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Methodology

Updated · 31 sections

Every formula, constant and threshold this site displays, written out in full with its primary source. Where a number we show has no primary source (because it is a convention, an industry habit, or a rule we set ourselves), this page says so in the section that uses it. Nothing is left off to make the page look tidier.

The engine behind every calculator is a single set of pure functions: no framework, no network, no database. The same code runs on our server to render a result into the page and in your browser when you change an input, so the two can never disagree. Full float precision is carried through every calculation and rounded only at the moment of display. Each function is covered by locked test vectors (hand-computed from the published formula, with the arithmetic written into the test) plus boundary cases and an impossible-input case, and the whole suite has to pass before anything ships. Where two published forms of a formula exist, the tests cross-check one against the other.

The full bibliography, grouped by topic, is on the references page. How we decide what belongs on a page is set out in our editorial policy, and every substantive correction is logged in the changelog.

BMI and classification

Body mass index and its classification systems

BMI = weight (kg) ÷ height (m)²

WHO standard international bands: under 16.0 severe thinness; 16.0–16.9 moderate thinness; 17.0–18.4 mild thinness; 18.5–24.9 normal range; 25.0–29.9 overweight (pre-obese); 30.0–34.9 obese class I; 35.0–39.9 obese class II; 40.0 and above obese class III.

WHO Asia-Pacific (WPRO 2000) bands: under 18.5 underweight; 18.5–22.9 normal range; 23.0–24.9 overweight (at risk); 25.0–29.9 obese class I; 30.0 and above obese class II.

WHO 2004 public-health action points: 23.0, 27.5, 32.5 and 37.5. These sit alongside the retained international cut-offs; they are triggers for public-health action, not a fourth category table.

Healthy weight range for a height = 18.5 × height (m)² to 24.9 × height (m)²

The three systems are shown separately and labelled separately. Merging WPRO 2000 with the 2004 action points into one table is a common error, and it produces cut-offs that no body ever published.

Multi-measure excess-adiposity screen

Criteria: BMI ≥ 25 plus at least one elevated fat-distribution measure, namely waist circumference at the WHO thresholds, waist-to-hip ≥ 0.90 (male) or ≥ 0.85 (female), or waist-to-height ≥ 0.50. BMI ≥ 40 on its own also meets the criteria.

The clinical versus preclinical distinction requires an assessment of organ function and is deliberately out of scope here.

BMI Prime, ponderal index and weight-change percentage

BMI Prime = BMI ÷ 25, so 1.00 is exactly the overweight threshold

Ponderal index = weight (kg) ÷ height (m)³, typically 11–15 in adults

Weight change (%) = (starting weight − current weight) ÷ starting weight × 100

Milestones shown: 3%, 5%, 7%, 10%, 15% and 20% of starting weight

No primary source for part of this section. The ponderal index is Rohrer's (1921), and the typical adult range of 11–15 is a descriptive convention: we could not find a citable modern reference range for it, so read the range as orientation rather than as a threshold. The 3%, 7%, 15% and 20% milestones are round numbers we show for context. Only the 5% and 10% marks carry the evidence cited below.

  • Gadzik J. "How much should I weigh?" Quetelet's equation, upper weight limits, and BMI prime. Conn Med 2006;70:81–8. pubmed.ncbi.nlm.nih.gov/16768059/
  • NICE. Obesity: identification, assessment and management. Clinical guideline CG189, 2014 (updated 2023); superseded by NG246. www.nice.org.uk/guidance/cg189
  • Magkos F, Fraterrigo G, Yoshino J, et al. Effects of moderate and subsequent progressive weight loss on metabolic function and adipose tissue biology in humans with obesity. Cell Metab 2016;23:591–601. doi.org/10.1016/j.cmet.2016.02.005
  • Wing RR, Lang W, Wadden TA, et al. Benefits of modest weight loss in improving cardiovascular risk factors in overweight and obese individuals with type 2 diabetes. Diabetes Care 2011;34:1481–6. doi.org/10.2337/dc10-2415
  • Bhutani S, Kahn E, Tasali E, Schoeller DA. Composition of two-week change in body weight under unrestricted free-living conditions. Physiol Rep 2017;5:e13336. doi.org/10.14814/phy2.13336

Healthy weight range and the ideal-weight formulas

All four take a base weight at 5 ft (60 in) plus a per-inch increment above it.

Hamwi (1964): 48.0 kg + 2.7 kg/in (male); 45.5 kg + 2.2 kg/in (female)

Devine (1974): 50.0 kg + 2.3 kg/in (male); 45.5 kg + 2.3 kg/in (female)

Robinson (1983): 52.0 kg + 1.9 kg/in (male); 49.0 kg + 1.7 kg/in (female)

Miller (1983): 56.2 kg + 1.41 kg/in (male); 53.1 kg + 1.36 kg/in (female)

The healthy BMI range gets the visual emphasis. None of the four is headlined.

No primary source for part of this section. Hamwi's 1964 formula appeared in a book chapter with no DOI and no stable open record; Pai and Paloucek's review is the citable source for it. All four came out of clinical drug dosing rather than health optimisation, and none was ever validated as a health target.

  • Pai MP, Paloucek FP. The origin of the "ideal" body weight equations. Ann Pharmacother 2000;34:1066–9. doi.org/10.1345/aph.19381
  • Devine BJ. Gentamicin therapy. Drug Intell Clin Pharm 1974;8:650–5, in the journal's Clinical Pharmacy: Case Studies column. doi.org/10.1177/106002807400801104
  • Robinson JD, Lupkiewicz SM, Palenik L, Lopez LM, Ariet M. Determination of ideal body weight for drug dosage calculations. Am J Hosp Pharm 1983;40:1016–9. doi.org/10.1093/ajhp/40.6.1016
  • Miller DR, Carlson JD, Lloyd BJ, Day BJ. Determining ideal body weight (and mass). Am J Hosp Pharm 1983;40:1622–5. doi.org/10.1093/ajhp/40.10.1622a
  • Lemmens HJM, Brodsky JB, Bernstein DP. Estimating ideal body weight: a new formula. Obes Surg 2005;15:1082–3. doi.org/10.1381/0960892054621350
  • The Acute Respiratory Distress Syndrome Network. Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome. N Engl J Med 2000;342:1301–8. doi.org/10.1056/NEJM200005043421801
  • WHO Expert Committee. Physical status: the use and interpretation of anthropometry. WHO Technical Report Series 854. Geneva: World Health Organization, 1995. www.who.int/publications/i/item/9241208546

Body fat and composition

ACE body fat interpretation bands

Male: 2–5% essential fat; 6–13% athletes; 14–17% fitness; 18–24% average; 25% and above obese.

