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Annex 1

A. Equations for predicting BMR from weight (kg) and height (m)

 Age rangeBMRraRSDb
 (kcalth in parentheses)  
Men10–1869.4W + 322.2H + 2 3920.89418
 (16.6W + 77H + 572) (100)
18–3064.4W - 113.0H + 3 0000.65632
 (15.4W - 27H + 717) (151)
30–6047.2W + 66.9H + 3 7690.60686
 (11.3W + 16H + 901) (164)
> 6036.8W + 4 719.5H - 4 4810.84552
 (8.8W + 1 128H - 1 071) (132)
Women10–1830.9W + 2 016.6H + 9070.77473
 (7.4W + 482H + 217) (113)
18–3055.6W + 1 397.4H + 1460.73502
 (13.3W + 334H + 35) (120)
30–6036.4W - 104.6H + 3 6190.70452
 (8.7W - 25H + 865) (108)
> 6038.5W + 2 665.2H - 1 2640.82393
 (9.2W + 637H - 302) (94)

ar = correlation coefficient.
bRSD = residual standard deviation.

The values for r and RSD are very close to those obtained using the equations predicting from weight only (Table 5), showing that inclusion of height does not significantly improve the precision of prediction.

B. Comparison of values of BMR in MJ (kcalth) predicted from weight only (I) (Table 6) or from weight and height (II)

 Age rangeWtaHtbBMRc% difference in
predicted BMR for 5-cm
difference in heightd
(years)(kg)(m)MJ (kcalth)
Men10–18b451.586.02(1 440)6.02(1 440)0.3
18–30651.727.01(1 675)6.99(1 670)0.1
30–60651.726.84(1 635)6.97(1 665)0.05
>   60651.725.71(1 365)6.02(1 440)3.9
Women10–18b441.545.35(1 280)5.26(1 285)1.9
18–30551.625.46(1 305)5.48(1 310)1.3
30–60551.625.48(1 310)5.46(1 305)0.1
>   60551.624.91(1 175)5.16(1 235)2.6

a Subjects of median weight for height.
b Children aged 13–14 years, of median weight and height for age.
c The two sets of equations give good absolute agreement, except in the elderly.
d The effect of height on predicted BMR is negligible except in teenage girls and the elderly.

There is a significant effect of height (at a fixed weight) on the predicted BMR in children, but the data are not given because the BMR has not been used for estimating energy expenditure in children below 10 years.

Annex 2

A. Weight (kg) for age of children a

 - 2SDMedian+ 2SD- 2SDMedian+ 2SD
  2.4   3.3   4.3   2.2   3.2   4.0
  4.1   6.0   7.7   3.9   5.4   7.0
  5.9   7.8   9.8   5.5   7.2   9.0
  7.2   9.211.3   6.6   8.610.5
1.0   7.4   9.511.6
  9.111.513.9   8.510.813.1
  9.912.615.2   9.411.914.5

a Figures taken from United States Public Health Service, Health Resources Administration NCHS growth charts. Rockville, MD, 1976 (HRA 76–1120, 25, 3).

Full details on weight for age, height for age, and weight for height are given in the original publication as reproduced by WHO (Measuring change in nutritional status. Geneva, World Health Organization, 1983).

B. Median weight (kg) for age and height of adolescent boys and girls

1. Adolescent boys a

 Age (years)
Height (cm)101112131415161718
155 41.542.142.743.443.544.8  
160  46.246.747.448.049.851.553.9
165   50.951.452.353.155.157.1
170    55.656.558.159.160.5
175    59.760.461.963.564.7
180     65.165.766.167.1
185      69.570.371.3

a Data from Baldwin (1925) as reproduced by Jelliffe, D. B. The assessment of the nutritional status of the community, Geneva, World Health Organization, 1966.The range of variation in weights at a given age is much greater than the range of variations at a given height, this reflects the variable timing of the pubertal growth spurt.

2. Adolescent girls

 Age (years)
Height (cm)101112131415161718
155 44.044.845.
160  48.949.249.851.551.952.853.1
165  52.453.
170   56.857.658.058.958.960.1
175    60.060.861.262.162.9
180    61.362.263.063.964.4

C. The average and the range of desirable weights for height in adults a

Height without shoesMenWomen
(m)Weight without clothes (kg)Weight without clothes (kg)
weight range
weight range
1.45   46.042–5364
1.48   46.542–5465
1.50   47.043–5566
1.52   48.544–5768
1.54   49.544–5870
1.56   50.445–5870
BMIb22.0     20.1–     18.7–23.828.6

a Source: Bray, G.A., ed., Obesity in America. Proceedings of the 2nd Fogarty International Center Conference on Obesity, Report No. 79. Washington, DC, Department of Health, Education and Welfare, 1979. Based on: Mortality among overweight men and women, Statistical Bulletin 41. New York, Metropolitan Life Insurance Co., 1960.
b Body mass index (BMI) = Wt (kg)/Ht2(m).

