Celsius temperature conversion formulae from Celsius to Celsius Fahrenheit [°F] = [°C] × 9⁄5 + 32 [°C] = ([°F] − 32) × 5⁄9 Kelvin [K] = [°C] + 273.15 [°C] = [K] − 273.15 Rankine [°R] = ([°C] + 273.15) × 9⁄5 [°C] = ([°R] − 491.67) × 5⁄9 For temperature intervals rather than specific temperatures,
1 °C = 1 K = 1.8 °F = 1.8 °R
Comparisons among various temperature scales
Celsius (formerly centigrade) is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale two years before his death. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale as well as a unit to indicate a temperature interval, a difference between two temperatures or an uncertainty. The unit was known until 1948 as centigrade from the Latin "centum" translated as 100 and "gradus" translated as "steps".
From 1744 until 1954, 0 °C was defined as the freezing point of water and 100 °C was defined as the boiling point of water, both at a pressure of one standard atmosphere with mercury being the working material. Although these defining correlations are commonly taught in schools today, by international agreement the unit "degree Celsius" and the Celsius scale are currently defined by two different points: absolute zero, and the triple point of VSMOW (specially prepared water). This definition also precisely relates the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature (symbol: K). Absolute zero, the hypothetical but unattainable temperature at which matter exhibits zero entropy, is defined as being precisely 0 K and −273.15 °C. The temperature value of the triple point of water is defined as being precisely 273.16 K and 0.01 °C.
This definition fixes the magnitude of both the degree Celsius and the kelvin as precisely 1 part in 273.16 (approximately 0.00366) of the difference between absolute zero and the triple point of water. Thus, it sets the magnitude of one degree Celsius and that of one kelvin as exactly the same. Additionally, it establishes the difference between the two scales' null points as being precisely 273.15 degrees Celsius (−273.15 °C = 0 K and 0 °C = 273.15 K).
In 1742 Swedish astronomer Anders Celsius (1701–1744) originally created a "reversed" version of the modern Celsius temperature scale wherein zero represented the boiling point of water and one hundred represented the freezing point of water. In his paper Observations of two persistent degrees on a thermometer, he recounted his experiments showing that the melting point of ice is essentially unaffected by pressure. He also determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure. He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level. This pressure is known as one standard atmosphere. The BIPM's 10th General Conference on Weights and Measures (CGPM) later defined one standard atmosphere to equal precisely 1013250dynes per square centimeter (101.325kPa).
In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carolus Linnaeus (1707–1778) reversed Celsius's scale upon receipt of his first thermometer featuring a scale where zero represented the melting point of ice and 100 represented the 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 and whose workshop was located in the basement of the Stockholm observatory. As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale; 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 instrument maker; and Mårten Strömer (1707–1770) who had studied astronomy under Anders Celsius.
The first known document 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 ..."
Centigrade and Celsius
For the last 204 years, the scientific and thermometry communities worldwide 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, as degrees centigrade. The symbol for temperature values on this scale was °C.
Because the term centigrade was also the Spanish and French language name for a unit of angular measurement (1/10,000 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.
For scientific use, "Celsius" is the term usually used with "centigrade" otherwise continuing to be in common use.
Some key temperatures relating the Celsius scale to other temperature scales are shown in the table below.
Key scale relations Kelvin Celsius Fahrenheit Absolute zero
(precisely, by definition)
0 K −273.15 °C −459.67 °F Boiling Point of liquid nitrogen 77.4 K −195.8 °C −320.3 °F Melting Point of dry ice. 195.1 K −78 °C −108.4 °F Melting point of H2O (purified ice)
273.15 K 0 °C 32 °F Water's triple point
(precisely, by definition)
273.16 K 0.01 °C 32.018 °F Normal human body temperature 310.15 K 37.0 °C 98.6 °F Water's boiling point at 1 atm (101.325 kPa)
(approximate: see Boiling point)
373.1339 K 99.9839 °C 211.971 °F
Name and symbol typesetting
The "degree Celsius" has been the only SI unit whose full unit name contains an uppercase letter since the SI base unit for temperature, the kelvin, became the proper name in 1967 replacing the term degree Kelvin. The plural form is degrees Celsius.
