# Kelvin

Kelvin temperature conversion formulae
from Kelvin to Kelvin
Template:Temperature/C/link [°C] = [K] − 273.15 [K] = [°C] + 273.15
Fahrenheit Template:Temperature/F/K Template:Temperature/K/F
Rankine Template:Temperature/R/K Template:Temperature/K/R
For temperature intervals rather than specific temperatures,
Template:Temperature/K/int
Comparisons among various temperature scales

The kelvin (symbol: K) is a unit increment of temperature and is one of the seven SI base units. The Kelvin scale is a thermodynamic (absolute) temperature scale where absolute zero, the theoretical absence of all thermal energy, is zero (0 K).

The Kelvin scale and the kelvin are named after the Northern Irish physicist and engineer William Thomson, 1st Baron Kelvin (1824-1907), who wrote of the need for an “absolute thermometric scale”.

## Definition of kelvin

The kelvin unit and its scale, by international agreement, are defined by two points: absolute zero, and the triple point of Vienna Standard Mean Ocean Water (VSMOW).[1] This definition also precisely relates the Kelvin scale to the Celsius scale. Absolute zero—the temperature at which nothing could be colder and no heat energy remains in a substance—is defined as being precisely 0 K and −273.15 °C. The triple point of water is defined as being precisely 273.16 K and 0.01 °C. This definition does three things:

1. It fixes the magnitude of the kelvin unit as being precisely 1 part in 273.16 parts the difference between absolute zero and the triple point of water;
2. It establishes that one kelvin has precisely the same magnitude as a one-degree increment on the Celsius scale; and
3. It establishes the difference between the two scales’ null points as being precisely 273.15 kelvins (0 K = −273.15 °C and 273.16 K = 0.01 °C). Temperatures in kelvin can be converted to other units per the table at top right.

### Temperature equivalents

 Kelvin Celsius Fahrenheit Absolute zero (precisely, by definition) 0 K −273.15 °C −459.67 °F Melting point of ice 273.15 K 0 °C 32 °F Water’s triple point (precisely, by definition) 273.16 K 0.01 °C 32.018 °F Water’s boiling point 373.1339 K 99.9839 °C 211.9710 °F

For Vienna Standard Mean Ocean Water (VSMOW) at one standard atmosphere (101.325 kPa) when calibrated solely per the two-point definition of thermodynamic temperature. Older definitions of the Celsius scale once defined the boiling point of water under one standard atmosphere as being precisely 100 °C. However, the current definition results in a boiling point that is actually 16.1 mK less. For more about the actual boiling point of water, see VSMOW in temperature measurement.

### SI prefixes

SI multiples for kelvin (K)

Submultiples Multiples
Value Symbol Name Value Symbol Name
10–1 K dK decikelvin 101 K daK decakelvin
10–2 K cK centikelvin 102 K hK hectokelvin
10–3 K mK millikelvin 103 K kK kilokelvin
10–6 K µK microkelvin 106 K MK megakelvin
10–9 K nK nanokelvin 109 K GK gigakelvin
10–12 K pK picokelvin 1012 K TK terakelvin
10–15 K fK femtokelvin 1015 K PK petakelvin
10–18 K aK attokelvin 1018 K EK exakelvin
10–21 K zK zeptokelvin 1021 K ZK zettakelvin
10–24 K yK yoctokelvin 1024 K YK yottakelvin

## Typographical and usage conventions

### Uppercase/lowercase, plural form usage, and written conventions

When reference is made to the unit kelvin (either a specific temperature or a temperature interval), kelvin is always spelled with a lowercase k unless it is the first word in a sentence. When reference is made to the "Kelvin scale", the word "kelvin"—which is normally a noun—functions adjectivally to modify the noun "scale" and is capitalized.

Until the 13th General Conference on Weights and Measures (CGPM) in 1967-1968, the unit kelvin was called a "degree", the same as with the other temperature scales at the time. It was distinguished from the other scales with either the adjective suffix "Kelvin" ("degree Kelvin") or with "absolute" ("degree absolute") and its symbol was °K. Note that the latter (degree absolute), which was the unit’s official name from 1948 until 1954, was rather ambiguous since it could also be interpreted as referring to the Rankine scale. Before the 13th CGPM, the plural forms were "degrees Kelvin" or "degrees absolute". The 13th CGPM changed the name to simply "kelvin" (symbol K).[2] The omission of "degree" indicates that it is not relative to an arbitrary reference point such as the Celsius and Fahrenheit scales, but rather an absolute unit of measure which can be manipulated algebraically (e.g. multiply by 2 to indicate twice the amount of heat).

### Temperatures and intervals

Because the kelvin is an individual unit of measure, it is particularly well-suited for expressing temperature intervals: differences between temperatures or their uncertainties (e.g., “Agar exhibited a melting point hysteresis of 25 kelvins.” and “The uncertainty was 10 millikelvins.”). Of course, the kelvin is also used to express specific temperatures along its scale (e.g. “Gallium melts at 302.9146 kelvin”).

