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Energy - The Atwater System

 Updated 2015-10-06

 Calculation of the energy content of foods according to Atwater

Let us take a closer look at the algorithm for energy calculations defined by Atwater and Bryant. The general algorithm is

    (1)  Energy content of food    =     protein content x energy from protein
+  fat content x energy from fat
+  carbohydrate content x energy from carbohydrate
+  alcohol content x energy content of alcohol

Until recently, almost all food composition tables (and also regulatory rules for nutrition labelling) there are only 4 variables on the right side of the equality sign in this equation.

The protein, fat and carbohydrate, alcohol contents are the variables, while the energy factors for the same compounds generally are treated as constants. However, in Atwater’s system there are eight variables on the right side of the equality sign as all the factors are variables.

As mentioned previously, Atwater’s energy factors, the specific energy factors, take into account the physiological availability of the energy from these foods. They adjust the energy content of a food according to the properties of the food matrix and thus the bioavailability of the energy from the energy supplying substances: protein, fat, carbohydrate and alcohol.

The specific energy factors are based on the amounts of energy liberated when the macronutrients are metabolically oxidised, allowing for incomplete intestinal absorption.

The energy yielding components, basis and recent recommendations

A closer look at Atwater’s definitions of the four energy-supplying components reveals some more food dependent variables.


Protein is defined as the nitrogen content (determined by the Kjeldahl procedure) of the food multiplied by a food dependent nitrogen-to-protein conversion factor (‘crude protein’). Thus, the protein content of a food is food matrix dependent (dependent of the ingoing amino acids in the foods). The protein content can therefore be expressed as

   (2)        Protein content      = nitrogen content  x  specific conversion factor

Note that protein content according to Atwater is determined both by a method of analysis and by a food specific conversion factor.

The specific conversion factors, the nitrogen-to-protein conversion factors (or NCFs), are listed in Table 1. The original work on the NCFs was carried out by D.B. Jones and published as Factors for Converting Percentages of Nitrogen in Foods and Feeds into Percentages of Proteins [11], originally from 1931 and slightly revised in 1941.

Jones determined the specific nitrogen to protein factors on the basis of the nitrogen content of more than 121 different proteins isolated from plant and animal sources. It is remarkable that no really serious attempt has been made since 1941 to enlarge this list. For the remaining foods the factor 6.25 is applied ‘until more is known regarding their protein’. Although the scientific literature shows attempts to question some of Jones’ findings, it is remarkable that only relatively little work has been done in this field – especially regarding the long timespan of more than seventy years.

Table 1.  Factors for calculating protein from nitrogen content of food (from [11]).

Animal origin:

Plant origin:
   Grains and cereals:
         Corn (maize)
            Whole kernel




Plant origin – Continued
   Legumes – Continued
      Beans – Continued
      Pine nuts





Although only little work has been done in the are of NCFs, there are a list of 'authoritative' references given for NCFs in the literature and especially in the documentation of food composition databases and tables-

Merrill and Watt [9] adapted the NCF data from the FAO tables on Amino Acid content of Foods and Biological Data on Proteins (1970) [10]. In turn, the FAO tables have their information from the original work of Jones, Factors for Converting Percentages of Nitrogen in Foods and Feeds into Percentages of Proteins [11], originally from 1931 and slightly revised in 1941.

Greenfield and Southgate (FAO Rome, 2003), part 1, page 103, refer to the Energy and protein requirements [12] published by FAO in 1973 as their source.

Annex 3 of the FAO/WHO Energy and Protein Requirements [12] gives a short list of nitrogen to protein conversion factors. This publication is generally regarded as the authoritative reference with regard to nitrogen to protein conversion factors within the food composition area. The data in the requirements report has been taken directly from FAO’s amino acid tables [10].