Female: 10–13% essential fat; 14–20% athletes; 21–24% fitness; 25–31% average; 32% and above obese.

In code the boundaries are half-open intervals (for men 2 to under 6, 6 to under 14, 14 to under 18, 18 to under 25, then 25 and above; for women 10 to under 14, 14 to under 21, 21 to under 25, 25 to under 32, then 32 and above), so a value can never fall between two bands.

Below 10% for men and below 16% for women we add a caveat, because the tape method drifts most in very lean people.

No primary source for part of this section. Convention, not a validated instrument. These are the American Council on Exercise's published categories, which ACE distributes in the ACE Personal Trainer Manual. We could not find a stable, free ACE page that reproduces the table, so the attribution is to the organisation rather than to a citable document, and no peer-reviewed derivation of these exact boundaries exists. Gallagher and colleagues (2000) is the closest published attempt at healthy body fat ranges by sex and age, and it does not reproduce the ACE numbers.

Skinfold equations and the density conversions

Jackson–Pollock 3-site, men (chest, abdomen, thigh): D = 1.10938 − 0.0008267·Σ + 0.0000016·Σ² − 0.0002574·age

Jackson–Pollock–Ward 3-site, women (triceps, suprailiac, thigh): D = 1.0994921 − 0.0009929·Σ + 0.0000023·Σ² − 0.0001392·age

Jackson–Pollock 7-site, men: D = 1.112 − 0.00043499·Σ + 0.00000055·Σ² − 0.00028826·age

Jackson–Pollock 7-site, women: D = 1.097 − 0.00046971·Σ + 0.00000056·Σ² − 0.00012828·age

Σ is the sum of the sites in millimetres and D is body density in g/cm³. The 7-site set is chest, midaxillary, triceps, subscapular, abdomen, suprailiac and thigh.

Siri (1961) conversion, the figure we headline: %BF = 495 ÷ D − 450

Brožek (1963) conversion, shown alongside: %BF = 457 ÷ D − 414.2

Any single skinfold over 80 mm is refused: it is beyond the range these equations were fitted on.

Accuracy stated on every result: about ±3–5 percentage points against a DEXA scan, and only with consistent site technique.

Body fat estimated from BMI

Deurenberg (1991): %BF = 1.20·BMI + 0.23·age − 10.8·sex − 5.4, with sex = 1 male, 0 female

CUN-BAE (2012): %BF = −44.988 + 0.503·age + 10.689·sex + 3.172·BMI − 0.026·BMI² + 0.181·BMI·sex − 0.020·BMI·age − 0.005·BMI²·sex + 0.00021·BMI²·age, with sex = 0 male, 1 female

Accuracy stated on every result: about ±4 percentage points for an average build, and materially worse for muscular or very lean people, because BMI is the only body measurement either equation sees.

  • Deurenberg P, Weststrate JA, Seidell JC. Body mass index as a measure of body fatness: age- and sex-specific prediction formulas. Br J Nutr 1991;65:105–14. doi.org/10.1079/BJN19910073
  • Gómez-Ambrosi J, Silva C, Catalán V, et al. Clinical usefulness of a new equation for estimating body fat (CUN-BAE). Diabetes Care 2012;35:383–8. doi.org/10.2337/dc11-1334
  • Deurenberg P, Deurenberg-Yap M, Guricci S. Asians are different from Caucasians and from each other in their body mass index/body fat per cent relationship. Obes Rev 2002;3:141–6. doi.org/10.1046/j.1467-789X.2002.00065.x

Lean mass: Boer, Hume and James

When body fat percentage is known: lean mass = weight × (1 − %BF ÷ 100), and fat mass is the remainder. That is arithmetic, not an estimate.

Boer (1984): male 0.407·kg + 0.267·cm − 19.2; female 0.252·kg + 0.473·cm − 48.3

Hume (1966): male 0.32810·kg + 0.33929·cm − 29.5336; female 0.29569·kg + 0.41813·cm − 43.2933

James (1976): male 1.10·kg − 128·(kg ÷ cm)²; female 1.07·kg − 148·(kg ÷ cm)²

All three are shown side by side with the spread between them, because that spread is the honest uncertainty of predicting lean mass from height and weight alone.

All three were fitted for clinical use (drug dosing and fluid volumes), not for fitness tracking. James drifts low at high body weight because of its squared weight-to-height term, which is why it has been argued against for contrast dosing at high BMI.

Fat-free mass index and its interpretation bands

FFMI = lean mass (kg) ÷ height (m)²

Normalised FFMI = FFMI + 6.1 × (1.8 − height in m), which removes the height bias so people of different heights can be compared

Male bands: under 18 below average; 18 to under 20 average; 20 to under 22 above average; 22 to under 25 muscular; 25 and above at or beyond the natural limit reported in research.

Female bands: under 14 below average; 14 to under 16 average; 16 to under 18 above average; 18 to under 21 muscular; 21 and above exceptionally muscular.

No primary source for part of this section. The women's boundaries are a derived convention, not a citation. Kouri and colleagues studied men only, and the widely quoted ceiling of about 25 is a male figure. Schutz and colleagues published fat-free mass index percentiles for both sexes, but as percentiles rather than as named bands, so the four female boundaries above are our own scaling of the male scheme, and should be read as orientation rather than as a published standard. Where the male bands carry a source, the female bands carry none, deliberately.

  • Kouri EM, Pope HG, Katz DL, Oliva P. Fat-free mass index in users and nonusers of anabolic-androgenic steroids. Clin J Sport Med 1995;5:223–8. doi.org/10.1097/00042752-199510000-00003
  • Schutz Y, Kyle UUG, Pichard C. Fat-free mass index and fat mass index percentiles in Caucasians aged 18–98 y. Int J Obes 2002;26:953–60. doi.org/10.1038/sj.ijo.0802037
  • Fields JB, Jones MT, Kuhlman NM, Magee MK, Feit A, Jagim AR. Fat-free mass index in a large sample of collegiate American football athletes. Int J Exerc Sci 2024;17:129–39. doi.org/10.70252/FGRL8917

Body frame size: the wrist ratio and elbow breadth

Wrist method: r = height (cm) ÷ wrist circumference (cm).

Male: r above 10.4 small frame; 9.6 to 10.4 medium; below 9.6 large.

Female: r above 11.0 small frame; 10.1 to 11.0 medium; below 10.1 large.

Elbow method: elbow breadth in millimetres read against the height row. Below the medium range is a small frame, above it a large frame.

Male medium ranges: 155–161 cm → 64–72 mm; 161–171 cm → 67–72 mm; 171–181 cm → 70–76 mm; 181–191 cm → 70–79 mm; 191–210 cm → 73–83 mm.