The general rule is that the numerical value always precedes the unit, and a space is always used to separate the unit from the number, e.g., "23 °C" (not "23°C" or "23° C"). Thus the value of the quantity is the product of the number and the unit, the space being regarded as a multiplication sign (just as a space between units implies multiplication). The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle, °, ′, and ″, respectively, for which no space is left between the numerical value and the unit symbol.
Unicode provides a compatibility character for the degree Celsius at U+2103 (decimal 8451), for compatibility with CJK encodings that provide such a character (as such, in most fonts the width is the same as for fullwidth characters). Its appearance is similar to the one synthesized by individually typing its two components (°) and (C). Shown below is the degree Celsius character followed immediately by the two-component version:
- ℃ °C
When viewed on computers that properly support Unicode, the above line may be similar to the image in the line below (enlarged for clarity):
The canonical decomposition is simply an ordinary degree sign and "C", so some browsers may simply display "°C" in its place due to Unicode normalization.
Temperatures and intervals
The degree Celsius is a special name for the kelvin for use in expressing Celsius temperatures. 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. This is sometimes solved by using the symbol °C (pronounced "degrees Celsius") for a temperature, and C° (pronounced "Celsius degrees") for a temperature interval, although this usage is non-standard.
What is often confusing about the Celsius measurement is that it follows an interval system but not a ratio system; that it follows a relative scale not an absolute scale. This is put simply by illustrating that while 10 °C and 20 °C have the same interval difference as 20 °C and 30 °C the temperature 20 °C is not twice the air heat energy as 10 °C. As this example shows degrees Celsius is a useful interval measurement but does not possess the characteristics of ratio measures like weight or distance.
Coexistence of Kelvin and Celsius scales
In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g., "…a measured value was 0.01023 °C with an uncertainty of 70 µK…"). This practice is permissible because the magnitude of the degree Celsius is 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 "microdegrees 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 recognised and could be confusing.
Melting and boiling points of water
One effect of defining the Celsius scale at the triple point of Vienna Standard Mean Ocean Water (VSMOW, 273.16 K and 0.01 °C), and at absolute zero (0 K and −273.15 °C), is that neither the melting nor boiling point of water under one standard atmosphere (101.325 kPa) remain 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 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 (approximately 36.61% thermodynamically hotter). When adhering strictly to the two-point definition for calibration, the boiling point of VSMOW 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 is slightly less, about 99.974 °C.
This boiling-point difference of 16.1 millikelvin between the Celsius scale's original definition and the current one (based on absolute zero and the triple point) has little practical meaning in common daily applications because water's boiling point is very sensitive to variations in barometric pressure. For example, an altitude change of only 28 cm (11 in) causes the boiling point to change by one millikelvin.
Throughout the world, except in the United States, Belize and a few other countries[specify], the Celsius temperature scale is used for practically all purposes. The only exceptions are some specialist fields (e.g., low-temperature physics, astrophysics, light temperature in photography) where the closely related Kelvin scale dominates instead.
Even in the U.S., almost the entire scientific field and many engineering fields, use the Celsius scale, and the metric system in general. However, most Americans remain more accustomed to the Fahrenheit scale, which is the scale that U.S. broadcasters use in weather forecasting. It is also commonly used in the U.S. for measurement of body temperature, and household use such as cooking, and is the scale commonly seen on ovens and in recipes. In Canada, due to its close relationship with the U.S., kitchen devices, literature, and packaging include both Fahrenheit and Celsius quotations.