It is interesting to note that the Annex 3 of the Requirements, which many food composition tables also refer to, gives a table to convert the protein content given in food composition tables from the protein content calculated with a specific factor to a protein content calculated with the general factor 6.25. The reason for this ‘back calculation’ is that the energy requirements are based on the calculation of protein with the general factor 6.25, i.e. protein expressed as 'crude protein')!

Newer findings (among these some presentations in Lahti/Rome) show that the protein conversion factors are usually a little too high.

For more information on protein, see also the page on Protein.


Fat or lipid is in the Atwater system determined by the extraction of fat (‘crude fat’) with organic solvent (typically ether)[ 9]. This is a ‘direct’ measurement and does not cause any extra variables in equation (1). As for protein, the ‘fat content’ according to Atwater is determined by a specific method of analysis.

The Joint FAO/WHO Expert Consultation on Fats and Oils in Human Nutrition (FAO 1994) [13] reviews the important role of dietary fats and oils in human nutrition. With respect to the energy values of fats, the Consultation discusses the specific Atwater factor of 8.37 kcal/g that has been used for many decades to convert grams of fats in cereals, fruits and vegetables (see also table 3), and the Consultation finds ‘this value unwarranted, particularly upon examination of its derivation’. It is explained as follows: In his original work, Atwater applied the heat of combustion for triglycerides to extracts of various foods, but for cereals, fruits and vegetables the “assumed or calculated” was given as 9.30 kcal/g. Merrill and Watt copied this figure from Atwater and Bryant [4] with the comment that ‘for fat as it occurs in cereals and other plant sources Atwater assumed the apparent digestibility to be 90 percent and we have continued this practice. The energy factor for fat in plant foods is therefore, assumed to be 8.37 kcal/g’. Atwater had used a coefficient of digestibility of 95 percent for butter, and it was also assigned to the separated fats of plant origin. The calculations for fats and oils as such became 95 percent of 9.30 kcal/g or 8.84 kcal/g. This seems incompatible compared to the assumed digestibility of 90 percent in fats and oils of cereals, fruits and vegetables.

Therefore, the Consultation finds that the corrections for digestibility have a long history of assumptions and therefore, are inappropriate for the dietary oils and fats commonly consumed; the rounded factor of 9 kcal/g for converting grams of all dietary fat to energy is more suitable and offers consistency.

On this basis, the Consultation concludes:

  •  The standard Atwater factor of 9.0 kilocalories (37.7 kJ) per gram of fat should be used for calculating the energy value of fat in all nutrition surveys and food composition tables;
  •  Standard methods and reference materials should be used in the analysis of the fatty acid content of foods and in the preparation of nutrient databases;
  •  Adequate food composition data on fats should be widely available and accessible with each food item being identified by unambiguous descriptive factors.

The conclusion concerning the energy value of dietary fats and oils is interesting, because the Consultation round off the energy value of 9.3 kcal/g before converting to kJ/g. If the rounding off takes place after conversion, the value expressed in kJ/g would be 39 (38.9 kJ/g).


Carbohydrate is in the Atwater system determined ‘by difference’, i.e. the difference between 100 and the sum of crude protein, fat, moisture, and ash. In addition to true carbohydrates, this definition of carbohydrates also includes compounds like organic acids [9].

 The Atwater system is often criticised for this indirect measurement of carbohydrate with the argument that all the errors of the direct determinations of nitrogen (converted to protein), fat, moisture, ash and, for alcohol containing foods, also alcohol, are summed up in the carbohydrate value.
The Atwater system is also criticised for including dietary fibre in the carbohydrate value.

These criticisms, though, does not take into consideration that the purpose of the Atwater system was not to measure carbohydrate, but to establish a way to determine the energy content of foods, or ‘fuel value’ as Atwater called it. Thus, one of the advantages of the Atwater system its robustness in the energy calculation, as any errors in protein determination is levelled out with a higher or smaller carbohydrate energy value (same energy factor), and partly levelled by errors in fat or alcohol determination. With regard to inclusion of dietary fibre in the ‘carbohydrate-by-difference’ value, Atwater took this into consideration by applying digestibility coefficients to the carbohydrate energy value to account for the food’s carbohydrate’s different physiological properties. Atwater also applied digestibility coefficients to protein and fat, thus yielding at a specific set of energy factors to be applied to every single food (see also Table 3 below).