Female medium ranges: 145–151 cm → 57–64 mm; 151–161 cm → 57–67 mm; 161–171 cm → 60–70 mm; 171–181 cm → 61–72 mm; 181–200 cm → 64–76 mm.

Heights were converted from the original feet and inches.

No primary source for part of this section. The height-to-wrist ratio is a convention, not a validated instrument: it is a clinical anthropometry rule of thumb with no outcome validation behind the boundaries, and we present it as exactly that. The elbow-breadth bands are the better documented of the two, since they come from the Metropolitan Life height and frame tables as tabulated by Frisancho (1984), but those tables were insurance data, never a health standard.

  • Frisancho AR. New standards of weight and body composition by frame size and height for assessment of nutritional status of adults and the elderly. Am J Clin Nutr 1984;40:808–19. doi.org/10.1093/ajcn/40.4.808
  • Metropolitan Life Insurance Company. 1983 Metropolitan height and weight tables. Stat Bull Metrop Life Insur Co 1983;64:3–9. pubmed.ncbi.nlm.nih.gov/6623350/
  • Capizzi M, Leto G, Petrone A, et al. Wrist circumference is a clinical marker of insulin resistance in overweight and obese children and adolescents. Circulation 2011;123:1757–62. doi.org/10.1161/CIRCULATIONAHA.110.012898
  • Jahangiri Noudeh Y, Hadaegh F, Vatankhah N, et al. Wrist circumference as a novel predictor of diabetes and prediabetes: results of cross-sectional and 8.8-year follow-up studies. J Clin Endocrinol Metab 2013;98:777–84. doi.org/10.1210/jc.2012-2416

Fat distribution

Waist-to-height ratio

WHtR = waist (cm) ÷ height (cm)

Bands: below 0.40 below the healthy range; 0.40–0.49 healthy; 0.50–0.59 increased central adiposity; 0.60 and above further increased.

The waist at the 0.5 line for a given height = height × 0.5, which is the actionable number.

We show Nevill and colleagues because they argue against a threshold we use: a single 0.5 boundary penalises shorter adults. Readers deserve the strongest counter-argument, not only the supporting evidence.

  • NICE. Overweight and obesity management. NICE guideline NG246, published 14 January 2025. www.nice.org.uk/guidance/ng246
  • Ashwell M, Gibson S. Waist-to-height ratio as an indicator of "early health risk": simpler and more predictive than using a "matrix" based on BMI and waist circumference. BMJ Open 2016;6:e010159. doi.org/10.1136/bmjopen-2015-010159
  • Browning LM, Hsieh SD, Ashwell M. A systematic review of waist-to-height ratio as a screening tool for the prediction of cardiovascular disease and diabetes: 0.5 could be a suitable global boundary value. Nutr Res Rev 2010;23:247–69. doi.org/10.1017/S0954422410000144
  • Nevill AM, Leahy GD, Mayhew J, Sandercock GRH, Myers TD, Duncan MJ. "At risk" waist-to-height ratio cut-off points recently adopted by NICE and US Department of Defense will unfairly penalize shorter adults. What is the solution? Obes Res Clin Pract 2023;17:1–8. doi.org/10.1016/j.orcp.2023.01.002
  • Ross R, Neeland IJ, Yamashita S, et al. Waist circumference as a vital sign in clinical practice: a Consensus Statement from the IAS and ICCR Working Group on Visceral Obesity. Nat Rev Endocrinol 2020;16:177–89. doi.org/10.1038/s41574-019-0310-7

Waist-to-hip ratio and waist circumference

WHR = waist (cm) ÷ hip (cm). Substantially increased risk at ≥ 0.90 (male) and ≥ 0.85 (female).

Waist alone, WHO thresholds: increased risk at ≥ 94 cm (male) and ≥ 80 cm (female); substantially increased at ≥ 102 cm (male) and ≥ 88 cm (female).

IDF ethnicity-specific waist thresholds: Europid, Sub-Saharan African, Eastern Mediterranean and Middle Eastern ≥ 94 cm male and ≥ 80 cm female; South Asian, Chinese, South and Central American ≥ 90 cm male and ≥ 80 cm female; Japanese ≥ 90 cm male and ≥ 80 cm female.

  • WHO. Waist circumference and waist–hip ratio: report of a WHO expert consultation, Geneva, 8–11 December 2008. Geneva: World Health Organization, 2011. www.who.int/publications/i/item/9789241501491
  • International Diabetes Federation. The IDF consensus worldwide definition of the metabolic syndrome. Brussels: IDF, 2006. idf.org/media/uploads/2023/05/attachments-30.pdf
  • Alberti KGMM, Zimmet P, Shaw J. Metabolic syndrome: a new world-wide definition. A consensus statement from the International Diabetes Federation. Diabet Med 2006;23:469–80. doi.org/10.1111/j.1464-5491.2006.01858.x
  • Yusuf S, Hawken S, Ôunpuu S, et al. Obesity and the risk of myocardial infarction in 27,000 participants from 52 countries: a case-control study (INTERHEART). Lancet 2005;366:1640–9. doi.org/10.1016/S0140-6736(05)67663-5
  • Ross R, Neeland IJ, Yamashita S, et al. Waist circumference as a vital sign in clinical practice: a Consensus Statement from the IAS and ICCR Working Group on Visceral Obesity. Nat Rev Endocrinol 2020;16:177–89. doi.org/10.1038/s41574-019-0310-7
  • Shungin D, Winkler TW, Croteau-Chonka DC, et al. New genetic loci link adipose and insulin biology to body fat distribution. Nature 2015;518:187–96. doi.org/10.1038/nature14132
  • Greendale GA, Sternfeld B, Huang M, et al. Changes in regional fat distribution and anthropometric measures across the menopause transition. J Clin Endocrinol Metab 2021;106:2520–34. doi.org/10.1210/clinem/dgab389
  • Sahakyan KR, Somers VK, Rodriguez-Escudero JP, et al. Normal-weight central obesity: implications for total and cardiovascular mortality. Ann Intern Med 2015;163:827–35. doi.org/10.7326/M14-2525

Shape indices: RFM, ABSI, BRI, BAI and conicity

Relative Fat Mass = 64 − 20 × (height ÷ waist) for men and 76 − 20 × (height ÷ waist) for women. Published standard error about 5 percentage points.

A Body Shape Index = waist (m) ÷ (BMI^(2/3) × √height (m)). Higher means a waist larger than a person's weight and height predict.

Body Roundness Index = 364.2 − 365.5 × √(1 − ((waist ÷ 2π)² ÷ (0.5 × height)²)), with waist and height in the same unit. It returns nothing when the geometry is impossible.

Body Adiposity Index = hip (cm) ÷ height (m)^1.5 − 18.

