The four scales and how they relate
Two of the scales are relative (Celsius, Fahrenheit — their zeros are arbitrary points like water's freezing) and two are absolute (Kelvin, Rankine — their zeros are absolute zero, the coldest possible temperature). Kelvin uses Celsius-sized steps; Rankine uses Fahrenheit-sized steps. All conversions flow from four relationships:
Worked example
A furnace runs at 850 °C. In the other scales:
- °F = 850 × 1.8 + 32 = 1562 °F
- K = 850 + 273.15 = 1123.15 K
- °R = 1562 + 459.67 = 2021.67 °R
Common reference points
| Point | °C | °F | K |
|---|---|---|---|
| Absolute zero | −273.15 | −459.67 | 0 |
| C/F crossing | −40 | −40 | 233.15 |
| Water freezes | 0 | 32 | 273.15 |
| Room temperature | 25 | 77 | 298.15 |
| Body temperature | 37 | 98.6 | 310.15 |
| Water boils (1 atm) | 100 | 212 | 373.15 |
The ΔT trap — the error instrumentation people actually make
Converting a temperature difference is not the same as converting a temperature. The 9/5 slope applies, but the +32 offset does not:
So a heat-exchanger approach of 10 °C is an 18 °F approach — not 50 °F. Likewise a span: a transmitter ranged 0–100 °C has a span of 100 K, and its Class B element tolerance of ±0.8 °C at 100 °C is ±1.44 °F, not ±33.4 °F. When a datasheet mixes units, convert the points with offsets and the spans without.
Frequently asked questions
What is the formula to convert Celsius to Fahrenheit?
°F = °C × 9/5 + 32. Going the other way, °C = (°F − 32) × 5/9.
At what temperature are Celsius and Fahrenheit equal?
At −40. It is the single crossing point of the two scales: −40 °C = −40 °F.
How do I convert a temperature DIFFERENCE between units?
For differences (ΔT), drop the offsets: a change of 1 °C equals a change of 1.8 °F and exactly 1 K. So a 10 °C temperature rise is an 18 °F rise — not 50 °F.
What is the Rankine scale used for?
Rankine is the absolute scale of the Fahrenheit system (0 °R = absolute zero, steps the size of °F). It appears in US thermodynamics and gas calculations, the way Kelvin does in SI.
Provided for reference and education. Verify independently before use in safety-critical work. See our disclaimer.