Annex 3

(expressed as a ratio to the BMR)

SexBody weightAgeSpeed of walking (m per min)
Mean ratio 2.362.983.835.02
Range of ratios 2.18–2.582.77–3.29(3.54–4.21)(4.52–5.37)

The ratio of the gross energy cost of level walking to the BMR was calculated from an earlier analysis.a Gross energy varied with sex, weight, and speed but not with age.

The BMR estimates were derived from those given in Table 5 and varied with sex, weight, and age.

a McDonald, I. Nutrition abstracts and reviews, 31: 739–762 (1961).

Annex 4

SubjectsReferenceEnergy cost
Premature infants(1)4.920.5
Premature infants(2)5.723.8
Normal infants(3)5.623.4
Infants, recovering from malnutrition(4)5.5523.2
Adults, recovering from anorexia nervosa(9)6.426.7
Adults, intentional overfeeding(10)  
PregnancyTheoretical estimatea6.426.7

a Calculated as 80 000 kcalth (335 MJ) stored (see section 6.2.1) for 12.5 kg of weight gain.


  1. Reichman, B.L. et al. Pediatrics, 69: 446–451 (1982).
  2. Brooke, O.G. ET AL. Pediat. Res., 13: 215–220 (1979).
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  5. Kerr, D. et al. Accelerated recovery from infant malnutrition with high calorie feeding. In: Gardner, L. & Amacher, L., ed. Endocrine aspects of malnutrition. Santa Ynez, CA, Kroc Foundation, 1973, pp. 467–479.
  6. Whitehead, R.G. The protein needs of malnourished children. In: Porter, J.W. & Rolls, B.A., ed. Proteins in human nutrition. London, Academic Press, 1973, pp. 103–117.
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  10. Goldman, R.F. et al. In: Bray, G., ed. Obesity in perspective. Washington, DC, Department of Health, Education, and Welfare, 1975, p. 165 (Pub. No. (NIH) 75–708).
  11. Passmore, R. ET AL. Brit. J. Nutr., 9: 20–27 (1955).
  12. Norgan, N.G. & Durnin, J.V.G.A. Am. J. Clin. Nutr., 33: 978–988 (1980).

Annex 5

Preliminary assessment of data (expressed in terms of the basal metabolic rate multiplied by a metabolic constant b)

