Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.
BMR, Mifflin-St Jeor equation, men
Mifflin-St Jeor mode, for men
- BMR
- energy used at rest, in calories a day (the paper calls it resting energy expenditure)
- W
- weight in kg
- H
- height in cm
- A
- age in years
For all three BMR equations, Imperial entries are converted first (lb × 0.453592, in × 2.54).
Source: Uses the formula in Mifflin and colleagues (1990) [1]. How it compares with measured resting energy use is in Frankenfield and colleagues (2005) [2]. The conversion factors are NIST's, rounded [3].
BMR, Mifflin-St Jeor equation, women
Mifflin-St Jeor mode, for women
- BMR
- energy used at rest, in calories a day (the paper calls it resting energy expenditure)
- W
- weight in kg
- H
- height in cm
- A
- age in years
Source: Uses the formula in Mifflin and colleagues (1990) [1], as for men.
BMR, revised Harris-Benedict equation, men
Harris-Benedict (revised) mode, for men
- BMR
- energy used at rest, in calories a day
- W
- weight in kg
- H
- height in cm
- A
- age in years
A 1984 re-fit of the Harris-Benedict data that added Benedict's 1928 and 1935 subjects.
Source: Uses the formula in Roza and Shizgal (1984), Table 3, equation 3 [4].
BMR, revised Harris-Benedict equation, women
Harris-Benedict (revised) mode, for women
- BMR
- energy used at rest, in calories a day
- W
- weight in kg
- H
- height in cm
- A
- age in years
Source: Uses the formula in Roza and Shizgal (1984), Table 3, equation 6 [4].
BMR, Katch-McArdle equation
Katch-McArdle mode, with a body fat percentage
- BMR
- energy used at rest, in calories a day
- LBM
- lean (fat-free) body mass in kg
- W
- weight in kg
- BF%
- the body fat percentage you enter
Without a usable body fat percentage (blank, 0, or 100 and over), the calculator uses Mifflin-St Jeor instead and says so.
Source: Uses the general equation in Cunningham (1991) [5]; the calculator calls it Katch-McArdle. Its accuracy in athletes was reviewed in 2023 [6]. The lean body mass line is a standard formula; no single publisher.
Total daily energy expenditure
Every mode
- TDEE
- total daily energy expenditure, in calories a day
- BMR
- from the equation above
- AF
- activity factor: Sedentary 1.2, Light Activity 1.375, Moderate Activity 1.55, Active 1.725, Very Active 1.9
A custom activity multiplier, when you set one, replaces AF. The calories at each activity level multiply BMR by each of the five factors.
Source: The five activity factors are widely used; no primary source found. Searched: the Harris and Benedict (1918), Mifflin and colleagues (1990) and Roza and Shizgal (1984) papers, the 1989 US Recommended Dietary Allowances, the FAO/WHO/UNU reports of 1985 and 2004, the National Academies' 2023 energy report [7], PubMed and Europe PMC.
Goal calories, Weight Loss
Weight Loss mode
- Goal Calories
- the daily calories for the goal
- TDEE
- from the formula above
Source: A 500 calorie daily deficit is one of the options in a 2013 US clinical guideline for adults with overweight or obesity [8].
Goal calories, Weight Gain
Weight Gain mode
- Goal Calories
- the daily calories for the goal
- TDEE
- from the formula above
Source: The 500 calorie surplus: no primary source found. Searched: the 2017 position stand of the International Society of Sports Nutrition on diets and body composition, which gives no surplus figure.
Planning bands
Weight Loss and Weight Gain modes
- band calories
- the daily calories for the band
- TDEE
- from the formula above
- offset
- the daily change for the band, in calories
- Conservative (loss)
- 300 calories below TDEE
- Moderate (loss)
- 500 calories below TDEE
- Aggressive (loss)
- 700 calories below TDEE
- Lean Gain
- 200 calories above TDEE
- Moderate (gain)
- 350 calories above TDEE
- Fast Gain
- 500 calories above TDEE
The weekly change shown for a band is the offset × 7 ÷ 7,700 calories per kg (Metric, the 3,500 per lb rule in kilograms, rounded) or ÷ 3,500 calories per lb (Imperial). Maintenance shows TDEE alone. The calculator notes a loss target below 1,200 calories a day for women or 1,500 for men, the low ends of the guideline's weight-loss ranges [8]: the loss bands when the goal is Weight Loss, otherwise the Weight Loss figure. Under 800 calories it adds the guideline's line that it keeps diets under 800 calories a day for medical settings with supervision.
