Celsius to Rankine Converter
Convert °C to °R, the absolute temperature scale used in US thermodynamics, propulsion and HVAC engineering. Works both ways.
°R = (°C + 273.15) × 9/5
What Is the Rankine Scale?
Rankine is an absolute temperature scale. It starts at absolute zero the same way Kelvin does, but its degrees are the same size as Fahrenheit degrees, not Celsius ones. That combination exists for a practical reason. American engineering has historically worked in Fahrenheit, pounds and BTUs. Rankine lets equations that need an absolute temperature, such as those for gas turbines, jet engines and compressible airflow, stay in the same unit system without a detour through Celsius and Kelvin.
Today you'll mostly meet it in US aerospace and mechanical engineering, particularly propulsion and combustion analysis, and in older thermodynamics textbooks and steam tables. Outside those fields it's rare. Unless a problem specifically calls for Rankine, Kelvin is usually the more useful absolute scale.
Converting from Celsius changes both the zero point and the degree size: 0°R is −273.15°C, and 1°C of change is 1.8°R of change. That's why the formula both adds and multiplies, unlike Celsius to Kelvin, which only adds.
Worked Example: Carnot Efficiency in Rankine
A steam cycle takes in heat at 540°C and rejects it at 25°C. Its maximum possible (Carnot) efficiency is 1 − Tcold ÷ Thot, and that ratio only works with absolute temperatures.
Step 1: Convert both temperatures to Rankine
Step 2: Apply the Carnot formula
Maximum efficiency is 63.3%. Kelvin gives the same answer (1 − 298.15 ÷ 813.15), because both scales start at absolute zero and the ratio cancels the degree size. Plugging in Fahrenheit (77°F and 1,004°F) gives 92.3%, which is wrong.
Three Ways to Write the Formula
Via Kelvin
Shift to absolute zero first, then scale to Fahrenheit-sized degrees. Best when you already have kelvin values.
Direct
Scale first, then add 491.67, which is the freezing point of water in °R. This is the quickest form on a calculator.
Via Fahrenheit
If your data is already in Fahrenheit, as US steam tables often are, just add 459.67.
Reverse (°R → °C)
Celsius to Rankine Table
Cryogenic, ambient, steam and combustion temperatures, rounded to 2 decimal places.
| °C | °R |
|---|---|
| -273.15°C | 0°R |
| -100°C | 311.67°R |
| -40°C | 419.67°R |
| 0°C | 491.67°R |
| 20°C | 527.67°R |
| 25°C | 536.67°R |
| 100°C | 671.67°R |
| 200°C | 851.67°R |
| 300°C | 1,031.67°R |
| 500°C | 1,391.67°R |
| 1,000°C | 2,291.67°R |
| 1,500°C | 3,191.67°R |
The Same Temperature on All Four Scales
Rankine makes most sense next to Celsius, Fahrenheit and Kelvin at the same reference points.
| Reference point | °C | °F | K | °R |
|---|---|---|---|---|
| Absolute zero | -273.15 | -459.67 | 0 | 0 |
| Dry ice sublimates | -78.5 | -109.3 | 194.65 | 350.37 |
| Water freezes | 0 | 32 | 273.15 | 491.67 |
| Room temperature | 20 | 68 | 293.15 | 527.67 |
| Body temperature | 37 | 98.6 | 310.15 | 558.27 |
| Water boils | 100 | 212 | 373.15 | 671.67 |
Celsius and Kelvin move together (same degree size, different zero point), and so do Fahrenheit and Rankine. That's why the C and K columns are always exactly 273.15 apart, and the F and R columns are always exactly 459.67 apart.
Frequently asked questions
Is Rankine still used today?
Yes, mainly in US aerospace and mechanical engineering, particularly gas turbine and combustion analysis. In those fields the surrounding units (BTU, psia, lbm) are already US customary rather than metric.
How does Rankine relate to Kelvin?
°R = K × 1.8. Both are absolute scales that start at zero. They differ only in degree size, the same relationship Fahrenheit has to Celsius.
Is it written °R or R?
Both appear. NIST lists the unit as the "degree Rankine" with the symbol °R. Some engineering texts drop the degree sign to match kelvin. Don't confuse °R with the obsolete Réaumur scale, which used °Ré or °Re.
Can Rankine be negative?
No. 0°R is absolute zero, so this converter rejects negative Rankine values and Celsius values below −273.15°C.
Sources
- NIST Special Publication 811, Guide for the Use of the International System of Units (SI): degree Rankine conversion factors.
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