A.Males - Developed and developing societies  
 Sleeping1.0(i.e.,BMR × 1.0)
 Sitting quietly1.2 
 Standing quietly1.4 
 Standing activities  
  chopping firewood4.1 
  singing and dancing3.2 
  washing clothes2.2 
  making bows and arrows, bags, etc.2.7 
  “around” or strolling2.5 
  at normal pace3.2 
  with 10-kg load3.5 
   at normal pace5.7 
   at normal pace with 10-kg load6.7 
   at normal pace3.1 
 Sitting activities  
  playing cards1.4 
  carving plates, combs, etc.2.1 
  stringing loom1.9 
  sharpening axe1.7 
  sharpening machete2.2 
 Household tasks  
  light cleaning2.7 
  moderate cleaning (polishing, window cleaning, chopping firewood)3.7 
 Office work  
  sitting at desk1.3 
  standing and moving around1.6 
 Light industryb  
  motor vehicle repairs3.6 
  electrical work3.1 
  machine tool industry3.1 
  chemical industry3.5 
  laboratory work2.0 
  driving lorry1.4 
 Building industryb  
  decorating and painting2.8 
 Agriculture (mechanized)  
  driving tractor2.1 
  loading sacks4.7 
  feeding animals3.6 
  repairing fences5.0 
 Agriculture (tropical)  
  milking cows by hand2.9 
  collecting and spreading manure5.2 
  loading manure6.4 
sorghum harvest-cutting ears
uprooting sweet potatoes
kneeling sorting sweet potatoes
  lifting grain sacks for weighing3.7 
  loading sacks on lorry7.4 
  cutting sugarcane6.5 
  clearing ground (depending on type of land)2.9–7.9 
  cutting trees4.8 
  tying fence posts2.7 
  making fence3.6 
  splitting wood for posts4.2 
  sharpening posts4.0 
  digging holes for posts5.0 
  cutting grass with machete4.7 
  digging irrigation channels5.5 
  feeding animals3.6 
 Hunting and fishing  
  padding canoe3.4 
  fishing from canoe2.2 
  fishing with line2.1 
  fishing with spear2.6 
  hunting flying-fox3.3 
  hunting pig3.6 
  hunting birds3.4 
  in nursery3.6 
  planting trees4.1 
  felling with axe7.5 
  trimming branches off trees7.3 
hand saw
power saw
wood planing
  making mud bricks - squatting3.0 
  kneading clay2.7 
  digging earth to make mud5.7 
  shovelling mud4.4 
  earth cutting6.2 
  brick breaking4.0 
  weaving bamboo wall2.9 
  roofing house2.9 
  cutting bamboo3.2 
  cutting palm tree trunks4.1 
  digging holes6.2 
  laying floor4.1 
 Coconut activities  
  collecting (including climbing trees)4.6 
  putting in bags4.0 
 Pedalling rickshaws  
  without passengers7.2 
  with passengers8.5 
 Pulling carts  
  without load5.3 
  with load5.9 
 Pushing wheelbarrow4.8 
  working with pick6.0 
  erecting roof supports4.9 
 Armed Services  
  cleaning kit2.4 
  route marching4.4 
  assault course5.1 
  jungle march5.7 
  jungle patrol3.5 
  helicopter pilots  
pre-flight checks
normal and low-level flying
  sedentary (playing cards, etc.)2.2 
  light (billiards, bowls, cricket, golf, sailing, etc.)2.2–4.4 
  moderate (dancing, swimming, tennis, etc.)4.4–6.6 
  heavy (football, athletics, jogging, rowing, etc.)6.6+ 
 Sleeping1.0(i.e., BMR × 1.0)
 Sitting quietly1.2 
 Sitting activities  
  sewing clothes1.4 
  sewing pandanus mat1.5 
  weaving carrying bag1.5 
  preparing rope1.5 
  “around” or strolling2.4 
  at normal pace3.4 
  with load4.0 
  uphill:at normal pace4.6 
   with load6.0 
   at normal pace3.0 
   with load4.6 
 Household tasks  
  light cleaning2.7 
  moderate cleaning (polishing, window cleaning, etc.)3.7 
  sweeping house3.0 
  sweeping yard3.5 
  washing clothes3.0 
  ironing clothes1.4 
  washing dishes1.7 
  cleaning house2.2 
  child care2.2 
  fetching water from well4.1 
  chopping wood with machete4.3 
  preparing tobacco1.5 
  deseeding cotton1.8 
  beating cotton2.4 
  spinning cotton1.4 
 Food preparation and cooking  
  collecting leaves for flavouring1.9 
  catching fish by hand3.9 
  catching crabs4.5 
  grinding grain on millstone3.8 
  stirring porridge3.7 
  making tortillas2.1 
  removing beans from pod1.5 
  breaking nuts (like peanuts)1.9 
  squeezing coconut2.4 
  peeling taro1.7 
  peeling sweet potato1.4 
  roasting corn1.3 
  loading earth oven with food2.6 
 Office work1.7 
 Light industryb  
  bakery work2.5 
  brewery work2.9 
  chemical industry2.9 
  electrical industry2.0 
  furnishing industry3.3 
  laundry work3.4 
  machine tool industry2.7 
 Agriculture (non-mechanized)  
  clearing ground3.8 
  digging ground4.6 
  digging holes for planting4.3 
  planting root crops3.9 
  cutting grass with machete5.0 
  binding sheaves4.2 
  harvesting root crops3.1 
  picking coffee1.5 
  winnowing corn or rice1.7 
  cutting fruit from tree3.4 
  sedentary (playing cards, etc.)2.1 
  lightcf. male categories2.1–4.2 

b These values apply only as approximate mean values for the time actually working at the relevant tasks,and not to the total day's shift: e.g., a labourer might be able to work for less than half of his 7- or 8-hour working shift, and the remainder would be more or less rest time.

b These values apply only as approximate mean values for the time actually working at the relevant tasks,and not to the total day's shift: e.g., a worker might be able to work for less than half of his 7- or 8-hour working shift, and the remainder would be more or less rest time.

a The data in this annex were assembled by Professor J.V.G.A. Durnin, Institute of Physiology, University of Glasgow, Scotland.

b For example, if an individual's BMR is 1.08 kcalth/min (4.51 KJ/min) and the energy cost for a task is 3.24 kcalth/min (13.55 KJ/min) the metabolic constant would be 3.24 divided by 1.08 = 3.0 (13.55 divided by 4.51 = 3.0).