The importance of carbohydrates in nutrition, being the single most important food energy source in the world and having physiological important properties, has lead to many discussions concerning the terminology of carbohydrates during the last century. The main problems being the divergence between various chemical analytical divisions of carbohydrate and on the other side the physiological and health aspects of carbohydrates.

The introduction of terms like available and unavailable carbohydrates (McCance and Lawrence 1929 [14]), dietary fibre (Trowell 1972 [15]), complex carbohydrates (McGovern report 1997 [16]), etc. has lead to many discussions and interpretations concerning the determination of carbohydrate, its components and its energy value.

With regard to dietary fibre, at present, there is not complete consensus as to which components of carbohydrate should be included as dietary fibre and different authors have variously included non-starch polysaccharides (NSP) and resistant starch.

Physiological definitions of dietary fibre as ‘edible plant and animal material not hydrolysed by the endogenous enzymes of the human digestive tract’ (Codex Alimentarius) [17]. It includes the digestion in the small intestine, but does not take into account the more or less complete fermentation of the dietary fibre components by the colonic microflora, has lead to the false assumption that dietary fibre does not contribute to the energy value of a food. This is often the case in nutrition labelling and food composition tables (see respective chapters below).  In the late 1960’es, Southgate and Durnin worked on an analytical approach for the determination of carbohydrates in the diet [18]. Southgate and Durnin explain some of the uncertainties of the Atwater system, especially the use of carbohydrate ‘by difference’, which is opposed to the British preference for ‘available carbohydrate’ measured directly (McCance and Widdowson [19]). The experiments of Southgate and Durnin were carried out in order to perform an evaluation of the calorie conversion factors applicable to diets similar to those eaten in Britain at that time. The major point of difference between the procedures of used in calculating the metabolizable energy in Great Britain and the United States was in the respect of carbohydrate (Widdowson [7]). Southgate and Durnin concluded that for practical purposes the classical Atwater factors can be used to calculate the metabolizable energy of a diet with reasonable accuracy, provided that when available carbohydrate (expressed as monosaccharides) values are used in the calculation a factor of 3.75 kcal/g (15.7 kJ/g) is used.

The analytical methods (Southgate [], Englyst [] and others) used were based on assays, which hydrolysed down to monosaccharides, the British carbohydrate data have since those days been expressed as monosaccharides, whereas most other analytical methods express the carbohydrate as the anhydrous form. This is a contributory cause of the discrepancies in carbohydrate values. It is worth noting that the ‘Southgate and Durning factor’ is the same specific carbohydrate factor that Atwater has established for monosaccharides (see also table 3).

The Joint FAO/WHO Expert Consultation on Carbohydrates in Human Nutrition (FAO1997) [20], reviews the role of carbohydrates in relation to nutrition, maintenance of health, dietary carbohydrate and disease. The Expert Consultation also deals with the issue of the fermentation of dietary fibre. One of the important recommendations derived from the Consultation discussions states ‘that the energy value of all carbohydrate in the diet be reassessed using modern nutritional and other techniques. However, for carbohydrates, which reach the colon, the Consultation recommends that the energy value be set at 2 kcal/g (8 kJ/g) for nutritional and labelling purposes’.

This conclusion is based on the fact that the colonic fermentation is an efficient digestive process since starch is almost totally degraded, as well as lactose, alcohol-sugars and fructans. More than half of the usually consumed fibres are degraded in the large intestine, the rest being excreted, see table 2 below.


