# Calorie

The calorie is a unit of energy widely used in nutrition.

For historical reasons, two main definitions of calorie are in wide use. The small calorie or gram calorie (usually denoted cal) is the amount of heat energy needed to raise the temperature of one gram of water by one degree Celsius (or one kelvin).  The large calorie, food calorie, or kilocalorie (Cal or kcal) is the amount of heat needed to cause the same increase in one kilogram of water. Thus, 1 kilocalorie (kcal) = 1000 calorie (cal). By convention the large calorie is often written Calorie (with a capital C) to distinguish from the smaller unit, and this is familiar usage in technical publications. (The convention is not followed in this article.) In most countries, labels of industrialized food products are required to indicate the nutritional energy value in (kilo or large) calories per serving or per weight.

Calorie relates directly to the metric system, and therefore to the SI system. It is regarded as obsolete, or deprecated, within the scientific community, since the adoption of the SI system, but still in some use. The SI unit of energy is the joule, with symbol "J": one small calorie is defined as exactly 4.184 J; one large calorie is 4184 J.

## History

The calorie was first introduced by Nicolas Clément, as a unit of heat energy, in lectures during the years 18191824. This was the "large" calorie, viz. modern kilocalorie. The term entered French and English dictionaries between 1841 and 1867. It comes from Latin calor, meaning 'heat'.

The "small" calorie (modern calorie) was introduced by Pierre Antoine Favre (Chemist) and Johann T. Silbermann (Physicist) in 1852. In 1879, Marcellin Berthelot distinguished between gram-calorie (modern calorie) and kilogram-calorie (modern kilocalorie). Berthelot also introduced the convention of capitalizing the kilogram-calorie, as Calorie.

The use of the kilogram-calorie (kcal) for nutrition was introduced to the American public by Wilbur Olin Atwater, a professor at Wesleyan University, in 1887.

The modern calorie (cal) was first recognized as a unit of the cm-g-s system (cgs) in 1896, 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. Use of the calorie was officially deprecated by the ninth General Conference on Weights and Measures, in 1948.

The alternate spelling calory is archaic.

## Definitions

The modern (small) calorie is 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). The definition depends on the atmospheric pressure and the starting temperature. Accordingly, several different precise definitions of the calorie have been used.

NameSymbolConversionsDefinition and notes
Thermochemical caloriecalth 4.184 J

0.003964 BTU 1.162×10−6 kWh 2.611×1019 eV

The amount of energy equal to exactly 4.184 joules  (a)
4 °C caloriecal4 ≈ 4.204 J

0.003985 BTU 1.168×10−6 kWh 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. (c)
15 °C caloriecal15 ≈ 4.1855 J

0.0039671 BTU 1.1626×10−6 kWh 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. (c) 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.
20 °C caloriecal20 ≈ 4.182 J

0.003964 BTU 1.162×10−6 kWh 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. (c)
Mean caloriecalmean ≈ 4.190 J

0.003971 BTU 1.164×10−6 kWh 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. (c)
International Steam table calorie (1929) ≈ 4.1868 J

0.0039683 BTU 1.1630×10−6 kWh 2.6132×1019 eV

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

0.0039683 BTU = 1.1630×10−6 kWh 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).
(a) 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.
(b) 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), 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.
(c) The standard atmospheric pressure can be taken to be 101.325 kPa.

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.

The calorie was first defined specifically to measure energy in the form of heat, especially in experimental calorimetry.

## Nutrition

In a nutritional context, the kilojoule (kJ) is the SI unit of food energy, although the kilocalorie is still in common use. The word calorie is popularly used with the number of kilocalories of nutritional energy measured. To avoid confusion, it is sometimes written Calorie (with a capital "C") to make the distinction, although this is not widely understood (in part because capitalization contravenes the SI rule that the initial letter of a unit name or its derivative shall be lower case in English).

To facilitate comparison, specific energy or energy density figures are often quoted as "calories per serving" or "kilocalories per 100 g". A nutritional requirement or consumption is often expressed in calories or kilocalories per day. One gram of fat in food contains nine kilocalories (kcal), while a gram of either a carbohydrate or a protein contains approximately four kilocalories (kcal). Alcohol in a food contains seven kilocalories (kcal) per gram.

## Chemistry

In other scientific contexts, the term calorie almost always refers to the small calorie. Even though it is not an SI unit, it is still used in chemistry. For example, the energy released in a chemical reaction per mole of reagent is occasionally expressed in kilocalories per mole. Typically, this use was largely due to the ease with which it could be calculated in laboratory reactions, especially in aqueous solution: a volume of reagent dissolved in water forming a solution, with concentration expressed in moles per litre (1 litre weighing 1 kg), will induce a temperature change in degrees Celsius in the total volume of water solvent, and these quantities (volume, molar concentration and temperature change) can then be used to calculate energy per mole. It is also occasionally used to specify energy quantities that relate to reaction energy, such as enthalpy of formation and the size of activation barriers. However, its use is being superseded by the SI unit, the joule, and multiples thereof such as the kilojoule.

## Measurement of energy content of food

In the past, a bomb calorimeter was used to determine the energy content of food by burning a sample and measuring a temperature change in the surrounding water. Today, this method is not commonly used in the United States and has been replaced by calculating the energy content indirectly from adding up the energy provided by energy-containing nutrients of food (such as protein, carbohydrates, and fats). The fibre content is also subtracted to account for the fact that fibre is not digested by the body.