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Equations to predict estimated energy requirements

Equations to predict estimated energy requirements
Children with healthy body weight
Girls 3 through 8 years:
Estimated energy requirements (kcal/d) = 135.3 – (30.8 × age [years]) + PA × (10 × weight [kg] + 934 × height [m]) + 20, where:
PA = 1.00 if sedentary (PAL ≥1.0 and <1.4)
PA = 1.16 if low active (PAL ≥1.4 and <1.6)
PA = 1.31 if active (PAL ≥1.6 and <1.9)
PA = 1.56 if very active (PAL ≥1.9 and <2.5)
The factor of 20 is included to account for the energy expended in tissue synthesis due to growth.
Boys 3 through 8 years:
Estimated energy requirements (kcal/d) = 88.5 – (61.9 × age [years]) + PA × (26.7 × weight [kg] + 903 × height [m]) + 20, where:
PA = 1.00 if sedentary (PAL ≥1.0 and <1.4)
PA = 1.13 if low active (PAL ≥1.4 and <1.6)
PA = 1.26 if active (PAL ≥1.6 and <1.9)
PA = 1.42 if very active (PAL ≥1.9 and <2.5)
The factor of 20 is included to account for the energy expended in tissue synthesis due to growth.
Girls 9 through 18 years:
Estimated energy requirements (kcal/d) = 135.3 – (30.8 × age [years]) + PA × (10.0 × weight [kg] + 934 × height [m]) + 25, where:
PA = 1.00 if sedentary (PAL ≥1.0 and <1.4)
PA = 1.16 if low active (PAL ≥1.4 and <1.6)
PA = 1.31 if active (PAL ≥1.6 and <1.9)
PA = 1.56 if very active (PAL ≥1.9 and <2.5)
The factor of 25 is included to account for the energy expended in tissue synthesis due to growth.
Boys 9 through 18 years:
Estimated energy requirements (kcal/d) = 88.5 – (61.9 × age [years]) + PA × (26.7 × weight [kg] + 903 × height [m]) + 25, where:
PA = 1.00 if sedentary (PAL ≥1.0 and <1.4)
PA = 1.13 if low active (PAL ≥1.4 and <1.6)
PA = 1.26 if active (PAL ≥1.6 and <1.9)
PA = 1.42 if very active (PAL ≥1.9 and <2.5)
The factor of 25 is included to account for the energy expended in tissue synthesis due to growth.
Children who are overweight or obese
Girls 3 through 18 years:
Total energy expenditure (kcal/day) = 389 – (41.2 × age [years]) + PA × (15.0 × weight [kg] + 701.6 × height [m]), where:
PA = 1.00 if sedentary (PAL ≥1.0 and <1.4)
PA = 1.18 if low active (PAL ≥1.4 and <1.6)
PA = 1.35 if active (PAL ≥1.6 and <1.9)
PA = 1.60 if very active (PAL ≥1.9 and <2.5)
This equation is intended to predict energy needs for weight maintenance and thus does not include a factor for the energy cost of growth.
Boys 3 through 18 years:
Total energy expenditure (kcal/day) = 114 – (50.9 × age [years]) + PA × (19.5 × Weight [kg] + 1161.4 × height [m]), where:
PA = 1.00 if sedentary (PAL ≥1.0 and <1.4)
PA = 1.12 if low active (PAL ≥1.4 and <1.6)
PA = 1.24 if active (PAL ≥1.6 and <1.9)
PA = 1.45 if very active (PAL ≥1.9 and <2.5)
This equation is intended to predict energy needs for weight maintenance and thus does not include a factor for the energy cost of growth.
These equations were developed by the National Academy (Institute) of Medicine, based on measurements by the doubly labeled water method, plus an average of 20 or 25 kcal/d for the energy deposited in newly synthesized tissues, based on rates of weight gains from the Fels Longitudinal Study.

Physical activity levels (PALs) are defined as follows: 
  • Sedentary (PAL ≥1 to <1.4, where PAL is a multiple of the basal metabolic rate) means a lifestyle that includes only the light physical activity associated with daily life, such as eating, sleeping, and walking around home and school.
  • Low active (PAL ≥1.4 to <1.6) means a lifestyle that includes physical activity equivalent to walking approximately 120 min at a rate of 2.5 mph or equivalent energy expenditure in other activities, in addition to that described for the sedentary level.
  • Active (PAL ≥1.6 to <1.9) means a lifestyle that includes physical activity equivalent to walking  approximately 230 min at a rate of 2.5 mph or equivalent energy expenditure in other activities, in addition to that described for the sedentary level. 
  • Very active (PAL ≥1.9 to <2.5) means a lifestyle that includes physical activity equivalent to walking approximately 400 min at a rate of 2.5 mph or equivalent energy expenditure in other activities, in addition to that described for the sedentary level. 
In general, children in the active or very active PAL categories are participating in moderate or vigorous activities, in addition to walking at 2.5 mph. The activity level is optimally estimated by recording an activity diary and calculating the PAL by applying the Youth Metabolic Equivalent (METy) to each activity. Refer to UpToDate content on estimation of dietary energy requirements in children.
PA: physical activity factor; PAL: physical activity level (expressed as multiples of the basal metabolic rate).
Data from: National Academy (Institute) of Medicine. Dietary Reference Intakes for Energy, Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and Amino Acids. National Academy of Science 2005. Available at: https://www.nap.edu/read/10490/chapter/7
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