Table 2.  Colonic fermentability of dietary fibres in humans (from [20])

 Dietary fibre Fermentability, %

Guar gum
Wheat bran
Resistant starch
Inulin, oligosaccharides
20 –80
60 – 90
100 (if not in excess)


The Consultation also recommends:

  • That the terminology used to describe dietary carbohydrate be standardised with carbohydrates classified primarily by molecular size, degree of polymerisation (DP), into sugars (DP 1-2), oligosaccharides (DP 3-9), and polysaccharides (DP 10+). Further subdivision can be made on the basis of monosaccharide composition. Nutritional groupings can then be made on the basis of physiological properties;
  • Against the use of the terms extrinsic and intrinsic sugars, complex carbohydrate and available and unavailable carbohydrate, and that the terms soluble and insoluble dietary fibre be gradually phased out;
  • That food laboratories measure total carbohydrate in the diet as the sum of individual carbohydrates and not ‘by difference’;
  • That the use of the term dietary fibre should always be qualified by a statement itemising the carbohydrates and other substances intended for inclusion. Dietary fibre is a nutritional concept, not an exact description of a component in the diet;
  • That the analysis and labelling of dietary carbohydrate, for whatever purpose, be based on the chemical divisions recommended. Additional groupings such as polyols, resistant starch, non-digestible oligosaccharides and dietary fibre can be used, provided the included components are clearly defined;
  • That the energy value of all carbohydrate in the diet be reassessed using modern nutritional and other techniques.

From the Consultation’s recommendations several questions raise with regard to the need for more standardisation and harmonisation of the carbohydrate concept in nutrition labelling and food composition databases/tables. This will be seen clearly from the examination of international regulations on nutrition labelling and national food composition practices below.


Alcohol is mentioned by Merill and Watt in [9], but not in the same details as protein, fat and carbohydrate. Atwater did not consider alcohol as complex in the energy calculations as the other basic constituent of foods. It is discussed, though, that alcohol’s energy contribution may be important in the diet of some individuals or some population groups.


The specific Atwater energy factors

The definitions listed above indicate several things with regard to energy calculations according to Atwater as summarised below.

Firstly, in the Atwater system the definitions of protein and fat are based on certain analytical methods, and in the case of protein also a conversion factor to recalculate from measured nitrogen content to protein content. Carbohydrate is ‘measured indirectly by difference’.

Secondly, in Atwater’s system the energy content of the basic food components, protein, fat, and carbohydrate is food matrix dependent. Atwater based the estimation of his so-called ‘physiological fuel values’, the specific energy values, on measurements of the digestibility (energy metabolism and digestibility) of the food components in the different foods and the heat of combustion measured for these foods.

Table 3 shows some data for calculating energy values of foods or food groups by the Atwater system with specific energy factors.


Table 3.  Some specific energy factors for the calculation of energy in food (from [9])

