The Rankine scale is to Fahrenheit what the Kelvin scale is to Celsius: it starts at absolute zero but uses Fahrenheit-sized degrees. You’ll meet it when metric input data — a European pump datasheet, a lab measurement in °C — has to go into an equation written in US customary units, where the gas constant and property tables expect temperatures in °R.
How to use the Celsius to Rankine converter
- Enter the temperature in Temperature in Celsius (°C). The lowest valid value is −273.15 °C, absolute zero.
- Read the answer in °R. Fahrenheit and kelvin equivalents are listed too.
- The steps show the two-stage calculation, and the chart lists Celsius values from absolute zero to 2,000 °C.
Celsius to Rankine formula
The addition shifts the zero to absolute zero (giving kelvins); the 9/5 converts kelvin-sized degrees into the smaller Rankine degrees. Multiplying out the constants gives a one-step version:
Worked example: boiling water
Step 1. 100 + 273.15 = 373.15 K.
Step 2. 373.15 × 1.8 = 671.67 °R.
Check. Using the one-step form: 100 × 1.8 + 491.67 = 671.67 °R. In Fahrenheit, that is 212 °F, and 212 + 459.67 gives the same 671.67.
Example: Carnot efficiency in either scale
The maximum efficiency of a heat engine running between a hot and a cold reservoir is 1 − Tcold ÷ Thot, using absolute temperatures. Take steam at 300 °C rejecting heat to surroundings at 25 °C:
| Kelvin | Rankine | |
|---|---|---|
| Hot reservoir (300 °C) | 573.15 K | 1,031.67 °R |
| Cold reservoir (25 °C) | 298.15 K | 536.67 °R |
| 1 − cold ÷ hot | 0.4798 | 0.4798 |
The efficiency is about 48% either way. Because Kelvin and Rankine are both absolute, their ratios are identical; only the size of the degree differs. Using Celsius or Fahrenheit directly would give nonsense — 1 − 25/300 suggests 92%.
Reference points on four scales
| Point | °C | °F | K | °R |
|---|---|---|---|---|
| Absolute zero | −273.15 | −459.67 | 0 | 0 |
| Water freezes | 0 | 32 | 273.15 | 491.67 |
| Standard sea-level air | 15 | 59 | 288.15 | 518.67 |
| Standard ambient (SATP) | 25 | 77 | 298.15 | 536.67 |
| Water boils (nominal) | 100 | 212 | 373.15 | 671.67 |
Where the scale comes from
The Scottish engineer William John Macquorn Rankine proposed the scale in 1859, at the same time that thermodynamics was taking shape. It never caught on outside engineering, but it remains in use wherever calculations are carried out in Btu, pounds and feet. The symbol is °R; some references write °Ra to avoid confusion with the long-obsolete Réaumur scale.
Related conversions
Starting from Fahrenheit instead? Fahrenheit to Rankine is just an addition. If you already have kelvins, Kelvin to Rankine is a single multiplication by 1.8. For metric absolute temperature, use Celsius to Kelvin.
Frequently asked questions
What is the formula to convert Celsius to Rankine?
°R = (°C + 273.15) × 9/5. Add 273.15 to get kelvins, then multiply by 1.8. An equivalent form is °R = °C × 1.8 + 491.67.
What is 0 °C in Rankine?
0 °C is 491.67 °R, the freezing point of water on the Rankine scale. Water boils at 671.67 °R.
Who uses the Rankine scale?
Mainly engineers working in US customary units: thermodynamics courses, gas-turbine and rocket propulsion work, refrigeration, and steam or gas tables expressed in Btu, psia and pounds. Science and most of industry use kelvins instead.
How big is one degree Rankine?
The same size as one degree Fahrenheit, which is 5/9 of a kelvin or Celsius degree. So a change of 1 °C equals a change of 1.8 °R.