Temperature scale fixed points in Celsius, Fahrenheit, Kelvin and Rankine
Four fixed points on all four scales. Absolute zero is -273.15 C, -459.67 F, 0 K and 0 R. Water freezes at 0 C, 32 F and 273.15 K, and boils at 100 C, 212 F and 373.15 K. The 37 C body reference is 98.6 F. Only the Celsius column is stored; the rest is calculated.
Fixed points on four temperature scales
Only the Celsius column is source data. Fahrenheit is calculated as C x 9/5 + 32, kelvin as C + 273.15, and Rankine as (C + 273.15) x 9/5. Because all three come from the one stored figure, a row can never contain four values that disagree with each other. 4 fixed points.
| Fixed point | What it is | Celsius (source) | Fahrenheit | Kelvin | Rankine |
|---|---|---|---|---|---|
| Absolute zero | the zero of the kelvin and Rankine scales | -273.15 C | -459.67 F | 0 K | 0 R |
| Water freezes (1 atm) | the conventional zero of the Celsius scale | 0 C | 32 F | 273.15 K | 491.67 R |
| Water boils (1 atm) | the conventional 100 degree point of the Celsius scale | 100 C | 212 F | 373.15 K | 671.67 R |
| Human body reference | the figure used in physiology and medicine | 37 C | 98.6 F | 310.15 K | 558.27 R |
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What the scales are actually anchored to
Since the 2019 revision of the SI, the kelvin is defined by fixing the Boltzmann constant, not by any property of water. The degree Celsius is then defined as the same size as the kelvin, offset so that 0 C is 273.15 K exactly. The offset is a definition; it is not measured and it does not drift.
That is why absolute zero is exactly -273.15 C and not approximately so. Kelvin and Rankine are absolute scales with their zero at that point; Celsius and Fahrenheit are interval scales with their zeros placed for convenience, which is the whole reason converting between them needs an offset as well as a factor.
Fahrenheit and Rankine share a degree size, 1.8 times smaller than the Celsius and kelvin degree, which is where every 9/5 in the formulas comes from. Rankine is Fahrenheit measured from absolute zero, so it is to Fahrenheit exactly what kelvin is to Celsius.
Why this matters: two of these points are conventions
The 0 C and 100 C water points are conventional definitions of the Celsius scale, not exact physical facts of the current temperature scale. On ITS-90, water at standard atmospheric pressure of 101.325 kPa boils at about 99.974 C, a small difference that matters in metrology and nowhere else.
The 37 C body reference is a convention too, and a coarser one. It comes from nineteenth-century measurements, and its familiar Fahrenheit form of 98.6 F is a conversion of 37 C rather than an independent figure. Human body temperature varies with the person, the time of day and the measurement site.
This is why the table stores only the Celsius column. The moment a table holds four independently typed numbers per row, someone eventually corrects one of them and leaves the others behind. Calculating three of the four makes that impossible.
Reading the formulas off the table
To convert Celsius to Fahrenheit, multiply by 9/5 and add 32. To go back, subtract 32 and multiply by 5/9. The two scales cross at -40 degrees, the one temperature that reads the same on both, which is the fastest way to sanity check a conversion in your head.
To convert Celsius to kelvin, add 273.15. There is no degree sign and no multiplication, because the two scales share a degree size. A temperature difference of 5 C is a difference of 5 K exactly, while a difference of 5 C is a difference of 9 F.
Rankine is the least used of the four and turns up almost only in American thermodynamics. It is kelvin scaled by 9/5, so water boiling at 373.15 K is 671.67 R, and absolute zero is 0 on both.
Frequently asked questions
What is absolute zero in Celsius and Fahrenheit?
Exactly -273.15 C, which is -459.67 F. It is 0 on both the kelvin and the Rankine scale. The Celsius figure is exact because the offset between Celsius and kelvin is a definition rather than a measurement.
Is normal body temperature 98.6 F or 98.2 F?
98.6 F is simply 37 C converted, and 37 C is a nineteenth-century average rather than a fixed physical constant. Later studies put the average slightly lower, and any individual reading varies with time of day and measurement site, so treat both numbers as references and not as thresholds.
Does water always boil at 100 C?
No. 100 C is the conventional definition at standard atmospheric pressure. On the current international temperature scale, water at 101.325 kPa boils at about 99.974 C, and at altitude the boiling point falls further, which is why cooking times change in the mountains.
At what temperature are Celsius and Fahrenheit the same?
At -40 degrees. Setting C x 9/5 + 32 equal to C gives C = -40, so -40 C is -40 F. It is the only point where the two scales meet, and it is a quick check that a conversion has been done the right way round.
What is Rankine and who uses it?
Rankine is Fahrenheit measured from absolute zero: R = (C + 273.15) x 9/5, so it shares its degree size with Fahrenheit and its zero with kelvin. It appears mainly in American thermodynamics and aerospace engineering, where absolute temperatures are needed in a Fahrenheit-based system.
Can I republish this table?
Yes, under Creative Commons Attribution 4.0 International (CC BY 4.0). Credit UnitGlide, https://unitglide.net and link back. The scale definitions are from the SI Brochure; the fixed points as compiled and the calculated columns are covered by this licence.
Sources
- BIPM, SI Brochure, 9th edition, for the definition of the kelvin, the degree Celsius and the exact 273.15 K offset between them.
- BIPM, International Temperature Scale of 1990 (ITS-90), for the practical temperature scale on which water at 101.325 kPa boils at about 99.974 C.
- NIST Special Publication 811, for the Fahrenheit and Rankine conversion formulas and their relationship to the kelvin.