Conicity index = waist (m) ÷ (0.109 × √(weight (kg) ÷ height (m))). The 0.109 constant makes a perfect cylinder read 1.00.

BRI bands: below 3.41 very lean shape; 3.41–4.44 lean; 4.45–5.45 average; 5.46–6.90 rounder; 6.91 and above roundest.

ABSI has no published universal cut-off (interpretation is by age- and sex-specific z-scores against a reference population), so we report the value and the direction of association rather than inventing a band. The BRI bands follow the NHANES mortality analysis, in which risk was lowest in the middle of the distribution and higher at both ends, so the lowest band is not the best band. Body Adiposity Index is here because people look for it; later validations found it no better than BMI in many populations, and the page says so.

  • Woolcott OO, Bergman RN. Relative fat mass (RFM) as a new estimator of whole-body fat percentage: a cross-sectional study in American adult individuals. Sci Rep 2018;8:10980. doi.org/10.1038/s41598-018-29362-1
  • Corrêa MM, Facchini LA, Thumé E, et al. External validation of the relative fat mass (RFM) index in adults from north-west Mexico using different reference methods. PLoS One 2019;14:e0226767. doi.org/10.1371/journal.pone.0226767
  • Krakauer NY, Krakauer JC. A new body shape index predicts mortality hazard independently of body mass index. PLoS One 2012;7:e39504. doi.org/10.1371/journal.pone.0039504
  • Thomas DM, Bredlau C, Bosy-Westphal A, et al. Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model. Obesity 2013;21:2264–71. doi.org/10.1002/oby.20408
  • Zhang X, Ma N, Lin Q, et al. Body roundness index and all-cause mortality among US adults. JAMA Netw Open 2024;7:e2415051. doi.org/10.1001/jamanetworkopen.2024.15051
  • Bergman RN, Stefanovski D, Buchanan TA, et al. A better index of body adiposity. Obesity 2011;19:1083–9. doi.org/10.1038/oby.2011.38
  • Valdez R. A simple model-based index of abdominal adiposity. J Clin Epidemiol 1991;44:955–6. doi.org/10.1016/0895-4356(91)90059-I

Energy and intake

Resting and basal metabolism

Mifflin–St Jeor (1990), the default and headline: 10·kg + 6.25·cm − 5·age + 5 (male) or − 161 (female)

Revised Harris–Benedict (Roza & Shizgal 1984): 88.362 + 13.397·kg + 4.799·cm − 5.677·age (male); 447.593 + 9.247·kg + 3.098·cm − 4.330·age (female)

Katch–McArdle, used automatically when body fat percentage is known: 370 + 21.6 × lean mass (kg)

Cunningham (1980), the sharpest for trained people: 500 + 22 × lean mass (kg)

Owen (1986–87), deliberately conservative for sedentary adults: 879 + 10.2·kg (male); 795 + 7.18·kg (female)

Resting metabolic rate sits about 10% above true basal metabolic rate, because it is measured after rest rather than under strict basal conditions.

No primary source for part of this section. Katch–McArdle was published in the Katch, McArdle and Katch Exercise Physiology textbook rather than in a journal, so it has no DOI and no article record to link. Cunningham's lean-mass equation (nearly the same idea, with a journal record behind it) is shown beside it for that reason.

  • Mifflin MD, St Jeor ST, Hill LA, Scott BJ, Daugherty SA, Koh YO. A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr 1990;51:241–7. doi.org/10.1093/ajcn/51.2.241
  • Roza AM, Shizgal HM. The Harris Benedict equation reevaluated: resting energy requirements and the body cell mass. Am J Clin Nutr 1984;40:168–82. doi.org/10.1093/ajcn/40.1.168
  • Harris JA, Benedict FG. A biometric study of human basal metabolism. Proc Natl Acad Sci USA 1918;4:370–3 (the full data appeared in the 1919 Carnegie Institution monograph). doi.org/10.1073/pnas.4.12.370
  • Cunningham JJ. A reanalysis of the factors influencing basal metabolic rate in normal adults. Am J Clin Nutr 1980;33:2372–4. doi.org/10.1093/ajcn/33.11.2372
  • Owen OE, Holup JL, D'Alessio DA, et al. A reappraisal of the caloric requirements of men. Am J Clin Nutr 1987;46:875–85. doi.org/10.1093/ajcn/46.6.875
  • Owen OE, Kavle E, Owen RS, et al. A reappraisal of caloric requirements in healthy women. Am J Clin Nutr 1986;44:1–19. doi.org/10.1093/ajcn/44.1.1
  • Frankenfield D, Roth-Yousey L, Compher C. Comparison of predictive equations for resting metabolic rate in healthy nonobese and obese adults: a systematic review. J Am Diet Assoc 2005;105:775–89. doi.org/10.1016/j.jada.2005.02.005
  • Pontzer H, Yamada Y, Sagayama H, et al. Daily energy expenditure through the human life course. Science 2021;373:808–12. doi.org/10.1126/science.abe5017

Total daily energy expenditure, the activity factors and the error band

TDEE = BMR × activity factor

Factors: 1.200 sedentary (desk job, little or no exercise); 1.375 lightly active (light exercise 1–3 days a week); 1.550 moderately active (moderate exercise 3–5 days); 1.725 very active (hard exercise 6–7 days); 1.900 extra active (physical job or twice-daily training).

Displayed with a ±10–15% band. In code we use the midpoint: low = TDEE × 0.875, high = TDEE × 1.125.

No primary source for part of this section. The five multipliers are a convention. The FAO/WHO/UNU framework defines physical activity levels as lifestyle bands; the specific figures 1.2, 1.375, 1.55, 1.725 and 1.9 are the widely used fitness-industry set rather than numbers that report published. The ±10–15% band is our honesty allowance, not a published confidence interval: non-exercise activity thermogenesis alone can vary by hundreds of calories a day between two people who would tick the same box.

Calorie deficit safety rails

Planning figure: about 7,700 kcal per kilogram of body mass.

Guard 1, rate cap: never faster than 1% of bodyweight per week.

Guard 2, deficit cap: the target is never below 80% of TDEE.

Guard 3, absolute floors: 1,500 kcal a day for men and 1,200 kcal a day for women.

Guard 4, goal floor: a goal weight below BMI 18.5 for the height is refused outright.

Guard 5: under 18, the adult calculation does not run at all.

Guard 6: no days-until-goal countdown is computed anywhere on this site.

These are enforced in the calculation layer, not merely written into the copy. When a guard changes your plan, the result says which one did.

