range where humans live. From a hard frost to a heatwave is roughly 0 °F to 100 °F, a hundred whole degrees of outdoor weather, where Celsius covers the same span in about 55. That is also its most common complaint from the other direction: a one-degree change in Fahrenheit is a smaller change than most people can feel, so thermostats in Fahrenheit-using countries argue over increments that would not exist on a Celsius dial.