The United Kingdom has almost exclusively used the Celsius scale since the 1970s, but it is sometimes called centigrade. A notable exception is that some broadcasters and publications still quote Fahrenheit air temperatures alongside Celsius in weather forecasts for the benefit of generations born before 1960, and air-temperature thermometers sold still show both scales for the same reason. Schools in the United Kingdom teach the Celsius scale exclusively.
- ^ "SI brochure, section 220.127.116.11". International Bureau of Weights and Measures. http://www1.bipm.org/en/si/si_brochure/chapter2/2-1/2-1-1/kelvin.html. Retrieved 9 May 2008.
- ^ "Essentials of the SI: Base & derived units". http://physics.nist.gov/cuu/Units/units.html. Retrieved 9 May 2008.
- ^ "Resolution 4 of the 10th meeting of the CGPM (1954)". http://www.bipm.org/en/CGPM/db/10/4/.
- ^ Citation: Uppsala University (Sweden), Linnaeus' thermometer
- ^ 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
- ^ Citations: University of Wisconsin–Madison, Linnæus & his Garden and; Uppsala University, Linnaeus' thermometer
- ^ "CIPM, 1948 and 9th CGPM, 1948". International Bureau of Weights and Measures. http://www.bipm.org/en/committees/cipm/cipm-1948.html. Retrieved 9 May 2008.
- ^ According to The Oxford English Dictionary (OED), the term "Celsius' 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 (PDF (146 KiB)) 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 was not even aware that "degree Celsius" was in sporadic, non-scientific use before that time. It is 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' 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.
- ^ "centigrade, adj. and n.". Oxford English Dictionary. Oxford University Press. http://www.oed.com. Retrieved 20 November 2011.
- ^ Lide, D. R., ed. (1990–1991). Handbook of Chemistry and Physics. 71st ed. CRC Press. p. 4–22.
- ^ The ice point of purified water has been measured to be 0.000 089(10) degrees Celsius - see Magnum, B.W. (June 1995). "Reproducibility of the Temperature of the Ice Point in Routine Measurements" (PDF). Nist Technical Note 1411. Archived from the original on Mar 07,2007. http://web.archive.org/web/20070307055524/http://www.cstl.nist.gov/div836/836.05/papers/magnum95icept.pdf. Retrieved 11 February 2007.
- ^ 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. There is a different approximation using ITS-90 which approximate the temperature to 99.974 °C
- ^ "Unit of thermodynamic temperature (kelvin)". The NIST Reference on Constants, Units, and Uncertainty: Historical context of the SI. National Institute of Standards and Technology (NIST). 2000. http://physics.nist.gov/cuu/Units/index.html. Retrieved 16 November 2011.
- ^ 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.
- ^ Note (e) of SI Brochure, Section, 2.2.2, Table 3
- ^ Decision #3 of Resolution 3 of the 13th CGPM
- ^ 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 kelvin 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 (PDF (1.39 MiB)).
- ^ H.D. Young, R.A. Freedman (2008). University Physics with Modern Physics (12th ed.). Addison Wesley. p. 573
- ^ This fact is demonstrated in the book 'Biostatistics: A Guide to Design, Analysis, and Discovery' By Ronald N. Forthofer, Eun Sul Lee and Mike Hernandez
- ^ "Resolution 3 of the 9th CGPM (1948)". International Bureau of Weights and Measures. http://www.bipm.org/en/CGPM/db/9/3/. Retrieved 9 May 2008.
- ^ Citation: London South Bank University, Water Structure and Behavior, notes c1 and c2
- ^ "Belize Weather Bureau". http://www.hydromet.gov.bz/. Retrieved 9 May 2008.
- NIST, Basic unit definitions: Kelvin
- The Uppsala Astronomical Observatory, History of the Celsius temperature scale
- London South Bank University, Water, scientific data
- BIPM, SI brochure, section 18.104.22.168, Unit of thermodynamic temperature
- TAMPILE, Comparison of temperature scales
Scales of temperature SI units Base units Derived units Accepted for use
See alsoBook:International System of Units · Category:SI base units
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