# Calorie

A 710-millilitre (24 US fl oz) energy drink with 330 calories

The calorie is a unit of energy that originated from the obsolete caloric theory of heat.[1][2] For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, dietary calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of one kilogram of water by one degree Celsius (or one kelvin).[1][3] The small calorie or gram calorie was defined as the amount of heat needed to cause the same increase in one gram of water.[3][4][5][1] Thus, 1 large calorie is equal to 1000 small calories.

In nutrition and food science, the term calorie and the symbol cal almost always refers to the large unit. It is generally used in publications and package labels to express the energy value of foods in per serving or per weight, recommended dietary caloric intake,[6][7] metabolic rates, etc. Some authors recommend the spelling Calorie and the symbol Cal (both with a capital C) to avoid confusion;[8] however, this convention is often ignored.[6][7][8]

In physics and chemistry the word calorie and its symbol usually refer to the small unit; the large one being called kilocalorie. However, this unit is not officially part of the metric system (SI), and is regarded as obsolete,[2] having been replaced in many uses by the SI unit of energy, the joule (J).[9]

The precise equivalence between calories and joules has varied over the years, but in thermochemistry and nutrition it is now generally assumed that one (small) calorie (thermochemical calorie) is equal to exactly 4.184 J, and therefore one kilocalorie (one large calorie) is 4184 J, or 4.184 kJ.[10][11]

## History

The term "calorie" was first introduced by Nicolas Clément, as a unit of heat energy, in lectures on experimental calorimetry during the years 1819–1824.[12] This was the "large" calorie.[2][13][14] The term (written with lowercase "c") entered French and English dictionaries between 1841 and 1867. It comes from Latin calor 'heat'.

The same term was used for the "small" unit by Pierre Antoine Favre (Chemist) and Johann T. Silbermann (Physicist) in 1852. This unit was used by U.S. physician Joseph Howard Raymond, in his classic 1894 textbook A Manual of Human Physiology.[15] He proposed calling the "large" unit "kilocalorie", but the term didn't catch on until some years later.

In 1879, Marcellin Berthelot distinguished between gram-calorie and kilogram-calorie, and proposed using "Calorie", with capital "C", for the large unit.[2] This usage was adopted by Wilbur Olin Atwater, a professor at Wesleyan University, in 1887, in an influential article on the energy content of food.[2][13]

The small calorie (cal) was recognized as a unit of the CGS system in 1896,[2][14] alongside the already-existing CGS unit of energy, the erg (first suggested by Clausius in 1864, under the name ergon, and officially adopted in 1882).

Already in 1928 there were serious complaints about the possible confusion arising from the two main definitions of the calorie and whether the notion of using the capital letter to distinguish them was sound.[16]

The joule was the officially adopted SI unit of energy at the ninth General Conference on Weights and Measures in 1948.[17][9] The calorie was mentioned in the 7th edition of the SI brochure as an example of a non-SI unit.[10]

The alternate spelling calory is considered nonstandard and dated.

## Definitions

The "small" calorie is broadly defined as the amount of energy needed to increase the temperature of 1 gram of water by 1 °C (or 1 K, which is the same increment, a gradation of one percent of the interval between the melting point and the boiling point of water).[4][5] The amount depends on the atmospheric pressure and the starting temperature, and different choices of these parameters have resulted in several different precise definitions of the unit.

Name Symbol Conversions Definition and notes
Thermochemical calorie calth 4.184 J

≈ 0.003964 BTU ≈ 1.162×10−6 kW⋅h ≈ 2.611×1019 eV

The amount of energy equal to exactly 4.184 J (joules) and 1 kJ ≈ 0.239 kcal.[18][19][20][11][a]
4 °C calorie cal4 ≈ 4.204 J

≈ 0.003985 BTU ≈ 1.168×10−6 kW⋅h ≈ 2.624×1019 eV

The amount of energy required to warm one gram of air-free water from 3.5 to 4.5 °C at standard atmospheric pressure.[b]
15 °C calorie cal15 ≈ 4.1855 J

≈ 0.0039671 BTU ≈ 1.1626×10−6 kW⋅h ≈ 2.6124×1019 eV

The amount of energy required to warm one gram of air-free water from 14.5 to 15.5 °C at standard atmospheric pressure.[b] Experimental values of this calorie ranged from 4.1852 to 4.1858 J. The CIPM in 1950 published a mean experimental value of 4.1855 J, noting an uncertainty of 0.0005 J.[18]
20 °C calorie cal20 ≈ 4.182 J

≈ 0.003964 BTU ≈ 1.162×10−6 kW⋅h ≈ 2.610×1019 eV

The amount of energy required to warm one gram of air-free water from 19.5 to 20.5 °C at standard atmospheric pressure.[b]
Mean calorie calmean ≈ 4.190 J

