# Kelvin

Kelvin temperature conversion formulas
To find From Formula
Celsius kelvin°C = K − 273.15
kelvin Celsius K = °C + 273.15
Rankine kelvin°R = K × 1.8
kelvin Rankine K = °R ÷ 1.8
Fahrenheit kelvin°F = (K × 1.8) − 459.67
kelvin Fahrenheit K = (°F + 459.67) ÷ 1.8
electronvolts kelvineV ≈ K ÷ 11,604.5
kelvin electronvolts K ≈ eV × 11,604.5
For temperature intervals rather than specific temperatures,
1 kelvin = 1 °C
and
1 kelvin = 1.8 °R
Comparisons among various temperature scales
Conversion calculator for units of temperature

The Kelvin scale is a thermodynamic (absolute) temperature scale where absolute zero—the lowest possible temperature where nothing could be colder and no heat energy remains in a substance—is defined as zero kelvin (0 K). The unit increment of the Kelvin scale is the kelvin (symbol: K), which is the SI unit of temperature and is one of the seven SI base units.

The Kelvin scale is named after Irish physicist and engineer William Thomson, 1st Baron Kelvin (1824–1907).

##  Definition of the kelvin

The unit “kelvin” and its scale by international agreement, defined by two points: absolute zero, and the triple point of specially prepared (VSMOW) water. 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.

Some key temperatures relating temperatures on the Kelvin and Celsius scales are shown in the below table.

 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 A 373.1339 K 99.9839 °C 211.9710 °F

A For Vienna Standard Mean Ocean Water 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 water in temperature measurement.

##  SI prefixed forms of kelvin

SI prefixes are often employed to denote decimal multiples and submultiples of the kelvin. The most commonly used factors of kelvin are listed below.<ref>The term “most commonly used” is based on those with more than 500 Google hits on the name.</ref>

 Submultiples Multiples Factor Name Symbol Factor Name Symbol 10−3 millikelvin mK 103 kilokelvin kK 10−6 microkelvin µK 106 megakelvin MK 10−9 nanokelvin nK 109 gigakelvin GK 10−12 picokelvin pK 1012 terakelvin TK

##  Typographical and usage conventions

##### Uppercase/lowercase and plural form usage

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, use an uppercase K.

Until the 13th General Conference on Weights and Measures (CGPM) in 1967-1968, this unit was called a degree just as other temperature degrees are, distinguished from other degrees with the adjective “Kelvin” in “degrees Kelvin,” or often as “degrees absolute” (which was more ambiguous, since it could also refer to degrees Rankine). When the units were degrees, the plural was formed by adding an “s” to degree and like other adjectives in English, the adjective identifying the scale was unchanged in the plural. After the name change, the plural of kelvin is “kelvins.”<ref>Webster's 11th Collegiate; NIST SP 811</ref> When reference is made to the “Kelvin scale,” the word “kelvin”—which is normally a noun—functions adjectivally to modify the noun “scale” (like “Georgia peach”) and is capitalized.

##### 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 both utilize the exact same symbol (e.g. “Agar exhibited a melting point hysteresis of 25 K,” and “The triple point of hydrogen is 13.8033 K”). Thus, wherever ambiguity might arise due to the dual use of the symbol K within a document, it is preferable to use the symbol for denoting temperatures and to express the intervals using the full unit name in its plural form, kelvins, (e.g. “The helium temperature was 650 mK… and our standard deviation in this set of experiments was 15 millikelvins.”)

##### Formatting and typestyle for the K symbol

The kelvin symbol is always a roman (non-italic) capital K since the lowercase version is the SI prefix for 1 × 103. 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”).<ref>For more information on conventions used in technical writing, see the informative SI Unit rules and style conventions by the NIST as well as the BIPM’s SI brochure: Subsection 5.3.3, Formatting the value of a quantity.</ref>

##### 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. One types `&#x212A;` when encoding this special kelvin character in a Web page. 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.

Accordingly, for Web use, it is better to use the simple uppercase K to represent the kelvin symbol so it can be properly viewed by the widest possible audience.

##  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: William Thomson, (1824 – 1907) also known as “Lord Kelvin,” 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. 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 four significant digits is −273.2 °C which is remarkably close to the true value of −273.15 °C.
• 1954: Resolution 3 of the 10th CGPM (Conférence Générale des Poids et Mesures, also known as the General Conference on Weights and Measures) gave the Kelvin scale its modern definition by choosing the triple point of water as its second defining point and assigned it a temperature of precisely 273.16 kelvin (what was actually written 273.16 “degrees Kelvin” at the time).
• 1967/1968: Resolution 3 of the 13th CGPM created the unit increment of thermodynamic temperature (as distinct from the scale) and gave it the name “kelvin”, symbol K, instead of “degree Kelvin”, symbol °K. In so doing, feeling it useful to explicitly define the magnitude of this new unit increment, 13th CGPM also decided in Resolution 4 that “The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.”
• 2005: The CIPM (Comité International des Poids et Mesures, also known as the International Committee for Weights and Measures) 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.

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