No primary source for part of this section. These rails are this site's editorial policy, not a published standard. No authority publishes "80% of TDEE" or "1% of bodyweight per week" as a rule. Helms and colleagues support a loss rate of roughly 0.5–1% of bodyweight per week for preserving lean mass in trained people, and the 1,200 and 1,500 kcal floors are the conventional lower limits in general dietetic practice, below which a self-directed diet is unlikely to meet micronutrient needs, but we set them, and we would rather say so than dress a house rule as a guideline. The 7,700 kcal per kilogram figure is Wishnofsky's and is known to overstate long-run loss, because expenditure falls as mass falls. Hall and colleagues quantify that, and it is why we cap rates rather than project a finish date.

  • Wishnofsky M. Caloric equivalents of gained or lost weight. Am J Clin Nutr 1958;6:542–6. doi.org/10.1093/ajcn/6.5.542
  • Hall KD, Sacks G, Chandramohan D, et al. Quantification of the effect of energy imbalance on bodyweight. Lancet 2011;378:826–37. doi.org/10.1016/S0140-6736(11)60812-X
  • Helms ER, Aragon AA, Fitschen PJ. Evidence-based recommendations for natural bodybuilding contest preparation: nutrition and supplementation. J Int Soc Sports Nutr 2014;11:20. doi.org/10.1186/1550-2783-11-20
  • Magkos F, Fraterrigo G, Yoshino J, et al. Effects of moderate and subsequent progressive weight loss on metabolic function and adipose tissue biology in humans with obesity. Cell Metab 2016;23:591–601. doi.org/10.1016/j.cmet.2016.02.005

Lean-gain rails

Guard 1: rate capped at 0.5% of bodyweight per week.

Guard 2: surplus capped at 20% above TDEE.

Guard 3: a goal weight above BMI 27.5 for the height is refused for a lean-gain plan.

Guard 4: protein carried through at 1.6–2.2 g per kg of bodyweight per day.

Guidance range shown on the page: 0.25–0.5% of bodyweight per week.

No primary source for part of this section. The BMI 27.5 ceiling on a lean-gain plan is our editorial policy. Nothing published says a bulk must stop there; we set the line because beyond it the word "lean" stops being an honest description of what is being added.

  • Garthe I, Raastad T, Refsnes PE, Sundgot-Borgen J. Effect of nutritional intervention on body composition and performance in elite athletes. Eur J Sport Sci 2013;13:295–303. doi.org/10.1080/17461391.2011.643923
  • Slater GJ, Dieter BP, Marsh DJ, Helms ER, Shaw G, Iraki J. Is an energy surplus required to maximize skeletal muscle hypertrophy associated with resistance training? Front Nutr 2019;6:131. doi.org/10.3389/fnut.2019.00131
  • Iraki J, Fitschen P, Espinar S, Helms E. Nutrition recommendations for bodybuilders in the off-season: a narrative review. Sports 2019;7:154. doi.org/10.3390/sports7070154
  • Morton RW, Murphy KT, McKellar SR, et al. A systematic review, meta-analysis and meta-regression of the effect of protein supplementation on resistance training-induced gains in muscle mass and strength in healthy adults. Br J Sports Med 2018;52:376–84. doi.org/10.1136/bjsports-2017-097608

Macronutrient split and protein

Protein grams = bodyweight (kg) × factor: 1.6 general, 1.8 active, 2.2 cutting or athletic.

Fat grams = the greater of bodyweight (kg) × 0.8 and 20% of calories ÷ 9. Whichever is higher becomes the floor.

Carbohydrate grams = (calories − protein grams × 4 − fat grams × 9) ÷ 4, the remainder.

Redistribution rule: if that remainder comes out negative, we hold 5% of calories as carbohydrate, then scale protein and fat down together, keeping their calorie ratio, to fit the budget. Grams are never shown as negative, and carbohydrate never reads zero while calories remain.

Energy values used: 4 kcal per gram of protein and of carbohydrate, 9 kcal per gram of fat.

No primary source for part of this section. The 0.8 g per kg fat floor and its 20%-of-calories alternative are conventions taken from the lower end of the Institute of Medicine's acceptable macronutrient distribution range for fat (20–35% of energy), applied as a floor so a low-calorie plan cannot strip fat intake to nothing. The 5% carbohydrate reserve in the redistribution rule is ours: it exists so the output stays usable, not to model anything physiological.

  • Morton RW, Murphy KT, McKellar SR, et al. A systematic review, meta-analysis and meta-regression of the effect of protein supplementation on resistance training-induced gains in muscle mass and strength in healthy adults. Br J Sports Med 2018;52:376–84. doi.org/10.1136/bjsports-2017-097608
  • Jäger R, Kerksick CM, Campbell BI, et al. International Society of Sports Nutrition position stand: protein and exercise. J Int Soc Sports Nutr 2017;14:20. doi.org/10.1186/s12970-017-0177-8
  • Helms ER, Aragon AA, Fitschen PJ. Evidence-based recommendations for natural bodybuilding contest preparation: nutrition and supplementation. J Int Soc Sports Nutr 2014;11:20. doi.org/10.1186/1550-2783-11-20
  • Helms ER, Zinn C, Rowlands DS, Brown SR. A systematic review of dietary protein during caloric restriction in resistance trained lean athletes: a case for higher intakes. Int J Sport Nutr Exerc Metab 2014;24:127–38. doi.org/10.1123/ijsnem.2013-0054
  • Schoenfeld BJ, Aragon AA. How much protein can the body use in a single meal for muscle-building? Implications for daily protein distribution. J Int Soc Sports Nutr 2018;15:10. doi.org/10.1186/s12970-018-0215-1
  • Devries MC, Sithamparapillai A, Brimble KS, Banfield L, Morton RW, Phillips SM. Changes in kidney function do not differ between healthy adults consuming higher- compared with lower- or normal-protein diets: a systematic review and meta-analysis. J Nutr 2018;148:1760–75. doi.org/10.1093/jn/nxy197
  • Lim MT, Pan BJ, Toh DWK, Sutanto CN, Kim JE. Animal protein versus plant protein in supporting lean mass and muscle strength: a systematic review and meta-analysis of randomized controlled trials. Nutrients 2021;13:661. doi.org/10.3390/nu13020661
  • Bauer J, Biolo G, Cederholm T, et al. Evidence-based recommendations for optimal dietary protein intake in older people: a position paper from the PROT-AGE Study Group. J Am Med Dir Assoc 2013;14:542–59. doi.org/10.1016/j.jamda.2013.05.021
  • WHO/FAO/UNU Expert Consultation. Protein and amino acid requirements in human nutrition. WHO Technical Report Series 935. Geneva, 2007. iris.who.int/handle/10665/43411
  • Institute of Medicine. Dietary Reference Intakes for Energy, Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and Amino Acids. Washington DC: National Academies Press, 2005. doi.org/10.17226/10490
  • Institute of Medicine. Dietary Reference Intakes summary tables (fibre adequate intake 38 g/day for men, 25 g/day for women). Washington DC: National Academies Press. www.ncbi.nlm.nih.gov/books/NBK56068/table/summarytables.t4/

Fluid intake

Baseline = bodyweight (kg) × 35 ml per kg per day.