≈ 0.003971 BTU ≈ 1.164×10−6 kW⋅h ≈ 2.615×1019 eV

Defined as 1100 of the amount of energy required to warm one gram of air-free water from 0 to 100 °C at standard atmospheric pressure.[b]
International Steam Table calorie (1929) ≈ 4.1868 J

≈ 0.0039683 BTU ≈ 1.1630×10−6 kW⋅h ≈ 2.6132×1019 eV

Defined as 1860 "international" watt hours = 18043 "international" joules exactly.[c]
International Steam Table calorie (1956) calIT ≡ 4.1868 J

≈ 0.0039683 BTU = 1.1630×10−6 kW⋅h ≈ 2.6132×1019 eV

Defined as 1.163 mW⋅h = 4.1868 J exactly. This definition was adopted by the Fifth International Conference on Properties of Steam (London, July 1956).[18]
1. ^ The 'Thermochemical calorie' was defined by Rossini simply as 4.1833 international joules in order to avoid the difficulties associated with uncertainties about the heat capacity of water. It was later redefined as 4.1840 J exactly.[22]
2. ^ a b c d The standard atmospheric pressure can be taken to be 101.325 kPa.
3. ^ The figure depends on the conversion factor between "international joules" and "absolute" (modern, SI) joules. Using the mean international ohm and volt (1.00049 Ω, 1.00034 V),[21] the "international joule" is about 1.00019 J, using the US international ohm and volt (1.000495 Ω, 1.000330 V) it is about 1.000165 J, giving 4.18684 and 4.18674 J, respectively.

The two definitions most common in older literature appear to be the 15 °C calorie and the thermochemical calorie. Until 1948, the latter was defined as 4.1833 international joules; the current standard of 4.184 J was chosen to have the new thermochemical calorie represent the same quantity of energy as before.[19]

## Usage

### Nutrition

In a nutritional context, the "large" unit is used almost exclusively. It is generally written "calorie" with lowercase "c" and symbol "cal", even in government publications,[6][7] although the capitalized form "Calorie" (with symbol "Cal") or the name "kilocalorie" (with symbol "kcal") are also used, and may be mandated by law. The SI unit of energy kilojoule (kJ) may be used instead, in legal or scientific contexts.[23][24]

In the United States, most nutritionists prefer the unit kilocalorie to the unit kilojoules, whereas most physiologists prefer to use kilojoules. In the majority of other countries, nutritionists prefer the kilojoule to the kilocalorie.[25]

On nutrition facts labels in the European Union, energy is expressed in both kilojoules and kilocalories.[26] In the United States and Canada, labels use "Calories", referring to the large unit.[27] In China, only kilojoules are given.[28]

### Food energy

The unit is most commonly used to express food energy, namely the specific energy (energy per mass) of metabolizing different types of food. For example, fat (lipids) contains 9 kilocalories per gram (kcal/g), while carbohydrates (sugar and starch) and protein contain approximately 4 kcal/g.[29] Alcohol in food contains 7 kcal/g.[30] The "large" unit is also used to express recommended nutritional intake or consumption, as in "calories per day".

Dieting is the practice of eating food in a regulated way to decrease, maintain, or increase body weight, or to prevent and treat diseases such as diabetes and obesity. As weight loss depends on reducing caloric intake, different kinds of calorie-reduced diets have been shown to be generally effective.[31]

### Chemistry and physics

In other scientific contexts, the term "calorie" and the symbol "cal" almost always refers to the small unit; the "large" unit being generally called "kilocalorie" with symbol "kcal". It is mostly used to express the amount of energy released in a chemical reaction or phase change, typically per mole of substance, as in kilocalories per mole.[32] It is also occasionally used to specify other energy quantities that relate to reaction energy, such as enthalpy of formation and the size of activation barriers.[33] However, it is increasingly being superseded by the SI unit, the joule (J); and metric multiples thereof, such as the kilojoule (kJ).

The lingering use in chemistry is largely due to the fact that the energy released by a reaction in aqueous solution, expressed in kilocalories per mole of reagent, is numerically close to the concentration of the reagent, in moles per liter, multiplied by the change in the temperature of the solution, in kelvin or degrees Celsius. However, this estimate assumes that the volumetric heat capacity of the solution is 1 kcal/L/K, which is not exact even for pure water.

