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Celsius temperature conversion formulas
To find From Formula
FahrenheitCelsius °F = (°C × 1.8) + 32
Celsius Fahrenheit °C = (°F − 32) ÷ 1.8
kelvinCelsiusK = °C + 273.15
Celsiuskelvin °C = K − 273.15
For temperature intervals rather than specific temperatures,
1 °C = 1 kelvin
1 °C = 1.8 °F
Comparisons among various temperature scales
Conversion calculator for units of temperature

Celsius is, or relates to, the Celsius temperature scale. Degrees Celsius (symbol: °C) refers to a specific temperature on the Celsius temperature scale. The degree Celsius is also a unit increment of temperature for use in indicating a temperature interval (a difference between two temperatures or an uncertainty). “Celsius” is named after the Swedish astronomer Anders Celsius (1701 – 1744), who first proposed a similar system two years before his death. 

Until 1954, 0 °C on the Celsius scale was defined as the melting point of ice and 100 °C was the boiling point of water under a pressure of one standard atmosphere. Today, the unit “degree Celsius” and the Celsius scale are, by international agreement, defined by two points: absolute zero, and the triple point of specially prepared (VSMOW) water. This new definition also precisely relates the Celsius scale to the Kelvin scale, which is the SI base unit of temperature (symbol: K). 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 degree Celsius 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 degree Celsius has precisely the same magnitude as a one kelvin; and 3) it establishes the difference between the two scales’ null points as being precisely 273.15 degrees Celsius (−273.15 °C = 0 K and 0.01 °C = 273.16 K).

Some key temperatures relating the Celsius scale to other temperature 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 The melting and boiling points of water below, as well as VSMOW water in temperature measurement.


[edit] History

Image:20050501 1315 2558-Bimetall-Zeigerthermometer.jpg
A thermometer calibrated in degrees Celsius. The blue zone denotes freezing temperatures.

In 1742, Anders Celsius (1701 – 1744) created a “backwards” version of the modern Celsius temperature scale whereby zero represented the boiling point of water and 100 represented the melting point of ice. In his paper Observations of two persistent degrees on a thermometer, he recounted his experiments showing that ice’s melting point was effectively unaffected by pressure. He also determined with remarkable precision how water’s boiling point varied as a function of atmospheric pressure. He proposed that zero on his temperature scale (water’s boiling point) would be calibrated at the mean barometric pressure at mean sea level. This pressure is known as one standard atmosphere. In 1954, Resolution 4 of the 10th CGPM (the General Conference on Weights and Measures) established internationally that one standard atmosphere was a pressure equivalent to 1,013,250 dynes per cm2 (101.325 kPa). 

In 1744, coincident with the death of Anders Celsius, the famous botanist Carolus Linnaeus (1707 – 1778) effectively reversed <ref>Citations: Thermodynamics-information.net, A Brief History of Temperature Measurement and; Uppsala University (Sweden), Linnaeus’ thermometer</ref> Celsius’s scale upon receipt of his first thermometer featuring a scale where zero represented the melting point of ice and 100 represented water’s boiling point. His custom-made “linnaeus-thermometer,” for use in his greenhouses, was made by Daniel Ekström, Sweden’s leading maker of scientific instruments at the time. As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale;</sup><ref>Citation for Daniel Ekström, Mårten Strömer, Christian of Lyons: The Physics Hypertextbook, Temperature; citation for Christian of Lyons: Le Moyne College, Glossary, (Celsius scale); citation for Linnaeus’ connection with Pehr Elvius and Daniel Ekström: Uppsala University (Sweden), Linnaeus’ thermometer; general citation: The Uppsala Astronomical Observatory, History of the Celsius temperature scale</ref> among them were Pehr Elvius, the secretary of the Royal Swedish Academy of Sciences (which had an instrument workshop) and with whom Linnaeus had been corresponding; Christian of Lyons; Daniel Ekström, the Swedish instrument maker; and Mårten Strömer (1707 – 1770) who had studied astronomy under Anders Celsius.