Exercise allowance = 590 ml per 30 minutes of exercise, the midpoint of the 0.5–2.0 litres per hour sweat-rate range.

Climate multipliers, applied to baseline plus exercise: temperate × 1.00; warm or humid × 1.15; hot, or working outdoors in heat, × 1.30.

Pregnancy adds 300 ml a day; breastfeeding adds 700 ml a day.

Of the total, about 80% is what you would drink; the remaining 20% typically arrives in food.

EFSA (2010) adequate intakes of total water, shown for comparison: 2.5 L a day for men and 2.0 L a day for women.

US Institute of Medicine adequate intakes of total water, shown for comparison: 3.7 L a day for men and 2.7 L a day for women.

No primary source for part of this section. The 35 ml per kg figure is a clinical planning heuristic used in nutrition support, not a population reference value, and we present it as exactly that, which is why the EFSA and IOM adequate intakes sit beside it rather than behind it. The climate multipliers of 1.15 and 1.30 are our own rounding of a real effect, with no published multiplier behind those specific numbers: treat them as a prompt to drink more in heat, not as a measurement. More is not always better, either: drinking past thirst during prolonged exercise carries a risk of its own.

  • EFSA Panel on Dietetic Products, Nutrition and Allergies. Scientific opinion on dietary reference values for water. EFSA J 2010;8:1459. doi.org/10.2903/j.efsa.2010.1459
  • Institute of Medicine. Dietary Reference Intakes for Water, Potassium, Sodium, Chloride, and Sulfate. Washington DC: National Academies Press, 2005 (the 2004 panel report). doi.org/10.17226/10925
  • Sawka MN, Burke LM, Eichner ER, Maughan RJ, Montain SJ, Stachenfeld NS. American College of Sports Medicine position stand: exercise and fluid replacement. Med Sci Sports Exerc 2007;39:377–90. doi.org/10.1249/mss.0b013e31802ca597
  • Maughan RJ, Watson P, Cordery PA, et al. A randomized trial to assess the potential of different beverages to affect hydration status: development of a beverage hydration index. Am J Clin Nutr 2016;103:717–23. doi.org/10.3945/ajcn.115.114769
  • Hew-Butler T, Rosner MH, Fowkes-Godek S, et al. Statement of the Third International Exercise-Associated Hyponatremia Consensus Development Conference, Carlsbad, California, 2015. Clin J Sport Med 2015;25:303–20. doi.org/10.1097/JSM.0000000000000221

Safe pace, check-in and reverse diet

Requested daily deficit (kcal) = requested kg/week × 7,700 ÷ 7. Intake is then lifted to the greater of 80% of TDEE and the sex floor (1,500 / 1,200 kcal).

Weeks = (current kg − goal kg) ÷ actual kg/week after those rails. No calendar date is computed.

Check-in expected kg = (TDEE − logged intake) × days ÷ 7,700.

Reverse diet week n = min(TDEE, current intake + n × weekly increase), weekly increase clamped to 50–200 kcal.

Fat-mass kg = weight × body-fat % ÷ 100; lean mass = weight − fat mass. Recomp is the change in each compartment between two readings.

No primary source for part of this section. The 7,700 kcal/kg planning constant is Wishnofsky's 3,500 kcal/lb expressed per kilogram and is labelled as a short-block forecast, not a twelve-month law. Metabolic age on this site is the age at which a BMI-22 person of the same height and sex has the closest Mifflin BMR; that is a marketing construct, not a tissue age. Fasting windows do not change weekly calories except on the 5:2 pattern, where two low days use 500 kcal (women) or 600 kcal (men) as the published 5:2 convention.

  • Mifflin MD, St Jeor ST, Hill LA, Scott BJ, Daugherty SA, Koh YO. A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr 1990;51:241–7. doi.org/10.1093/ajcn/51.2.241
  • Hall KD, Sacks G, Chandramohan D, et al. Quantification of the effect of energy imbalance on bodyweight. Lancet 2011;378:826–37. doi.org/10.1016/S0140-6736(11)60812-X
  • Wishnofsky M. Caloric equivalents of gained or lost weight. Am J Clin Nutr 1958;6:542–6. doi.org/10.1093/ajcn/6.5.542

Fibre targets and drink energy

EFSA adequate intake of dietary fibre: 25 g a day for adults.

IOM: 14 g fibre per 1,000 kcal; adequate intakes 38 g (men 19–50), 25 g (women 19–50), 30 g and 21 g from age 51.

Drink energy uses typical serving values: regular beer 153 kcal / 355 ml, light beer 103, wine 125 / 148 ml, spirits 40% 97 / 44 ml, cider 140 / 355 ml.

No primary source for part of this section. The drink kilocalorie values are typical labelled servings used for planning, not a laboratory analysis of the glass in hand. Mixers and craft beer run higher.

  • Institute of Medicine. Dietary Reference Intakes for Energy, Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and Amino Acids. Washington DC: National Academies Press, 2005. doi.org/10.17226/10490

Energy cost of activity (METs)

One MET is the energy cost of sitting quietly, defined as 3.5 ml of oxygen per kilogram per minute, roughly 1 kcal per kilogram per hour.

Gross kcal/min = MET × 3.5 × bodyweight (kg) ÷ 200

Net kcal/min = (MET − 1) × 3.5 × bodyweight (kg) ÷ 200, the extra cost above resting, which is the honest figure.

MET-minutes = MET × minutes. WHO's adult activity recommendation corresponds to roughly 500–1,000 MET-minutes a week.

Moderate intensity is 3 to under 6 METs; vigorous is 6 METs and above.

Fat equivalent shown for scale = net kcal ÷ 7,700 × 1,000 grams.

MET values are population averages across people of differing fitness and technique. Treat any single figure as ±15–30%. Trackers and gym machines usually report gross rather than net, which is one reason their numbers read high.