## References

1. ^ a b c Christopher W. Morris (1992) Academic Press Dictionary of Science and Technology. 2432 pages. ISBN 9780122004001
2. Allison Marsh (2020): "How Counting Calories Became a Science: Calorimeters defined the nutritional value of food and the output of steam generators Archived 2022-01-21 at the Wayback Machine" Online article on the IEEE Spectrum Archived 2022-01-20 at the Wayback Machine website, dated 29 December 2020. Accessed on 2022-01-20.
3. ^ a b "Definition of Calorie". Merriam-Webster. 1 August 2017. Retrieved 4 September 2017.
4. ^ a b "Cambridge Dictionary: calorie". Retrieved 9 November 2019.
5. ^ a b "Definition of calorie noun from the Oxford Advanced American Dictionary". Retrieved 9 November 2019.
6. ^ a b c U. S. Food and Drug Administration (2019): "Calories on the Menu - Information for Archived 2022-01-20 at the Wayback Machine". Online document at the FDA Website Archived 2013-09-15 at the Wayback Machine, dated 5 August 2019. Accessed on 2022-01-20.
7. ^ a b c U. K. National Health Service (2019): "What should my daily intake of calories be? Archived 2022-01-21 at the Wayback Machine". Online document at the NHS website Archived 2020-05-02 at the Wayback Machine, dated 24 October 2019. Accessed on 2022-01-20.
8. ^ a b Conn, Carole; Len Kravitz. "Remarkable Calorie". University of New Mexico. Retrieved 1 March 2019.
9. ^ a b Bureau International des Poids et Mesures (2019): The International System of Units (SI) Archived 2022-01-20 at the Wayback Machine, 9th edition.
10. ^ a b Bureau International des Poids et Mesures (1998): The International System of Units (SI) Archived 2022-01-20 at the Wayback Machine, 7th edition.
11. ^ a b United Nations Food and Agriculture Organization (2003): "FAO Food and Nutrition Paper 77: Food energy - methods of analysis and conversion factors Archived 2010-05-24 at the Wayback Machine". Accessed on 21 January 2022.
12. ^ Allain, Rhett (23 February 2016). "Calculating Calories by Burning Gummy Bears to Death". Scientific American. Retrieved 7 September 2017.
13. ^ a b Hargrove, James L (2007). "Does the history of food energy units suggest a solution to "Calorie confusion"?". Nutrition Journal. 6 (44): 44. doi:10.1186/1475-2891-6-44. PMC 2238749. PMID 18086303.
14. ^ a b JL Hargrove, "history of the calorie in nutrition", J Nutr 136/12 (December 2006), pp. 2957–2961.
15. ^ Joseph Howard Raymond (1894): A Manual of Human Physiology: Prepared with Special Reference to Students of Medicine Archived 2022-01-21 at the Wayback Machine. W.B. Saunders, 376 pages.
16. ^ Marks, Percy L. (14 January 1928). "The Two Calories, Percy L. Marks". Nature. 121 (3037): 58. doi:10.1038/121058d0. S2CID 4068300.
17. ^
18. ^ a b c International Standard ISO 31-4: Quantities and units, Part 4: Heat. Annex B (informative): Other units given for information, especially regarding the conversion factor. International Organization for Standardization, 1992.
19. ^ a b Rossini, Fredrick (1964). "Excursion in Chemical Thermodynamics, from the Past into the Future". Pure and Applied Chemistry. 8 (2): 107. doi:10.1351/pac196408020095. Retrieved 21 January 2013. both the IT calorie and the thermochemical calorie are completely independent of the heat capacity of water.
20. ^ Lynch, Charles T. (1974). Handbook of Materials Science: General Properties, Volume 1. CRC Press. p. 438. ISBN 9780878192342. Retrieved 8 March 2014.
21. ^ International Union of Pure and Applied Chemistry (IUPAC) (1997). "1.6 Conversion tables for units" (PDF). Compendium of Analytical Nomenclature (3 ed.). ISBN 0-86542-615-5. Archived (PDF) from the original on 2003-10-16. Retrieved 31 August 2013.
22. ^
23. ^ "Prospects improve for food energy labelling using SI units". Metric Views. UK Metric Association. 24 February 2012. Retrieved 17 April 2013.
24. ^ "SI Conventions". National Physical Laboratory. Retrieved 8 February 2016.
25. ^ Kevin T. Patton; Gary A. Thibodeau (11 January 2017). The Human Body in Health & Disease - E-Book. Elsevier Health Sciences. p. 537. ISBN 978-0-323-40206-4.
26. ^ "EU Regulation No 1169/2011 of the European Parliament and of the Council of 25 October 2011 on the provision of food information to consumers". eur-lex.europa.eu. Retrieved 18 April 2022.
27. ^ Nutrition, Center for Food Safety and Applied (7 March 2022). "Changes to the Nutrition Facts Label". FDA.
28. ^ USDA (2013). "China, General Rules for Nutrition Labeling of Prepackaged Foods" (PDF). Retrieved 18 April 2022.
29. ^ "How Do Food Manufacturers Calculate the Calorie Count of Packaged Foods?". Scientific American. Retrieved 8 September 2017.
30. ^
31. ^ Strychar, I. (3 January 2006). "Diet in the management of weight loss". Canadian Medical Association Journal. 174 (1): 56–63. doi:10.1503/cmaj.045037. ISSN 0820-3946. PMC 1319349. PMID 16389240.
32. ^ Zvi Rappoport ed. (2007), "The Chemistry of Peroxides", Volume 2 page 12.
33. ^ Bhagavan, N. V. (2002). Medical Biochemistry. Academic Press. pp. 76–77. ISBN 9780120954407. Retrieved 5 September 2017.