Kelvin

For other uses, see Kelvin (disambiguation).

Kelvin temperature conversion formulas

To find	From	Formula
Celsius	kelvin	°C = K − 273.18
kelvin	Celsius	K = °C + 273.18
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	kelvin	eV ≈ 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 (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 coldest possible temperature—is defined as being equivalent to zero kelvin (0 K).

The Kelvin scale and the kelvin are named after the Irish-born 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 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 minimal 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 table below.

	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 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.

Submultiples				Multiples
Factor	Name	Symbol		Factor	Name	Symbol
10−1	decikelvin	dK		101	decakelvin	daK
10−2	centikelvin	cK		102	hectokelvin	hK
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
10−15	femtokelvin	fK		1015	petakelvin	PK
10−18	attokelvin	aK		1018	exakelvin	EK
10−21	zeptokelvin	zK		1021	zettakelvin	ZK
10−24	yoctokelvin	yK		1024	yottakelvin	YK

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” (like “Georgia peach”) 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”). Note that the latter, 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.” After the name change to simply “kelvin,” the plural form became “kelvins.” . As a consequence, when abbreviated the unit kelvin is represented simply by "K" and never with the degree symbol "^o".

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”).

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 K 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 (K), 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.

Why technical articles use a mix of Kelvin and Celsius scales

In science (especially) 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. Notwithstanding the official endorsement provided by decision #3 of Resolution 3 of the 13th CGPM, which stated “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 “millidegrees Celsius”) to express a temperature interval has not been well-adopted.

This practice should be avoided for literature directed to lower-level technical fields and in non-technical articles intended for the general public where both the kelvin and its symbol, K, are not well recognized and could be confusing.

Colour temperature

The kelvin is often used in the measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light whose colour 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. Colour temperature is important in the fields of image projection and photography where a colour 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: 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 renamed the unit increment of thermodynamic temperature “kelvin”, symbol K, replacing “degree absolute”, symbol °K. Further, feeling it useful to more explicitly define the magnitude of the unit increment, the 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.

See also

• Absolute zero
• Celsius
• Fahrenheit
• Heat

• ITS-90
• Rankine
• Thermodynamic temperature
• Triple point

External links

• BIPM brochure on the kelvin
• Barry N. Taylor, Guide for the Use of the International System of Units (SI), Washington, D.C.:Government Printing Office, 1995 (html version, pdf version)