Annex 6

(for N loss/day)(with numbers observed)
Integumental (sweat)b   
Adultsmg/kg3–4(1, 2)c
Young infantsmg40–250(3, 4)
Infants 1 yearmg/kg7.8±2.9 (12)(5)
Boys 1.5 yearsmg/kg8–12 (4)(6)
Children 7.5–9.5 yearsmg/kg7–11 (27)(7, 8)
Hair and nails   
Young menmg30(1)
Old menmg15(9)
No contraceptives   
Teenagersmg/dayd36 (95)(10)
Mature womenmg/dayd43±24 (6)(11)
Premenopausalmg/dayd67 (37)(10)
Hormonal contraceptives (oralmg/dayd20(12)
or IUD)   
IUDs - plastic or coppermg/dayd57–104(13)
Semen and fluidsmg/ejaculation37±10(1)
Breath, ammoniamg/day50±6(1)
Urinary/faecal nitratemg/day75–130(14)
Expectorated salivamg/gram1(1)
Excreta rests on tissue   
Blood (samples/wounds)mg/g32±2(1)

a Adults unless otherwise specified.
b Temperate conditions, light activity. Increases with heat and physical activity. See text.
c Inoue, G. & Fujita, Y. Unpublished data, 1971.
d Averaged over a 28-day cycle.


  1. Calloway, D.H. et al. J. Nutr., 101: 775–786 (1971).
  2. Kraut, H. & Müller-Wecker, H. Hoppe-Seylers Z. Physiol: Chem., 320: 241–245 (1960).
  3. Hawawini, E. & Schreier, K. Z. Kinderheilk., 92: 333–342 (1965).
  4. Cooke, R.E. et al. Yale J. Biol. Med., 22: 227–249 (1950).
  5. Huang, P.C. ET AL. J. Nutr., 110: 1727–1735 (1980).
  6. Viteri, F.E. & Martinez, C. Integumental nitrogen losses of preschool children with different levels and sources of dietary protein intake. In: Torun, B. et al., ed. Protein-energy requirements of developing countries: Evaluation of new data.. Tokyo, United Nations University, 1981. (Also in FAO Food and Nutrition Bull., 5 (Suppl.): 164–168 (1981)).
  7. Howat, P.M. et al. Am. J. Clin. Nutr., 28: 879–882 (1975).
  8. Korslund, M.K. et al. Am. J. Clin. Nutr., 29: 600–603 (1976).
  9. Zanni, E.D. ET AL. J. Nutr., 109: 573–524 (1979).
  10. Hallberg, L. ET AL. Acta Obstet, Gynaecol. Second., 45: 320–351 (1966).
  11. Calloway, D.H. & Kurzer, M.S. J. Nutr., 112: 356–366 (1982).
  12. Hess, F. Effect of zinc intake and oral contraceptive agents on zinc and nitrogen excretion in young women. Doctoral thesis, Berkeley, University of California, 1976.
  13. Rowe, P.J. The intrauterine device: a review of recent advances and controversies. In: Finn, C.A., ed. Oxford reviews of reproductive biology, Vol. 13. Oxford, Clarendon Press, 1981, pp. 49–94.
  14. Kurzer, M.S. & Calloway, D.H. Am. J. Clin. Nutr., 34: 1305–1313 (1981).
  15. King, J.C. et al. J. Nutr., 103: 772–785 (1973).

