Convert °C to K

Celsius puts zero at the freezing point of water and 100 at its boiling point, at sea level. Anders Celsius originally had the scale the other way up, with zero as boiling.

Kelvin starts at absolute zero, the point where there is no thermal energy left to remove, and its degrees are the same size as Celsius ones. It takes no degree sign — it is 300 K, not 300 °K.

Celsius and Kelvin do not start counting from the same place, so no single number converts between them. Multiplying is the mistake this page exists to prevent: it is right at exactly one temperature and wrong everywhere else, and the error grows the further you get from that point.

The two ends of this page's own scale show it. 0 °C is 273.15 K and 100 °C is 373.15 K — a hundred steps on one side, 100 on the other, and the two zeros in different places. That is why the formula above has two parts, something to multiply by and something to add; drop the addition and the answer stops being wrong slowly and starts being wrong badly.

Kelvin starts at absolute zero, the point where there is no thermal energy left to remove, and nothing below it exists to measure. That is what makes it a scale you can multiply on: 200 K really is twice 100 K, in a way that 200 °C is not twice 100 °C.

Neither Celsius nor Fahrenheit can say that. Their zeros were chosen, not found, which is why doubling a Celsius reading means nothing at all.

Every other conversion on this site rescales a quantity. This one moves an origin. A kelvin is defined to be exactly the same size as a degree Celsius, so the two scales differ only in where zero sits, and the conversion is 273.15 added to the Celsius figure and nothing more. 20 °C is 293.15 K, 0 °C is 273.15 K, and −273.15 °C is 0 K.

That makes this the only conversion in the temperature category with no multiplication in it, and the easiest one to check. The two figures must always differ by exactly 273.15, so an answer out by 273 or by 0.15 has lost a digit rather than made a rounding error. If a result looks approximately right, subtract and confirm it exactly — approximately right is not a state this conversion has.

Zero kelvin is the point at which a system holds no thermal energy that could be removed from it. It is not "very cold" on the same continuum as a freezer; it is the lower bound the temperature scale has, which is why an absolute scale carries no negative readings and why physics is written in it rather than in Celsius.

It cannot be reached, and that is the third law of thermodynamics rather than an engineering limitation: each stage of cooling removes a fraction of what remains, so the number of stages needed to arrive at zero is unbounded. Laboratories have worked in billionths of a kelvin without closing the gap. The background temperature of empty space is 2.725 K, or −270.4 °C, and a few nebulae have been measured colder still.

The unit is the kelvin, the symbol is K, and it takes neither a degree sign nor the word "degrees". It is 300 K, read aloud as three hundred kelvin. This has been the case since 1967, when the name "degree Kelvin" and the symbol °K were formally retired, so anything printed with a °K since then reflects a habit rather than a standard.

Two smaller conventions travel with it. The unit name is lowercase in running text — a kelvin, three hundred kelvins — while the symbol is capital, which is the general rule for SI units named after a person; Lord Kelvin took his title from the river running through Glasgow. And there is a space between number and symbol, 300 K rather than 300K, the same rule that gives 20 °C its space before the degree sign.

Because the two scales share a degree size, any temperature difference is the same number in both. A process that warms something by 15 °C warms it by 15 K, and there is nothing to add. This is the one place where the conversion is not merely simple but absent, and it is the reason datasheets quote temperature coefficients per K while meaning per degree Celsius.

So a resistor rated 50 ppm/K drifts fifty parts per million for every Celsius degree of change, and a thermal resistance of 3 K/W lifts a junction 3 °C for every watt it dissipates. Adding 273.15 to either would be a category error, because neither was ever a reading. The test is whether the number would still mean the same thing if the zero moved — if it would, no offset applies to it.

A ratio of two Celsius readings means nothing, and that is the practical case for converting at all. Warming air from 20 °C to 40 °C does not double anything. In kelvin the same change is 293.15 K to 313.15 K, a rise of 6.8 per cent, and it is that figure rather than the doubling that any physical law will use.

Worked through: a sealed vessel of gas at 20 °C and 1 bar, warmed to 40 °C, reaches about 1.068 bar, because pressure at constant volume follows absolute temperature. Doing it in Celsius and doubling gives 2 bar, which is out by nearly a factor of two and is a dangerous answer to give about a pressure vessel. The same applies to radiated heat, which follows the fourth power of absolute temperature, and to thermodynamic efficiency limits, which are ratios of kelvin figures.

Until 2019 the kelvin was defined by water: exactly 1/273.16 of the thermodynamic temperature of water’s triple point, the single combination of temperature and pressure at which ice, liquid and vapour coexist. That point sits at 273.16 K, or 0.01 °C, and the hundredth of a degree in it is what put the .15 into every conversion on this page.

Since the 2019 revision of the SI, the kelvin has been fixed instead by giving the Boltzmann constant the exact value 1.380649 × 10⁻²³ joules per kelvin — a link to energy rather than to a substance. Nothing measurable changed at the point of redefinition; what changed is that the triple point became a measured quantity with an uncertainty. The 273.15 offset was left exactly where it was, so this conversion is a definition and will not be revised.

A short set covers most work: absolute zero at 0 K, water freezing at 273.15 K, standard laboratory ambient at 298.15 K, water boiling at 373.15 K, and body temperature at 310.15 K. Every one ends in .15, which doubles as a sanity check — a whole Celsius number always converts to a kelvin figure with .15 on the end, and anything else means a digit went astray.

The two standard conditions are worth separating, because published work uses both and rarely says which. IUPAC’s standard temperature and pressure is 273.15 K with 100 kPa; standard ambient temperature and pressure is 298.15 K at the same pressure. A molar volume quoted without naming one of them is ambiguous by about nine per cent, which is the difference between 22.7 and 24.8 litres per mole.

The constant is exact, so the only question is how many digits the Celsius figure deserves. A room measured to the nearest degree at 21 °C becomes 294.15 K, and those two trailing digits were inherited from the constant rather than from the thermometer — writing them implies a hundredth of a degree that nobody measured. In a report, 294.2 K or 294 K is the honest figure.

Above a few hundred kelvin the .15 stops competing at all. A furnace at 1,200 °C is 1,473.15 K, and 1,473 K makes exactly the same claim. The offset only rivals the measurement’s own precision at ordinary temperatures, which is precisely where laboratory work sits, so the habit that survives review is to carry the .15 through the calculation and drop it when the number is written down.