                Protein                    Fat        Carbohydrate
  Coeffi- Heat of   Factor to be Coeffi- Heat of   Factor to be Coeffi- Heat of   Factor to be
  cient of combus-   applied to in- cient of combus-   applied to in- cient of combus-   applied to in-
Food or food group digesti- tion less gested nutrients digesti- tion gested nutrients digesti- tion  gested nutrients
  bility 1.25     bility       bility      
    % kcal/g kcal/g kJ/g % kcal/g kcal/g kJ/g % kcal/g kcal/g kJ/g
Eggs, Meat products, Milk products                        
  Eggs 97 4.50 4.37 18.3 95 9.50 9.03 37.8 98 3.75 3.68 15.4
  Gelatin 97 4.02 3.90 16.3 95 9.50 9.03 37.8        
  Glycogen                 98 4.19 4.11 17.2
  Meat, fish 97 4.40 4.27 17.9 95 9.50 9.03 37.8        
  Milk, milk products 97 4.40 4.27 17.9 95 9.25 8.79 36.8 98 3.95 3.87 16.2
Fats, separated                        
  Butter 97 4.40 4.27 17.9 95 9.25 8.79 36.8 98 3.95 3.87 16.2
  Other animal fats         95 9.50 9.03 37.8        
  Margarine, vegetable 97 4.40 4.27 17.9 95 9.30 8.84 37.0 98 3.95 3.87 16.2
  Other vegetable fats and oils         95 9.30 8.84 37.0        
  All (except lemons, limes) 85 3.95 3.36 14.0 90 9.30 8.37 35.0 90 4.00 3.60 15.1
  Lemons 85 3.95 3.36 14.0 90 9.30 8.37 35.0 98 2.75 2.70 11.3
  Limes 85 3.95 3.36 14.0 90 9.30 8.37 35.0 98 2.75 2.70 11.3
Grain products                        
  Barley, pearled 78 4.55 3.55 14.8 90 9.30 8.37 35.0 94 4.20 3.95 16.5
  Buckwheat flour, dark 74 4.55 3.37 14.1 90 9.30 8.37 35.0 90 4.20 3.78 15.8
  Buckwheat flour, white 78 4.55 3.55 14.8 90 9.30 8.37 35.0 94 4.20 3.95 16.5
  Cornmeal, whole ground 60 4.55 2.73 11.4 90 9.30 8.37 35.0 96 4.20 4.03 16.9
  Cornmeal, degermed 76 4.55 3.46 14.5 90 9.30 8.37 35.0 99 4.20 4.16 17.4
  Dextrin                 98 4.11 4.03 16.9
  Macaroni, spaghetti 86 4.55 3.91 16.4 90 9.30 8.37 35.0 98 4.20 4.12 17.2
  Oatmeal, rolled oats 76 4.55 3.46 14.5 90 9.30 8.37 35.0 98 4.20 4.12 17.2
  Rice, brown 75 4.55 3.41 14.3 90 9.30 8.37 35.0 98 4.20 4.12 17.2
  Rice, white or polished 84 4.00 3.36 14.1 90 9.30 8.37 35.0 99 4.20 4.16 17.4
  Rye flour, dark 65 4.55 2.96 12.4 90 9.30 8.37 35.0 90 4.20 3.78 15.8
  Rye flour, whole grain 67 4.55 3.05 12.8 90 9.30 8.37 35.0 92 4.20 3.86 16.2
  Rye flour, medium 71 4.55 3.23 13.5 90 9.30 8.37 35.0 95 4.20 3.99 16.7
  Rye flour, light 75 4.55 3.41 14.3 90 9.30 8.37 35.0 97 4.20 4.07 17.0
  Sorghum (kaoliang), whole or nearly whole meal 20 4.55 0.91 3.8 90 9.30 8.37 35.0 96 4.20 4.03 16.9
  Wheat, 97-100 percent extraction 79 4.55 3.59 15.0 90 9.30 8.37 35.0 90 4.20 3.78 15.8
  Wheat, 85 - 93 percent extraction 83 4.55 3.78 15.8 90 9.30 8.37 35.0 94 4.20 3.95 16.5
  Wheat, 70 - 74 persent extraction 89 4.55 4.05 16.9 90 9.30 8.37 35.0 98 4.20 4.12 17.2
  Wheat, flaked, puffed, rolled, shredded, whole meal  79 4.55 3.59 15.0 90 9.30 8.37 35.0 90 4.20 3.78 15.8
  Wheat bran (100 percent) 40 4.55 1.82 7.6 90 9.30 8.37 35.0 56 4.20 2.35 9.8
  Other cereals, refined 85 4.55 3.87 16.2 90 9.30 8.37 35.0 98 4.20 4.12 17.2
  Wild rice 78 4.55 3.55 14.8 90 9.30 8.37 35.0 94 4.20 3.95 16.5
Legumes, nuts                        
  Mature dry beans, cowpeas, peas, other legumes 78 4.45 3.47 14.5 90 9.30 8.37 35.0 97 4.20 4.07 17.0
  Immature lima beans, cowpeas, peas, other legumes 78 4.45 3.47 14.5 90 9.30 8.37 35.0 97 4.20 4.07 17.0
  Soybeans, dry; soy flour, flakes, grits 78 4.45 3.47 14.5 90 9.30 8.37 35.0 97 4.20 4.07 17.0
  Cane or beet sugar                 98 3.95 3.87 16.2
  Glucose                 98 3.75 3.68 15.4
  Mushrooms 70 3.75 2.63 11.0 90 9.30 8.37 35.0 85 4.10 3.49 14.6
  Potatoes and starchy roots 74 3.75 2.78 11.6 90 9.30 8.37 35.0 96 4.20 4.03 16.9
  Other underground crops 74 3.75 2.78 11.6 90 9.30 8.37 35.0 96 4.00 3.84 16.1
  Other vegetables 65 3.75 2.44 10.2 90 9.30 8.37 35.0 85 4.20 3.57 14.9
Miscellaneous foods                        
  Chocolate, cocoa 42 4.35 1.83 7.6 90 9.30 8.37 35.0 32 4.16 1.33 5.6
  Vinegar                 98 2.45 2.40 10.0
  Yeast 80 3.75 3.00 12.6 90 9.30 8.37 35.0 80 4.20 3.36 14.1