Annex 7

 Age (years)
Weight (kg)
BMR/dayc1 2151 2991 3671 4741 5721 6661 7481 789
 5 0845 4355 7206 1676 5776 9717 3147 485
Calculation of energy expenditure 
BMR24 h24 h24 h24 h24 h24 h24 h24 h
 1 2151 2991 3671 4741 5721 6661 7481 789
 5 0845 4355 7206 1676 5776 9717 3147 485
School (+ 0.6 BMR)4 h5 h5 h5 h6 h6 h6 h6 h
 5086797157719871 0461 0971 123
Light activity (+ 0.6 BMR)4 h4 h5 h6 h7 h7 h7 h7 h
 5085447159251 1511 2201 2801 310
Moderate activity6.5 h5.5 h4.5 h3.5 h2.5 h2.5 h2.5 h2.5 h
( + 1.5 BMR)494466384332246260273280
 2 0651 8681 6091 3491 0281 0891 1431 170
High activity (+ 6.0 BMR)0.5 h0.5 h0.5 h0.5 h0.5 h0.5 h0.5 h0.5 h
Daily growthd   62   71   78   90   101   55   30   31
Total daily energy2 1402 2442 3142 4452 5922 6972 8012 867
expenditure89539388968110 23010 84711 28311 72111 997
Daily energy expenditure/   66.5   60.6   56.6   52.0   49.3   47.0   44.7   44.1
kg body weight278.0253.7236.7217.7206.1195.0186.9184.6
Weight (kg)33.738.744.048.851.453.054.054.4
BMR/dayc1 1571 2181 2821 3411 3731 3931 4051 410
 4 8415 0965 3645 6115 7455 8285 8795 899
Calculation of energy expenditure 
BMR24 h24 h24 h24 h24 h24 h24 h24 h
 1 1571 2181 2821 3411 3731 3931 4051 410
 4 8415 0965 3645 6115 7455 8285 8795 899
School (+0.5 BMR)4 h5 h5 h5 h6 h6 h6 h6 h
Light activity (+0.5 BMR)4 h4 h5 h6 h7 h7 h7 h7 h
Moderate activity6.5 h5.5 h4.5 h3.5 h2.5 h2.5 h2.5 h2.5 h
(+1.2 BMR)376335288235172174175176
 1 5721 4021 205983719729734738
High activity (+5.0 BMR)0.5 h0.5 h0.5 h0.5 h0.5 h0.5 h0.5 h0.5 h
Daily growthd   64   74   84   93   98   51   26   26
Total daily energy1 9101 9822 0542 1172158214021332142
Daily energy expenditure/   56.7   51.2   46.7   43.4   42.0   40.4   39.5 39.4
kg body weight237.2214.3195.3181.5175.7169.0165.3164.7

a The figures in italics give the daily duration of the activity in question; the balance, up to 24 h, is made up by the period of sleep (1.0 BMR). The figures in bold type give the amount of energy in kcalth and those in ordinary type(unless otherwise stated) the amount of energy in kJ.
b In calculating the total daily energy expenditure, the BMR is applied to the whole 24 h, additional amounts being added for the various specified types of activity, e.g., for boys aged 10.5 years, + 0.6 BMR for 4 h of light activity.
c BMR (kcalth/day): for boys = 17.5 W + 651; for girls = 12.2 W + 746.
d The energy expenditure on growth was taken as 8 kJ/kg of body weight at 10–15 years; 4 kJ/kg at 15 years;and 2 kJ/kg at 16–18 years.

Annex 8

In section 9 it was suggested that catch-up growth requires a relatively greater increase in the supply of protein than of energy. The expected rate of catch-up in weight at any given level of protein intake can be calculated from a simple model if it is assumed:

  1. that protein is limiting;
  2. that the amount of N available for tissue gain depends on the difference between the intake and the average maintenance requirement;
  3. that the daily intake of protein (g/day) is fixed at a certain level.

For children, the levels shown in the examples (Fig. 2 of this Annex) correspond to one or other of the strategies set out in Table 52.

If I = protein intake (g/day);
F = efficiency of utilization of protein for tissue deposition (taken as 0.7 — see section 6.3.2);
A = grams of tissue deposited per gram of protein retained (taken as 7.0, corresponding to a protein content of 14.3%);
M = maintenance requirement, grams protein/gram body weight;
Wt = weight (grams) at time t;

Then dW/dt = AF(I - MW) and
Wt = I/M + Cexp(-pt)
where C is the constant of integration, and p = A × F × M.

This expression generates the curves shown in Fig. 1 and 2.

Fig. 1. Expected rate of weight gain of an adult, height 1.78 m, median Wt for Ht 70 kg (BMI 22), actual weight 50 kg (BMI 15.7)

Fig. 1

• Protein intake based on median Wt for Ht = 0.75 × 70 g/day = 52.5 g/day.
• The dotted line represents the lower level of acceptable Wt for Ht (BMI 19).
• The curve shows that it takes 4 months to enter the zone of acceptable weight, and 10 months to reach median Wt for Ht. The curve eventually reaches a weight of more than 70 kg because the intake represents the safe level, whereas the value used for the maintenance requirement is the average (100 mg N/kg per day).

