Celsius to Kelvin (°C to K)

The degree Celsius (°C) is an SI-derived unit of temperature defined by the equation t/°C = T/K − 273.15, where T is the thermodynamic temperature in kelvin (the SI base unit). The Celsius and kelvin scales differ only by a fixed offset of exactly 273.15: a temperature change of 1 °C is identical to a temperature change of 1 K, but the absolute reference point of 0 °C is the freezing point of water at standard atmospheric pressure (273.15 K) rather than absolute zero. The two scales are interconvertible by addition or subtraction without any multiplicative factor, distinguishing the Celsius/kelvin pair from the Fahrenheit/Rankine pair (where the same fixed-offset relationship holds with a different offset) and from any pair across the two systems (where the conversion is affine: scale by 9/5 or 5/9 plus an offset). Since the 2019 SI redefinition, the kelvin — and so the Celsius scale — is defined by fixing the Boltzmann constant k at exactly 1.380649 × 10⁻²³ J/K. The earlier definitional anchor at the triple point of water (exactly 273.16 K, or 0.01 °C, by the 1954 CGPM) survives as a useful realisation rather than as a definition. The Celsius scale is part of the International System of Units in the sense that it is fully derivable from kelvin, even though kelvin is the SI base unit for temperature. The unit is recognised by every national metrology institute and is the legal scale for trade, weather reporting, medicine and engineering across nearly every country in the world.

The Celsius scale is the only major temperature scale whose original direction was the opposite of its modern form. Anders Celsius, professor of astronomy at Uppsala University, presented his thermometric scale to the Royal Swedish Academy of Sciences in 1742 with 0° marked at the boiling point of water and 100° at its freezing point — an inversion that placed warm temperatures at low numbers and cold at high. Celsius's choice was deliberate: an inverted scale avoided negative readings during the Swedish winter, when temperatures regularly dropped below the freezing point of water but rarely above its boiling point. The scale was used in this inverted form during Celsius's lifetime and on the thermometers built at Uppsala under his direction. Celsius died of tuberculosis in 1744, two years after publishing the scale, and within a year of his death the inversion had been reversed by his colleagues at Uppsala. The reversal is conventionally credited to the botanist Carl Linnaeus in correspondence dated December 1745, although the Swedish instrument maker Daniel Ekström and the astronomer Mårten Strömer have both been put forward as alternative or co-authors of the change. The reversed scale, with 0° at the freezing point of water and 100° at its boiling point, was the form that spread through European science across the second half of the eighteenth century. The name "centigrade" — from the Latin centum gradus, "a hundred steps" — was the dominant English term for the scale into the mid-twentieth century. The 9th General Conference on Weights and Measures (CGPM) renamed the scale "Celsius" in 1948, partly to honour the original author and partly to avoid confusion with the centesimal grade (gon, gradian — 1/100 of a right angle) used in French surveying. The 10th CGPM in 1954 anchored the scale to the triple point of water at exactly 273.16 K (0.01 °C), and the 2019 SI redefinition tied the kelvin — and transitively the Celsius scale — to the Boltzmann constant fixed at exactly 1.380649 × 10⁻²³ J/K.

