# Calorie

The calorie is a unit of energy.

There are actually two units with that name that have been widely used. 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 on one kilogram of water. Thus, 1 kcal = 1 Cal = 1000 cal.

The large calorie is sometimes written Calorie (with a capital C) to distinguish from the other unit. However, this convention cannot be relied upon, since it is often ignored – especially in non-technical publications.

Although both units related to the metric system, they have been considered obsolete, or deprecated, in scientific usage, since the adoption of the SI system. The SI unit of energy is the joule, with symbol "J"; one small calorie is now defined as exactly 4.184 J, and one large calorie is 4184 J.

However, the two units are still used occasionally in technical work, and the large calorie is still widely used in nutrition. In most countries, the labels of industrialized food products are required to indicate the nutritional energy value in (large) calories per serving or per weight.

## History

The (large) calorie was first defined by Nicolas Clément in 1824 as a unit of heat energy. It entered French and English dictionaries between 1841 and 1867. The word comes from Latin calor, meaning 'heat'. The small calorie was introduced by Pierre Antoine Favre (Chemist) and Johann T. Silbermann (Physicist) in 1852. In 1879, Marcellin Berthelot introduced the convention of capitalizing the large Calorie to distinguish the senses. The use of the (large) calorie for nutrition was introduced to the American public by Wilbur Olin Atwater, a professor at Wesleyan University, in 1887.

The alternate spelling calory is archaic.

## Definitions

The (small) calorie was intended to be the amount energy needed to increase the temperature of 1 gram of water by 1 °C (or 1 K, which is the same increment). That amount however depends on the atmospheric pressure and the starting temperature. Accordingly, several different precise definitions of the calorie have been used.

Name Symbol Conversions Definition and notes
Thermochemical calorie calth 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 calorie cal4 ≈ 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 calorie cal15 ≈ 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 calorie cal20 ≈ 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 calorie calmean ≈ 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 per day. One gram of fat in food contains nine calories, while a gram of either a carbohydrate or a protein contains approximately four calories. Alcohol in a food contains seven calories 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 liter (1 liter 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 utilised 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 USA and has been succeeded 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.