Fig. 2. Expected rate of weight gain of a child aged 2 years, initial weight 9 kg, height/age 1 year, at 3 levels of protein intake (see Table 51)

Fig. 2
  1. Protein requirement per kg appropriate for chronological age: 1.15 g/kg; Maintenance requirement per kg appropriate for chronological age: 110 mg N/kg = 0.69 g protein/kg; Total intake based on actual body weight = 10.35 g/day (1.15 × 9.0)
  2. As for A, but total protein intake calculated on basis of median Wt for age (12.6 kg) = 14.5 g/day (1.15 × 12.6)
  3. Protein requirement per kg appropriate for height/age: 1.37 g/kg; Maintenance requirement per kg appropriate for height/age: 120 mg N/kg = 0.75 g protein/kg; Total intake based on median weight for height (9.8 kg) = 13.4 g/day

Curve C represents the approach recommended by the 1977 informal consultation.1 If no further setbacks occur, satisfactory catch-up would be achieved in 5–6 months.

An example, for the conditions illustrated by Curve A of Fig. 2, would be:

At t = 0, W = 9 × 103 g
I = 10.35 g/day
M = 0.69 × 10-3 grams/gram body weight/day.

Therefore, I/M = 15 × 103 g. The exponential term = 1, therefore, C = -6 × 103 g.

1 World Health Organization. Protein and energy requirements: a joint FAO/WHO memorandum. Bulletin of the World Health Organization, 57: 65–79 (1979).

At infinite time W = I/M = 15 × 103 g. This is the limit to which the weight tends at a fixed protein intake. For intermediate times the value of p, in the given conditions, is 7 × 0.7 × 0.69 × 10-3 = 0.0034/day.

Annex 9

A. Derivation of reference PE ratio, individual diets

The following equation1 will provide an estimate of the PE ratio that ensures, with whatever probability is desired, that a diet with the calculated PE ratio will meet or exceed the actual protein requirements on the condition that enough is consumed to meet the energy requirements of the randomly selected individual. For explanation and comment on interpretation, see section 10.

Fig. 2


is the value of the PE ratio requirement that would be expected to be exceeded by a certain proportion (α) of individuals (changing α alters the probability of adequacy or inadequacy of the ratio for the random individual).
is the standardized normal deviation above which α of the distribution lies (e.g., Z.025 = 1.96).
E is the average energy requirement for the specified class of individual (specified by age, weight, activity, etc.).
P is the average protein requirement for the specified class of individual, expressed as energy equivalents.
SE is the standard deviation of energy requirements.
SP is the standard deviation of protein requirements.
r is the correlation between energy and protein requirements among individuals in the specified class.

(Note that the equation is written in two parts only for convenience).

1 Derived from the equations presented in: Beaton, G.H. & Swiss, L.D. Evaluation of the nutritional quality of food supplies: prediction of “desirable” or “safe” protein : calorie ratios. American journal of clinical nutrition, 27: 485–504 (1974). (Based on the arguments and approach of Lorstad, M. FAO Nutritional Newsletter, 9 (No. 1): 18 (1971).

B. Derivation of variance for protein requirement per person per day: estimation of the variance of a product.

The coefficient of variation of protein requirement is 12.5% when requirement is expressed as g/kg per day. If weight is omitted from this expression and requirement is expressed as g/day referring to a group of persons with differing weights, the variance and coefficient of variation will increase since there are now two sources of variation —requirement per unit weight and weight. Statistical estimates of the new variance can be obtained as outlined below.

If weight and requirement are not correlated, and
R = [RW × W] + [r × V(W) × V(RW], if the correlation between them is r, given a knowledge of
W mean weight of the group
V(W) variance of the weight within the group
RW mean requirement per unit body weight
V(RW) variance of the requirement per unit body weight (in the case of protein this would be 12.5% of the mean requirement)
then R, mean requirement per day, may be calculated as R = RW × W.

Further, V(R) variance of the requirement per day, may be calculated by the following equations:

  1. If weight and requirement per kg are not correlated, then V(R) = RW2 × V(W) + W2 × + V(RW) + V(W) × V(RW)
  2. If weight and requirement per kg are correlated, then an approximate estimate can be obtained
Fig. 2

Some caution must be exercised in the use and interpretation of V(R). First, although equation (i) is an exact equation given no correlation, equation (ii) is an approximation only.1 Perhaps more important, it is unlikely that the distribution of a product of two variables will be Gaussian. Therefore the mean ± a constant times the standard deviation may not be readily interpretable as covering a fixed percentage of the population, as in the probability approach described in section 11. (As presented, that approach assumes that requirement has an essentially normal distribution). However, on an empirical basis it is found that if weight and requirement per unit weight both have distributions close to normal, and if the variances are small in comparison to the means (low CVs) then the distribution of the product, requirement per person per day, gives a reasonable approximation of the Gaussian distribution and may be used in the probability approach. The shapes of the original distributions are important. If actual weights are known, it would be much better to describe intakes and requirements per unit body weight and to make interpretive judgements on that base.