Global weather reporting is the Celsius scale's single largest public-facing domain. Every national meteorological service except the US National Weather Service reports temperature in degrees Celsius: the UK Met Office, Météo-France, the Deutscher Wetterdienst, the Japan Meteorological Agency, the China Meteorological Administration, the Australian Bureau of Meteorology and the World Meteorological Organization (WMO) all denominate surface-air-temperature observations and forecasts in °C. The WMO's Manual on Codes (WMO-No. 306) specifies Celsius as the international meteorological standard for SYNOP, METAR, TAF and upper-air radiosonde reports, and even US-domestic aviation weather reports use Celsius for terminal aerodrome forecasts (TAFs) and METARs while the same airport's public-facing weather page reports in Fahrenheit. Medical practice worldwide uses Celsius for body temperature. The WHO's 2008 Pocket Book of Hospital Care for Children, the British National Formulary, the European Medicines Agency clinical guidelines and clinical-laboratory norms across the world denominate normal core body temperature at 37.0 °C, with thresholds at 38.0 °C (low-grade fever), 39.0 °C (significant fever) and 40.0 °C (medical emergency in adults, often life-threatening in infants). Even US clinical practice has been moving toward Celsius for inpatient charting since the early 2000s, although outpatient consumer thermometers continue to display Fahrenheit on the US-domestic retail market. WHO Cold Chain handling of vaccines specifies storage in degrees Celsius (2 to 8 °C standard refrigeration; −25 to −15 °C for frozen mRNA vaccines). European, Asian and Australian cooking: domestic ovens, commercial bakeries and food-safety regulators denominate temperatures in °C. EU Regulation (EC) No 178/2002 on food safety, and the UK Food Standards Agency's Cooking Temperatures guidance, both denominate cooking and holding temperatures in Celsius (cook poultry to 75 °C, hold hot food above 63 °C, cold-chain food below 8 °C). UK cookery shows occasional historical "gas mark" references — a parallel scale running gas mark 1/4 ≈ 110 °C through gas mark 9 ≈ 240 °C, inherited from pre-decimal British gas-cooker dial markings — but modern UK recipes give Celsius as primary. HVAC and building services: ASHRAE Standard 55 (Thermal Environmental Conditions for Human Occupancy) specifies the comfortable indoor air-temperature range as 20–25 °C in winter and 23–27 °C in summer, the values that underlie the BREEAM (UK), LEED (international metric specs) and Passivhaus building-certification schedules. Domestic thermostats in metric countries (Honeywell, Nest, Tado, Hive in EU/UK markets) display in °C by default, with 18–22 °C the residential heating setpoint range. Industrial process control: the IEC 60584 thermocouple standard, the ISO 17025 calibration-laboratory accreditation framework and most national-standard reference thermometers calibrate in Celsius. Pharmaceutical cold-chain logistics under WHO Pre-Qualification (PQ) standards specify transport temperatures in °C, with deviations triggering regulatory reporting. Power-station condenser water, refining process streams and food-processing pasteurisation cycles are all denominated in degrees Celsius outside US-domestic facilities.

The kelvin (K) is the SI base unit of thermodynamic temperature, defined since 20 May 2019 by fixing the numerical value of the Boltzmann constant k at exactly 1.380649 × 10⁻²³ when expressed in J/K (which is kg·m²·s⁻²·K⁻¹). Because the joule, kilogram, metre and second appearing in that expression are themselves anchored to fixed constants of nature (the speed of light c, the caesium-133 hyperfine transition frequency Δν_Cs and the Planck constant h), the kelvin rides transitively on those constants and can be realised in any sufficiently equipped laboratory without reference to any specific physical substance. The kelvin is the only temperature scale that begins at absolute zero (0 K = −273.15 °C = −459.67 °F), the temperature at which all thermal motion of particles ceases — a state that the third law of thermodynamics establishes can be approached but not reached. Conversion to Celsius is by simple offset: T/K = t/°C + 273.15, with no multiplicative factor. The unit name "kelvin" is written lowercase except at the start of a sentence; the symbol "K" is uppercase but takes no degree sign (a temperature of "300 K", not "300 °K"; a temperature change of "5 K", not "5 degrees kelvin"). These conventions, set by the 13th CGPM in 1967 and reaffirmed by the 26th CGPM in 2018, are routinely violated in non-scientific writing but are mandatory in any context governed by SI conformity rules.