Source: Based on a 2013 US clinical guideline's 500 calorie deficit [8] and the NHLBI's 1998 ranges for adults with a BMI of 27 or more, 300 to 500 and 500 to 1,000 calories a day [9]. The weekly change uses the 3,500 calories per pound rule in Wishnofsky (1958) [10]; its limits are in Hall and colleagues (2011) [11]. No primary source was found for the gain offsets.
Sources
- Mifflin MD, St Jeor ST, Hill LA, Scott BJ, Daugherty SA, Koh YO. A new predictive equation for resting energy expenditure in healthy individuals. American Journal of Clinical Nutrition, 1990; 51(2): 241-247.
- Frankenfield D, Roth-Yousey L, Compher C. Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review. Journal of the American Dietetic Association, 2005; 105(5): 775-789.
- National Institute of Standards and Technology. NIST Guide to the SI, Appendix B.9: Factors for units listed by kind of quantity or field of science, length and mass. Special Publication 811.
- Roza AM, Shizgal HM. The Harris Benedict equation reevaluated: resting energy requirements and the body cell mass, Table 3, equations 3 and 6. American Journal of Clinical Nutrition, 1984; 40(1): 168-182.
- Cunningham JJ. Body composition as a determinant of energy expenditure: a synthetic review and a proposed general prediction equation. American Journal of Clinical Nutrition, 1991; 54(6): 963-969.
- O'Neill JER, Corish CA, Horner K. Accuracy of Resting Metabolic Rate Prediction Equations in Athletes: A Systematic Review with Meta-analysis. Sports Medicine, 2023; 53(12): 2373-2398.
- National Academies of Sciences, Engineering, and Medicine. Dietary Reference Intakes for Energy, chapter 5, Table 5-4 and the text on physical activity levels. 2023.
- Jensen MD, Ryan DH, Apovian CM, et al. 2013 AHA/ACC/TOS guideline for the management of overweight and obesity in adults: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines and The Obesity Society, recommendation 3a, diets for weight loss. Circulation, 2014; 129(25 Suppl 2): S102-S138.
- National Heart, Lung, and Blood Institute. Clinical Guidelines on the Identification, Evaluation, and Treatment of Overweight and Obesity in Adults: The Evidence Report, pages 72 and 74 (pages 104 and 106 of the PDF). NIH Publication No. 98-4083, September 1998.
- Wishnofsky M. Caloric equivalents of gained or lost weight, summary, page 546. American Journal of Clinical Nutrition, 1958; 6(5): 542-546.
- Hall KD, Sacks G, Chandramohan D, et al. Quantification of the effect of energy imbalance on bodyweight. The Lancet, 2011; 378(9793): 826-837.
What this calculator does not cover
- The Mifflin-St Jeor equation was derived from adults aged 19 to 78 [1], but the calculator accepts any age from 1 to 120.
- It has no inputs for pregnancy or breastfeeding, and it does not account for medical conditions or medicines that change energy use.
- The equations estimate an average. A 2005 review found notable individual errors, and older adults and US ethnic minorities were underrepresented in the studies [2].
- Katch-McArdle is only as good as the body fat percentage entered. In a 2023 review of studies in athletes, every equation's results varied widely between studies [6].
- The weekly change of each planning band is a straight line. Real change slows: about half of the eventual weight change from a lasting change in intake comes in the first year [11].
- The National Academies' 2023 energy report removed physical activity levels (total energy ÷ basal energy) above 2.5 as unsustainable [7]. The custom multiplier here accepts up to 3.0.
Sources checked on .