1 For a more exact expression, see Mood, A.M. et al. Introduction to the theory of statistics, 3rd ed. New York, McGraw-Hill, 1973.

Two examples are offered, assuming a Gaussian distribution and no correlation between requirement per kg and body weight. Consider adult men with an average body weight of 70 kg and an average protein requirement of 0.6 g/kg per day. The CV of requirement in this unit is 12.5%. If the CV of body weight is 10%, then the mean protein requirement would be 42 g per day, with a CV of about 16%. The safe level of protein intake would be about 55 g/day rather than the 52.5 g/day that might have been assumed. If the CV of body weight were 15%, then the CV of requirement per person per day would increase to about 19.5% and the safe level of intake would increase to about 58 g/day. To generate probability statements, the intervals shown in Table 54 would have to be adjusted to reflect the new CV estimates.

In working with children, the statistical issues are somewhat more complex since the protein requirement per kg body weight changes with age. If all children in the interest group were the same age, then the approach would be the same as described above for adults. However, if different ages are included in the group then consideration would have to be given to including still another component of variance (age) and to recognition that, across age, there would be some relationship between mean body weight and protein requirement per kg. In older children it is likely that these effects could be ignored and only the distribution of weights need be considered. In young children, when protein requirements per kg change rapidly with age, the effects of age would have to be considered.

C. Some considerations relevant to the impact of variability of activity on the estimated variability of energy requirement

The present report adopts a factorial approach to the estimation of energy requirements. That is, for adults, total energy requirement is estimated as the sum of energy needed for BMR and the additional energy needed for specific activities. BMR is predictable from a knowledge of the age, sex, and body size of the individual (Table 5 and Annex 1). The additional costs of specific activities are estimated from a knowledge of the time spent in various activities and the estimated energy cost of those activities (Annex 5). The report suggests that the variance of BMR has a CV of about 12.5% and that this may be a reasonable descriptor of the variability of energy requirement of any specific activity expressed as a multiple of BMR. Thus, for the individual for whom a record of actual activities is available, it is reasonable to assume that the CV attached to the total energy requirement estimate is about 12.5%.

However, at present there are limited data describing the profiles of activities for different individuals. For that reason, there are not available good estimates of the variability that should be associated with groups of individuals performing different profiles of activity -or the variance that should be attached to any assumption of an average energy expenditure for activity. Below, the potential impact of this gap in present information is discussed.

The report presents examples of estimated total energy expenditures associated with various types of occupation (Section 6.1, Tables 10–13). These suggest that total mean requirements may range between 1.5 and 2.1 BMR or that the additional cost of activities above basal metabolic rate may be 0.5 to 1.1 BMR (group means). Using this as an extreme example of the range that might exist in a population group, some estimates can be made for the worst case situation:

where is the average total energy expenditure for a population in which the average additional cost of activity is 0.75 BMR and it is assumed that:

  1. the coefficient of variation of is 12.5% and hence the standard deviation is 0.125
  2. the standard deviation associated with the factor 0.75 is ± 0.375. The variance of this term may be calculated as the variance of a product assuming no correlation (Annex 9 (B)).

Then the variance of E estimated as the sum of the variances of the two terms of the equation, again assuming no correlation, would be:

and the coefficient of variation of total energy requirement would be:

In this worst-case situation, where it is assumed that the CV of the additional costs of activity is 50% of the average additional cost, and in which a fairly high average additional cost is assumed, the predicted impact would be to raise the coefficient of variation from 12.5% to about 23%.1 A variability estimate of this order of magnitude seems consistent with information in the literature although direct comparison is not justified. The observed variance would be affected by the actual range of activities involved and by the range of weights of the individuals performing them.

This may be a measure of the potential impact of having to assume an average profile of activity rather than having detailed information about the individuals.

As for studies of food intake, the activity descriptors must describe patterns of “usual activity” persisting over moderate periods of time. If information is available only for activity (and energy expenditure) on a single day, there is likely to be a major error in the description of usual energy needs attributable to intraindividual variation (see discussion of time-frame of requirement and intake, section 11.3).

1 If it is assumed that there is a correlation between basal metabolism (B) and the additional need for activity (A) then the correct equation for the estimation of the variance of the sum would be:

V(R) = V(B) + V(A) + 2 Corr(B,A) × SD(B) × SD(A)

Such an assumption would be reasonable if it is believed that the relative efficiency of energy metabolism is comparable in the maintenance and activity components of total requirement. (This may be taken as implicit in the approach used to describe energy requirement as multiples of BMR but there is no direct experimental evidence to support it). Perfect correlation (r = 1) would raise the CV to 30.4%.