The kelvin scale began as a thought experiment in absolute thermodynamics rather than as a practical measuring system. William Thomson — later Baron Kelvin of Largs, the title taken in 1892 from the River Kelvin that flowed past his laboratory at the University of Glasgow — published "On an Absolute Thermometric Scale" in the Philosophical Magazine in 1848, proposing a scale whose zero point corresponded to the absolute absence of thermal energy rather than to any conventional reference like the freezing point of water. Thomson derived the scale from Sadi Carnot's 1824 theoretical analysis of ideal heat engines, which implied a thermodynamic limit below which no further heat could be extracted from any substance. The unit retained the name "degree absolute" or "degree Kelvin" through the first half of the twentieth century. The 10th CGPM formally named the unit "degree Kelvin" with the symbol °K in 1954, anchoring the definition to the triple point of water at exactly 273.16 K — the unique thermodynamic state at which solid, liquid and gaseous water coexist in stable equilibrium. The 13th CGPM in 1967 made two changes that survive in modern usage: the "degree" was dropped from the unit's name (it became simply "kelvin", lowercase, with the symbol "K" without a degree sign), and the kelvin was confirmed as the SI base unit for thermodynamic temperature. The 2019 SI redefinition cut the kelvin's last remaining dependence on a specific material property by fixing the Boltzmann constant k at exactly 1.380649 × 10⁻²³ J/K, parallel to the simultaneous untethering of the kilogram from the International Prototype. The triple point of water — which had been the definitional anchor since 1954 — became a useful realisation rather than a definition, reproducible to within experimental uncertainty rather than exact by definition.

Cryogenics and superconductivity research are the kelvin's most prominent scientific domains. Critical-temperature (Tc) values for superconducting materials are universally tabulated in kelvin: niobium-titanium at 9.2 K (the workhorse alloy in MRI-machine and particle-accelerator superconducting magnets), niobium-tin at 18.3 K, magnesium diboride at 39 K, the YBCO cuprate at about 93 K (the first material to exceed liquid-nitrogen boiling at 77 K), and the more recent hydride superconductors reaching 250–280 K under extreme pressure. Cold-atom physics laboratories operate routinely at microkelvin and nanokelvin temperatures: laser-cooling and evaporative-cooling techniques have produced Bose-Einstein condensates below 1 nK, and the lowest reliably reported laboratory temperature is approximately 38 picokelvin, achieved at the University of Bremen drop-tower facility in 2021 in microgravity rubidium-atom experiments. Cosmology and astrophysics: the cosmic microwave background (CMB) — the relic radiation from the recombination epoch about 380,000 years after the Big Bang — has a measured blackbody temperature of 2.72548 K, with anisotropies at the part-in-100,000 level mapped by the COBE, WMAP and Planck satellite missions. Stellar effective temperatures are denominated in kelvin (the Sun at 5,778 K, Sirius at 9,940 K, Betelgeuse at about 3,500 K), and the temperature axis of the Hertzsprung-Russell diagram — astronomy's central tool for stellar classification — runs in kelvin from about 2,500 K (M-class red dwarfs) to over 50,000 K (O-class blue giants). Colour temperature in photography, lighting and display: the kelvin scale is the universal unit for the apparent colour of a black-body radiator, with the CIE D65 standard white point at about 6,504 K used as the reference for sRGB monitor calibration, paper-printing standards and most consumer-display colour management. Tungsten incandescent lighting runs at about 2,700–3,200 K (warm yellow-white), noon sunlight at about 5,500 K, overcast daylight at 6,500–7,500 K, and clear north-sky shade at 9,000–11,000 K. Photography white-balance settings on every digital camera (Canon, Nikon, Sony, Fujifilm) are graduated in kelvin, and professional video lighting rigs (Aputure, ARRI, Litepanels) advertise colour-temperature specifications in K to two-significant-figure precision. Materials science and engineering: phase diagrams for metals, ceramics and polymer systems are conventionally plotted with temperature on the kelvin axis. ASM International's metallurgical reference handbooks, the NIST WebBook for thermophysical properties and the major engineering textbooks (Callister's Materials Science and Engineering, Reed-Hill's Physical Metallurgy Principles) all denominate phase-transition temperatures in K. Thermodynamic process calculations — Carnot-cycle efficiencies, ideal-gas-law substitutions, entropy and enthalpy tabulations — must use kelvin rather than Celsius because the underlying equations require absolute temperature; an engineer using Celsius in PV = nRT or Δs = c·ln(T₂/T₁) makes a quantitative error proportional to the 273.15 K offset.