The first known document<ref>Citations: University of Wisconsin–Madison, Linnæus & his Garden and; Uppsala University, Linnaeus’ thermometer</ref> reporting temperatures in this modern “forward” Celsius scale is the paper Hortus Upsaliensis dated 16 December 1745 that Linnaeus wrote to a student of his, Samuel Nauclér. In it, Linnaeus recounted the temperatures inside the orangery at the Botanical Garden of Uppsala University:

“…since the caldarium (the hot part of the greenhouse) by the angle
of the windows, merely from the rays of the sun, obtains such heat
that the thermometer often reaches 30 degrees, although the keen
gardener usually takes care not to let it rise to more than 20 to 25
degrees, and in winter not under 15 degrees…”

For the next 204 years, the scientific and thermometry communities world-wide referred to this scale as the “centigrade scale.” Temperatures on the centigrade scale were often reported simply as “degrees” or, when greater specificity was desired, “degrees centigrade.” The symbol for temperature values on this scale was °C (in several formats over the years). Because the term “centigrade” was also the French-language name for a unit of angular measurement (one-hundredth of a right angle) and had a similar connotation in other languages, the term “centesimal degree” was used when very precise, unambiguous language was required by international standards bodies such as the Bureau international des poids et mesures (BIPM). The 9th CGPM (Conférence générale des poids et mesures) and the CIPM (Comité international des poids et mesures) formally adopted “degree Celsius” (symbol: °C) in 1948.<ref>According to The Oxford English Dictionary (OED), the term “Celsius’s thermometer” had been used at least as early as 1797. Further, the term “The Celsius or Centigrade thermometer” was again used in reference to a particular type of thermometer at least as early as 1850. The OED also cites this 1928 reporting of a temperature: “My altitude was about 5,800 metres, the temperature was 28° Celsius.” However, dictionaries seek to find the earliest use of a word or term and are not a useful resource as regards the terminology used throughout the history of science. According to several writings of Dr. Terry Quinn CBE FRS, Director of the BIPM (1988 – 2004), including Temperature Scales from the early days of thermometry to the 21st century (148 kB PDF, here) as well as Temperature (2nd Edition / 1990 / Academic Press / 0125696817), the term Celsius in connection with the centigrade scale was not used whatsoever by the scientific or thermometry communities until after the CIPM and CGPM adopted the term in 1948. The BIPM wasn’t even aware that “degree Celsius” was in sporadic, non-scientific use before that time. It’s also noteworthy that the twelve-volume, 1933 edition of OED didn’t even have a listing for the word Celsius (but did have listings for both centigrade and centesimal in the context of temperature measurement). The 1948 adoption of Celsius accomplished three objectives:

1) All common temperature scales would have their units named after someone closely associated with them; namely, Kelvin, Celsius, Fahrenheit, Réaumur and Rankine.
2) Notwithstanding the important contribution of Linnaeus who gave the Celsius scale its modern form, Celsius’s name was the obvious choice because it began with the letter C. Thus, the symbol °C that for centuries had been used in association with the name centigrade could continue to be used and would simultaneously inherit an intuitive association with the new name.
3) The new name eliminated the ambiguity of the term “centigrade,” freeing it to refer exclusively to the French-language name for the unit of angular measurement.</ref> For lay-people worldwide — including school textbooks — the full transition from centigrade to Celsius required nearly two decades after this formal adoption.

[edit] Formatting

The “degree Celsius” is the only SI unit whose full unit name in English contains an uppercase letter.

The word “degree” may be abbreviated as “deg”. Accordingly, the following are permissible ways to express degree Celsius: singular / (plural)

degree Celsius / (degrees Celsius)
deg Celsius / (same)
degree C / (degrees C)
deg C / (same)
°C / (same)

As with most other unit symbols and all the temperature symbols, a space is placed between the numeric value and the °C symbol; e.g., “23 °C” (not “23°C” or “23° C”). Only the unit symbols for angles are placed immediately after the numeric value without an intervening space; e.g., “a 90° turn”.<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>

[edit] Temperatures and intervals

The degree Celsius is a special name for the kelvin for use in expressing Celsius temperatures.<ref>Note (e) of SI Brochure, Section, 2.2.2, Table 3</ref> The degree Celsius is also subject to the same rules as the kelvin with regard to the use of its unit name and symbol. Thus, besides expressing specific temperatures along its scale (e.g. “Gallium melts at 29.7646 °C” and “The temperature outside is 23 degrees Celsius”), the degree Celsius is also suitable for expressing temperature intervals: differences between temperatures or their uncertainties (e.g. “The output of the heat exchanger is hotter by 40 degrees Celsius,” and “Our standard uncertainty is ±3 °C”). Because of this dual usage, one must not rely upon the unit name or its symbol to denote that a quantity is a temperature interval; it must be unambiguous through context or explicit statement that the quantity is an interval.<ref>In 1948, Resolution 7 of the 9th CGPM stated, “To indicate a temperature interval or difference, rather than a temperature, the word ‘degree’ in full, or the abbreviation ‘deg’ must be used.” This resolution was abrogated in 1967/1968 by Resolution 3 of the 13th CGPM which stated that [“The names "degree Kelvin" and "degree", the symbols "°K" and "deg" and the rules for their use given in Resolution 7 of the 9th CGPM (1948),] …and the designation of the unit to express an interval or a difference of temperatures are abrogated, but the usages which derive from these decisions remain permissible for the time being.” Consequently, there is now wide freedom in usage regarding how to indicate a temperature interval. The most important thing is that one’s intention must be clear and the basic rule of the SI must be followed; namely that the unit name or its symbol must not be relied upon to indicate the nature of the quantity. Thus, if a temperature interval is, say, 10 K or 10 °C (which may be written 10 kelvins or 10 degrees Celsius), it must be unambiguous through obvious context or explicit statement that the quantity is an interval. Rules governing the expressing of temperatures and intervals are covered in the BIPM’s SI Brochure, 8th edition (1.4 MB PDF, here).</ref>