Annex 10


Dr T. Atinmo, Department of Human Nutrition, University of Ibadan, Ibadan, Nigeria

Professor G.H. Beaton, Professor and Chairman, Department of Nutrition and Food Science, Faculty of Medicine, University of Toronto, Toronto, Ontario, Canada

Dr D. Calloway, Professor of Nutrition and Chairman, Department of Nutrition Sciences, University of California, Berkeley, CA, USA

Dr Chen Xue-cun, Institute of Health, Chinese Academy of Medical Sciences, Beijing, China

Professor G. Debry, Department of Nutrition and Metabolic Disorders, University of Nancy, Nancy, France

Professor J. Durnin, Department of Physiology, University of Glasgow, Glasgow, Scotland

Dr A. Ferro-Luzzi, National Institute of Nutrition, Rome, Italy

Dr G.B. Forbes, Professor of Pediatrics, The University of Rochester Medical Center, Rochester, NY, USA

Dr L. Garby, Department of Physiology, Odense University, Odense, Denmark

Dr G. Inoue, Department of Nutrition, School of Medicine, Tokushima City, Tokushima Prefecture, Japan

Dr H. Munro, Human Nutrition Research Centre on Aging at Tuft's University, Boston, MA, USA (Rapporteur)

Dr I. Ozalp, Hacettepe University, Department of Biochemistry, Faculty of Medicine, Haceteppe, Ankara, Turkey

Dr J. Parizkova, Research Institute FTVS, Charles University, Prague, Czechoslovakia

Dr S.G. Srikantia, Jayalakshmipuram, Mysore, India

Dr Kraisid Tontisirin, Institute of Nutrition, c/o Ramathibodi Hospital, Mahidol University, Bangkok, Thailand

Dr B. Torún, Chief, Division of Biology and Human Nutrition, Institute of Nutrition of Central America and Panama (INCAP), Guatemala, Guatemala

Dr R. Uauy, Institute of Nutrition and Food Technology (INTA), University of Chile, Santiago, Chile

Professor J.C. Waterlow, Professor of Human Nutrition, London School of Hygiene and Tropical Medicine, London, England (Chairman)

Dr R.C. Whitehead, Director, MRC Dunn Nutrition Unit, Dunn Nutritional Laboratory, Cambridge, England

Dr V. Young, Department of Nutrition and Food Science, Massachusetts Institute of Technology, Cambridge, MA, USA


Dr H.J.L. Burgess, Secretary, ACC Sub-Committee on Nutrition, Food and Agriculture Organization of the United Nations, Rome, Italy

Professor Dr F. Fidanza, Institute of Nutrition and Food Science, Perugia, Italy


Dr M. Béhar, Chief, Nutrition, WHO, Geneva, Switzerland

Dr E.M. DeMaeyer, Medical Officer, Nutrition, WHO, Geneva, Switzerland (Joint Secretary)

Dr P. François, Nutrition Officer, Nutrition Planning Assessment and Evaluation Service, FAO, Rome, Italy

Dr W. James, Assistant Director, Dunn Nutritional Laboratory, Cambridge, England (Temporary Adviser)

Dr W. Keller, Medical Officer, Nutrition, WHO, Geneva, Switzerland (Joint Secretary)

Dr P. Lunven, Chief, Nutrition Planning Assessment and Evaluation Service, FAO, Rome, Italy

Mr L. Naiken, Statistics Officer, Statistics Division, FAO, Rome, Italy

Dr C.L. Quance, Director, Statistics Division, FAO, Rome, Italy

Dr J. Périssé, Senior Officer, Nutrition Planning, Assessment and Evaluation Service, FAO, Rome, Italy (Joint Secretary)

Dr W.M. Rand, Research Coordinator UNU/WHP, Massachusetts Institute of Technology, Cambridge, MA, USA (Temporary Adviser)

Dr Z.I. Sabry, Director, Food Policy and Nutrition Division, FAO, Rome, Italy

Dr N. Scrimshaw, Senior Advisor, World Hunger Programme, UNU, Massachusetts Institute of Technology, Cambridge, MA, USA

Dr V. Valverde, Division of Human Development, Institute of Nutrition of Central America and Panama, Guatemala CA, Guatemala (Temporary Adviser)

Dr R. Weisell, Nutrition Officer, Nutrition Planning, Assessment and Evaluation Service, FAO, Rome, Italy


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