degree Rankine
Temperatureexact by definition
The degree Rankine is the absolute temperature scale built on the Fahrenheit degree: its zero is absolute zero, and its step is the same size as a Fahrenheit degree, so T/K = T/°R × 5/9 with no offset. The 5/9 factor is exact by definition. Zero degrees Rankine is −459.67 °F, and water freezes at 491.67 °R.
Watch out: Rankine is written °R and shares that symbol with the Réaumur degree in older European sources, which is a different scale entirely. In modern engineering work °R means Rankine. Note also that Rankine, unlike Fahrenheit, takes no offset: it is a pure scaling of the kelvin.
| 1 °R | -272.59444 °C |
Proposed in 1859 by the Scottish engineer William John Macquorn Rankine, one of the founders of thermodynamics, as the Fahrenheit counterpart of the absolute scale Lord Kelvin had argued for a decade earlier.
About the degree rankine
Rankine exists for the same reason kelvin does. The gas law \(pV = nRT\), the efficiency of a Carnot cycle, and every radiation calculation need an absolute temperature, one whose zero is the true zero of thermal energy. An engineer working in pounds, feet and BTU who reaches for such an equation cannot substitute Fahrenheit into it. Rankine is the fix: keep the Fahrenheit-sized degree so the numbers stay familiar, but move the zero down to absolute zero.
The relationships are simple and all exact. \(T_R = t_F + 459.67\), \(T_R = 1.8 \, T_K\), and \(T_K = T_R \times 5/9\). Standard conditions in US practice are often quoted as 60 °F, which is 519.67 °R, and the ideal gas constant in those units is 10.7316 psia·ft³/(lb-mol·°R). Steam tables published for American power plants, compressor calculations, and combustion work all carry Rankine somewhere in the fine print even when the surface numbers are Fahrenheit.
It is the least-used of the four scales in this catalog, and outside US mechanical and chemical engineering it is almost never seen. But it is not obsolete: an absolute temperature in the wrong units is one of the more expensive unit errors available, and Rankine is what keeps a Fahrenheit calculation honest.