  • Jetté M, Sidney K, Blümchen G. Metabolic equivalents (METS) in exercise testing, exercise prescription, and evaluation of functional capacity. Clin Cardiol 1990;13:555–65. doi.org/10.1002/clc.4960130809
  • Ainsworth BE, Haskell WL, Herrmann SD, et al. 2011 Compendium of Physical Activities: a second update of codes and MET values. Med Sci Sports Exerc 2011;43:1575–81. doi.org/10.1249/MSS.0b013e31821ece12
  • Herrmann SD, Willis EA, Ainsworth BE, et al. 2024 Adult Compendium of Physical Activities: a third update of the energy costs of human activities. J Sport Health Sci 2024;13:6–12. doi.org/10.1016/j.jshs.2023.10.010
  • Compendium of Physical Activities: the maintained MET value tables (Adult, Older Adult and Wheelchair compendia). pacompendium.com/
  • WHO. WHO guidelines on physical activity and sedentary behaviour. Geneva: World Health Organization, 2020. www.who.int/publications/i/item/9789240015128
  • Shcherbina A, Mattsson CM, Waggott D, et al. Accuracy in wrist-worn, sensor-based measurements of heart rate and energy expenditure in a diverse cohort. J Pers Med 2017;7:3. doi.org/10.3390/jpm7020003
  • Pontzer H, Durazo-Arvizu R, Dugas LR, et al. Constrained total energy expenditure and metabolic adaptation to physical activity in adult humans. Curr Biol 2016;26:410–17. doi.org/10.1016/j.cub.2015.12.046
  • LaForgia J, Withers RT, Gore CJ. Effects of exercise intensity and duration on the excess post-exercise oxygen consumption. J Sports Sci 2006;24:1247–64. doi.org/10.1080/02640410600552064

Children and pregnancy

Child and teen BMI-for-age

BMI is computed the adult way, then read against the CDC growth reference for the child's exact age in months and sex. Adult categories are never applied to a child.

LMS transform: z = ((BMI ÷ M)^L − 1) ÷ (L × S) when L ≠ 0, and z = ln(BMI ÷ M) ÷ S when L = 0.

Percentile = Φ(z) × 100, where Φ is the standard normal cumulative distribution.

L, M and S are interpolated linearly between the published monthly rows, so an exact age is used rather than a rounded one.

Percent of the 95th percentile = BMI ÷ (BMI at the 95th percentile for that age and sex) × 100.

Bands: below the 5th percentile underweight; 5th to below 85th healthy weight; 85th to below 95th overweight; 95th and above obesity; 120% of the 95th percentile and above class 2; 140% and above class 3.

Valid range 2 to 20 years. Under 2, weight-for-length charts are used instead, and we say so rather than guessing.

Percent of the 95th percentile is used above the 95th because z-scores compress at the top of the distribution, so two very different children can share a percentile of 99. This tool answers only where one measurement sits on a reference distribution. It does not diagnose, and no number here replaces a paediatric assessment.

Pregnancy weight gain

The category is set by pre-pregnancy BMI, not by current weight.

Underweight (BMI below 18.5): total 12.5–18 kg; second and third trimester 0.44–0.58 kg a week; no twin range is published.

Healthy weight (18.5–24.9): total 11.5–16 kg; 0.35–0.50 kg a week; twins 16.8–24.5 kg.

Overweight (25–29.9): total 7–11.5 kg; 0.23–0.33 kg a week; twins 14.1–22.7 kg.

Obesity (30 and above): total 5–9 kg; 0.17–0.27 kg a week; twins 11.3–19.1 kg.

First-trimester gain is 0.5–2 kg and is not rate-based in the guidance; the weekly rates apply from week 14.

The 2009 report gives no twin range for an underweight pre-pregnancy BMI, so we return none rather than inventing one. These ranges are guidance for a conversation with a midwife or obstetrician, not a target to chase.

  • Institute of Medicine and National Research Council. Weight Gain During Pregnancy: Reexamining the Guidelines. Washington DC: National Academies Press, 2009. doi.org/10.17226/12584
  • American College of Obstetricians and Gynecologists. Committee Opinion No. 548: Weight gain during pregnancy. Obstet Gynecol 2013;121:210–12. doi.org/10.1097/01.AOG.0000425668.87506.4c
  • NICE. Maternal and child nutrition: nutrition and weight management in pregnancy, and nutrition in children up to 5 years. NICE guideline NG247, 2025. www.nice.org.uk/guidance/ng247
  • WHO. WHO recommendations on antenatal care for a positive pregnancy experience. Geneva: World Health Organization, 2016. www.who.int/publications/i/item/9789241549912

Fitness

Maximum heart rate and training zones

Tanaka (2001), the default: HRmax = 208 − 0.7 × age

Gellish (2007): HRmax = 207 − 0.7 × age

Fox (1971), shown for comparison only: HRmax = 220 − age

Karvonen (1957) target from the heart-rate reserve: HR = ((HRmax − HRrest) × intensity) + HRrest

Heart-rate reserve = HRmax − HRrest

Zones as a percentage of HRmax: zone 1 very light 50–60%; zone 2 light 60–70%; zone 3 moderate 70–80%; zone 4 hard 80–90%; zone 5 maximum 90–100%.

Every prediction is printed with a standard deviation of roughly 10–12 beats per minute.

Tanaka pooled 351 studies covering 18,712 people plus a 514-person laboratory validation, and the regression did not differ between men and women. 220 minus age over-predicts in young adults and under-predicts after about 40; we keep it only so you can see the difference.

One-repetition maximum

Epley (1985): 1RM = w × (1 + r ÷ 30)

Brzycki (1993): 1RM = w × 36 ÷ (37 − r)

Lombardi (1989): 1RM = w × r^0.10

O'Conner (1989): 1RM = w × (1 + 0.025 × r)

Lander (1985): 1RM = 100w ÷ (101.3 − 2.67123 × r)

Mayhew (1992): 1RM = 100w ÷ (52.2 + 41.9 × e^(−0.055 × r))

Wathan (1994): 1RM = 100w ÷ (48.8 + 53.8 × e^(−0.075 × r))

w is the weight lifted and r the repetitions completed. All seven are shown, with the spread between them.

Sets above 12 repetitions are refused: these equations were fitted on sets of about ten or fewer and diverge sharply beyond that.

No primary source for part of this section. Epley, Lombardi, O'Conner, Lander and Wathan originate in coaching textbooks and charts with no DOI or journal record of their own. LeSuer and colleagues' comparison reproduces all seven equations and is the citable source for them. Separately, the percentage-of-1RM repetition table uses the conventional NSCA-style ranges: a training convention rather than a published regression. True repetition counts at a given percentage vary widely between individuals.