A more comprehensive list of specific energy factors can be found in the documentation of the USDA Database for Standard Reference [21].




9.  Merrill, A.L. and Watt, B.K.: Energy Value of Foods … basis and derivation. Agriculture Handbook No. 74, revised February 1973. Human Nutrition Research Branch, Agricultural Research Service, United States Department of Agriculture.

10.  Amino acids of foods and biological data on proteins. FAO Nutritional Studies, No. 24.  Rome 1970.

11.  Jones, D.B.: Factors for Converting Percentages of Nitrogen in Foods and Feeds into Percentages of Protein. United States Department of Agriculture, Circular No. 183. Slightly revised edition 1941 (Original version 1931). nitrogen-protein conversion cir183.pdf

12.  Food and Agriculture Organization /World Health Organization. Energy and protein requirements. Report of a Joint FAO/WHO Ad Hoc Expert Committee. FAO Nutrition Meetings No. 52. FAO, Rome 1973.
Annex 3: NCF 1973.pdf

13.  FAO/WHO: Fats and Oils in Human Nutrition. Report of a Joint FAO/WHO Expert Consultation, Rome, 19 – 126 October 1993. FAO Food and Nutrition Paper 57, FAO, Rome 1994.

14.  McCance, R.A. and Lawrence, R.D.: The carbohydrate contents of foods. Medical Research Council Special Report Series 135. Her Majesty’s Stationary Office, London 1929.

15.  Trowell, H.: Dietary fibre and coronary heart disease. Revue Européenne d’Études Cliniques et Biologiques 17(4), pp. 345-349, 1972.

16.  U.S. Senate Select Committee on Nutrition and Human Needs: Dietary goals for the United States. 2nd Ed. U.S. Government Printing Office, Washington D.C., 1977.

17.  Codex Alimentarius Commission: Codex Guidelines for Nutritional Labelling. CAC/GL – 1985 (Rev. 1 – 1993), Joint FAO/WHO Food Standards Programme, FAO, Rome 1993.

18.  Southgate, D.A.T. and Durnin, J.V.G.A.: Calorie conversion factors. An experimental reassessment of the factors used in the calculation of energy value of human diets. Br. J. Nutr., 24, 517, 1970.

19.  McCance, R.A. and Widdowson, E.M.: Medical Research Council Special Report No. 297, 1960.

20.  FAO/WHO: Carbohydrates in Human Nutrition. Report of a Joint FAO/WHO Expert Consultation, Rome, 14 – 18 April 1997. FAO Food and Nutrition Paper 66, FAO, Rome 1998.

21.  U.S. Department of Agriculture, Agricultural Research Service. 2010. USDA Nutrient Database for Standard Reference, Release 27. Nutrient Data Laboratory Home Page,


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