Rankine equals Celsius plus 273.15, times 9/5. The Rankine scale is what kelvin would be if it had been built on Fahrenheit-sized degrees, and it survives in one place: American engineering thermodynamics.
About the units
William Rankine proposed the scale in 1859, eleven years after Kelvin proposed his in 1848. Both start at absolute zero; they differ only in degree size. A Rankine degree is the same size as a Fahrenheit degree, which is 5/9 of a kelvin. Water freezes at 491.67 °R and boils at 671.67 °R. The scale exists because American engineers working in Fahrenheit needed an absolute temperature for gas laws and thermodynamic cycles, and rescaling every equation to kelvin would have meant abandoning the rest of their unit system. It is written °R, sometimes with the degree sign omitted, and it should not be confused with Réaumur, which is also sometimes abbreviated R and is an entirely different scale.
The exact factor
The formula is °R = (°C + 273.15) × 9/5, which is equivalent to °R = K × 1.8. Some reference values: absolute zero is 0 °R and 0 K; room temperature at 20 °C is 527.67 °R; and the boiling point of water at 100 °C is 671.67 °R. The relationship to Fahrenheit is a pure offset, °R = °F + 459.67, exactly parallel to kelvin and Celsius differing by 273.15.
Where you meet this conversion
Thermodynamics and heat transfer in American engineering practice, particularly in combustion, refrigeration and steam cycle calculations. Textbooks published in the United States present the ideal gas law and the Carnot efficiency in Rankine alongside the kelvin versions. HVAC and process engineering software written for American users offers it. Outside that specific corner the scale is essentially unused, which is why an unexpected °R in a document usually signals an American engineering source.