  • Brzycki M. Strength testing: predicting a one-rep max from reps-to-fatigue. J Phys Educ Recreat Dance 1993;64:88–90. doi.org/10.1080/07303084.1993.10606684
  • Mayhew JL, Ball TE, Arnold MD, Bowen JC. Relative muscular endurance performance as a predictor of bench press strength in college men and women. J Appl Sport Sci Res 1992;6:200–6. doi.org/10.1519/00124278-199211000-00002
  • LeSuer DA, McCormick JH, Mayhew JL, Wasserstein RL, Arnold MD. The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift. J Strength Cond Res 1997;11:211–13. doi.org/10.1519/00124278-199711000-00001
  • Reynolds JM, Gordon TJ, Robergs RA. Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry. J Strength Cond Res 2006;20:584–92. doi.org/10.1519/R-15304.1
  • Grgic J, Lazinica B, Schoenfeld BJ, Pedisic Z. Test-retest reliability of the one-repetition maximum (1RM) strength assessment: a systematic review. Sports Med Open 2020;6:31. doi.org/10.1186/s40798-020-00260-z
  • American College of Sports Medicine. Position stand: progression models in resistance training for healthy adults. Med Sci Sports Exerc 2009;41:687–708. doi.org/10.1249/MSS.0b013e3181915670
  • Richens B, Cleather DJ. The relationship between the number of repetitions performed at given intensities is different in endurance and strength trained athletes. Biol Sport 2014;31:157–61. doi.org/10.5604/20831862.1099047

US Army and Department of Defense body composition standards

AR 600-9 Table B-2, maximum allowable percent body fat by age: 17–20, 20% male and 30% female; 21–27, 22% and 32%; 28–39, 24% and 34%; 40 and older, 26% and 36%.

Performance exemption: a soldier scoring 540 or more on the Army Combat Fitness Test with at least 80 points in every event is exempt from the body fat assessment even if they exceed the height and weight screening table.

DoDI 1308.03 bounds on what any service may set: for men no higher than 26% and no lower than 18%; for women no higher than 36% and no lower than 26%.

The Army authorises three assessment methods: the multi-site circumference tape method of AR 600-9 Appendix B, a one-site abdominal circumference method, and a supplemental assessment by DXA, bioelectrical impedance or air-displacement plethysmography after a failed tape test and confirmation test. The one-site method is published as a lookup table, not as a closed-form equation, and we deliberately do not reproduce a reverse-engineered formula for it. Our calculator estimates body fat with the multi-site Hodgdon–Beckett method, which is also authorised, and says so on the page.

No primary source for part of this section. One link cited elsewhere on this site, to the Army Resilience Directorate's Army Body Composition Program page, no longer resolves. We have left it out of the references rather than list a dead URL, and the regulation itself is the document of record. If you are being assessed, the current directive your unit holds beats anything on this site.

Measurement and statistics

Body surface area

Mosteller (1987), the usual clinical default: √(cm × kg ÷ 3600)

Du Bois & Du Bois (1916): 0.007184 × cm^0.725 × kg^0.425

Haycock (1978): 0.024265 × cm^0.3964 × kg^0.5378

Gehan & George (1970): 0.0235 × cm^0.42246 × kg^0.51456

Fujimoto (1968): 0.008883 × cm^0.663 × kg^0.444

Takahira (1925): 0.007241 × cm^0.725 × kg^0.425

All six are shown with their mean and the spread between them, because the spread is the point.

Cardiac index = cardiac output (L/min) ÷ BSA (m²); the normal adult range is about 2.5–4.0 L/min/m².

No primary source for part of this section. Fujimoto (1968, Japanese Journal of Hygiene) and Takahira (1925, Imperial Government Institute for Nutrition) predate DOI assignment, and we could not locate a stable open record for either. We reproduce their coefficients as they appear in the body surface area literature, and we flag that we have not verified them against the original papers. Clinical protocols specify which formula to use; these pages say so, and never suggest adjusting a dose.

  • Mosteller RD. Simplified calculation of body-surface area. N Engl J Med 1987;317:1098. doi.org/10.1056/NEJM198710223171717
  • Du Bois D, Du Bois EF. Clinical calorimetry: a formula to estimate the approximate surface area if height and weight be known. Arch Intern Med 1916;17:863–71. doi.org/10.1001/archinte.1916.00080130010002
  • Haycock GB, Schwartz GJ, Wisotsky DH. Geometric method for measuring body surface area: a height–weight formula validated in infants, children and adults. J Pediatr 1978;93:62–6. doi.org/10.1016/S0022-3476(78)80601-5
  • Gehan EA, George SL. Estimation of human body surface area from height and weight. Cancer Chemother Rep 1970;54:225–35. pubmed.ncbi.nlm.nih.gov/5527019/
  • Verbraecken J, Van de Heyning P, De Backer W, Van Gaal L. Body surface area in normal-weight, overweight, and obese adults: a comparison study. Metabolism 2006;55:515–24. doi.org/10.1016/j.metabol.2005.11.004
  • Sacco JJ, Botten J, Macbeth F, Bagust A, Clark P. The average body surface area of adult cancer patients in the UK: a multicentre retrospective study. PLoS One 2010;5:e8933. doi.org/10.1371/journal.pone.0008933
  • Lang RM, Badano LP, Mor-Avi V, et al. Recommendations for cardiac chamber quantification by echocardiography in adults: an update from the American Society of Echocardiography and the European Association of Cardiovascular Imaging. J Am Soc Echocardiogr 2015;28:1–39. doi.org/10.1016/j.echo.2014.10.003
  • Griggs JJ, Bohlke K, Balaban EP, et al. Appropriate systemic therapy dosing for obese adult patients with cancer: ASCO guideline update. J Clin Oncol 2021;39:2037–48. doi.org/10.1200/JCO.21.00471

Units, rounding and the 7,700 kcal per kilogram figure

Canonical internal units everywhere: kilograms, centimetres, years. Every input is converted on entry.

1 lb = 0.45359237 kg; 1 in = 2.54 cm; 1 stone = 14 lb; 1 kcal = 4.184 kJ.

1 US fluid ounce = 29.5735295625 ml; 1 US nutrition-labelling cup = 240 ml; 1 imperial fluid ounce = 28.4130625 ml; 1 imperial pint = 568.26125 ml.

Energy in a kilogram of body mass, used for planning only: 7,700 kcal.

Rounding happens at display and nowhere else: one decimal place for BMI, body fat percentage and kilograms, and to the nearest 10 for calories.

The numerical methods behind the percentiles

z-score to percentile uses the Abramowitz & Stegun 7.1.26 error-function approximation, whose absolute error is below 1.5 × 10⁻⁷, ample for reporting a percentile to one decimal place.

Percentile back to BMI, used to draw the reference curves, uses Acklam's rational approximation to the inverse normal, with relative error below 1.15 × 10⁻⁹.

No primary source for part of this section. Acklam's inverse-normal approximation was published as an algorithm on the web rather than in a journal, so it has no DOI and we do not list it in the references. We name it here because you should know which approximation drew a curve you are reading.

Found an error? That is worth more to us than a compliment. Tell us on the contact page and the correction goes into the changelog with your finding credited.