One disadvantage of the kelvin is that intervals and specific temperatures on the Kelvin scale use exactly the same symbol (e.g., “Agar exhibited a melting point hysteresis of 25 K,” and “The triple point of hydrogen is 13.8033 K”).

### Formatting and typestyle for the K symbol

The kelvin symbol is always a roman, non-italic capital K. In the SI naming convention, all symbols named after a person are capitalized; in the case of the kelvin, capitalizing also distinguishes the symbol from the SI prefix “kilo”, which has the lowercase k as its symbol. The admonition against italicizing the symbol K applies to all SI unit symbols; only symbols for variables and constants (e.g. P = pressure, and c = 299,792,458 m/s) are italicized in scientific and engineering papers. As with most other SI unit symbols (angle symbols, e.g. 45° 3′ 4″, are the exception) there is a space between the numeric value and the kelvin symbol (e.g. “99.987 K”).[3][4]

### The special Unicode kelvin sign

Unicode, which is an industry standard designed to allow text and symbols from all of the writing systems of the world to be consistently represented and manipulated by computers, includes a special “kelvin sign” at U+212A. Its appearance is similar to an ordinary uppercase K. To better see the difference between the two, below in maroon text is the kelvin character followed immediately by a simple uppercase K:

KK

When viewed on computers that properly support Unicode, the above line appears as follows (size may vary):

Depending on the operating system, Web browser, and the default font, the “K” in the Unicode character may be narrower and slightly taller than a plain uppercase K; precisely the opposite may be true on other platforms. However, there will usually be a discernible difference between the two. If the computer being used to view a particular Web page doesn’t support the Unicode kelvin sign character (`&#x212A;`), it may be canonically decomposed by the browser into U+004B (uppercase K) and the two would appear identical. In still other computers, the kelvin symbol is mapped incorrectly and produces an odd character.

### Mixed use of Kelvin and Celsius scales in technical articles

In science and in engineering, the Celsius scale and the kelvin are often used simultaneously in the same article (e.g. “…its measured value was 0.01023 °C with an uncertainty of 70 µK…”). This practice is permissible because the degree Celsius is a special name for the kelvin for use in expressing Celsius temperatures and the magnitude of the degree Celsius is precisely equal to that of the kelvin.[5] Notwithstanding the official endorsement provided by Resolution 3 of the 13th CGPM, states “a temperature interval may also be expressed in degrees Celsius,” the practice of simultaneously using both “°C” and “K” remains widespread throughout the scientific world as the use of SI prefixed forms of the degree Celsius (such as “µ°C” or “microdegrees Celsius”) to express a temperature interval has not been well-adopted.[6]

## Color temperature

The kelvin is often used in the measure of the color temperature of light sources. Color temperature is based upon the principle that a black body radiator emits light whose color depends on the temperature of the radiator. Black bodies with temperatures below about 4000 K appear reddish whereas those above about 7500 K appear bluish. Color temperature is important in the fields of image projection and photography where a color temperature of approximately 5500 K is required to match “daylight” film emulsions. In astronomy, the stellar classification of stars and their place on the Hertzsprung-Russell diagram are based, in part, upon their surface temperature. The Sun, for instance, has an effective photosphere temperature of 5778 K.

## History of the Kelvin scale

Below are some historic milestones in the development of the Kelvin scale and its unit increment, the kelvin. For more on the history of thermodynamic temperature, see Thermodynamic temperature: History of thermodynamic temperature.

• 1848: Lord Kelvin (William Thomson), wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby “infinite cold” (absolute zero) was the scale’s null point, and which used the degree Celsius for its unit increment. Thomson calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time.[7] This absolute scale is known today as the Kelvin thermodynamic temperature scale. It’s noteworthy that Thomson’s value of “−273” was actually derived from 0.00366, which was the accepted expansion coefficient of gas per degree Celsius relative to the ice point. The inverse of −0.00366 expressed to five significant digits is −273.22 °C which is remarkably close to the true value of −273.15 °C.
• 1954: Resolution 3 of the 10th CGPM gave the Kelvin scale its modern definition by designating the triple point of water as its second defining point and assigned its temperature to precisely “273.16 degrees Kelvin.”[8]
• 1967/1968: Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature “kelvin”, symbol K, replacing “degree absolute”, symbol °K.[6] Further, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM also held in Resolution 4 that “The kelvin, unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.”[9]
• 2005: The Comité International des Poids et Mesures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the Kelvin thermodynamic temperature scale would refer to water having an isotopic composition defined as being precisely equal to the nominal specification of VSMOW water.[1]

7. Thomson, William (1848). "On an Absolute Thermometric Scale". Philosophical Magazine. Retrieved 2008-02-06. Unknown parameter `|month=` ignored (help)