In science (especially) and in engineering, the Celsius and Kelvin scales are often used simultaneously in the same article (e.g. “…its measured value was 0.01023 °C with an uncertainty of 70 µK…”) Notwithstanding the official endorsements of Resolution 3 of the 13th CGPM (1967/68)] and Resolution 7 of the 9th CGPM (1948), the practice of simultaneously using both “°C” and “K” remains widespread throughout the technical world as the use of SI prefixed forms such as “µ°C” or “millidegrees Celsius” to express a temperature interval has not been well-adopted.

[edit] The melting and boiling points of water

The effect of defining the Celsius scale at the triple point of VSMOW water (273.16 kelvins and 0.01 °C), and at absolute zero (zero kelvins and −273.15 °C), is that both the melting and boiling points of water under one standard atmosphere (1013.25 mbar) are no longer the defining points for the Celsius scale. In 1948 when the 9th General Conference on Weights and Measures (CGPM) in Resolution 3 first considered using the triple point of water as a defining point, the triple point was so close to being 0.01 °C greater than water’s known melting point, it was simply defined as precisely 0.01 °C. However, current measurements show that the triple and melting points of VSMOW water are actually very slightly (<0.001 °C) greater than 0.01 °C apart. Thus, the actual melting point of ice is very slightly (less than a thousandth of a degree) below 0 °C. Also, defining water’s triple point at 273.16 K precisely defined the magnitude of each 1 °C increment in terms of the absolute thermodynamic temperature scale (referencing absolute zero). Now decoupled from the actual boiling point of water, the value “100 °C” is hotter than 0 °C — in absolute terms — by a factor of precisely <math>\textstyle\frac{373.15}{273.15}</math> (approximately 36.61% thermodynamically hotter). When adhering strictly to the two-point definition for calibration, the boiling point of VSMOW water under one standard atmosphere of pressure is actually 373.1339 K (99.9839 °C). When calibrated to ITS-90 (a calibration standard comprising many definition points and commonly used for high-precision instrumentation), the boiling point of VSMOW water is slightly less, about 99.974 °C.<ref>Citation: London South Bank University, Water Structure and Behavior, notes c1 and c2</ref>

This boiling–point difference of 16.1 millikelvins (thousandths of a degree Celsius) between the Celsius scale’s original definition and the current one (based on absolute zero and the triple point) has little practical meaning in real life because water’s boiling point is extremely sensitive to variations in barometric pressure. For example, an altitude change of only 28 cm (11 inches) causes water’s boiling point to change by one millikelvin.

[edit] World-wide adoption

Throughout the world (except for the U.S.), the Celsius scale is used for most temperature measuring purposes. The entire scientific world (the U.S. included) uses the Celsius scale. Many engineering fields in the U.S., especially high-tech ones, also use the Celsius scale. The bulk of the U.S. however, (its lay people, industry, meteorology, and government) relies upon the Fahrenheit scale. Jamaica is currently converting to Celsius.

[edit] The special Unicode °C character

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 “°C” character at U+2103. One types  &#x2103; when encoding this special character in a Web page. Its appearance is similar to the one synthesized by individually typing its two components (°) and (C). To better see the difference between the two, below in brown text is the degree Celsius character followed immediately by the two-component version:


When viewed on computers that properly support and map Unicode, the above line may be similar to the line below (size may vary):

Image:Unicode °C comparison.jpg

Depending on the operating system, Web browser, and the default font, the “C” in the Unicode character may be narrower and slightly taller than a plain uppercase C; precisely the opposite may be true on other platforms. However, there will usually be a discernible difference between the two.

[edit] See also

[edit] Notes

<references />

[edit] External links

Temperature scales
Celsius Fahrenheit Kelvin
Delisle Leiden Newton Rankine Réaumur Rømer
Conversion formulas

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