Trefethen BMI Formula Calculator
Compare the proposed Oxford/Trefethen formula (2013) with standard adult BMI and see how its different height exponent changes results for taller and shorter adults.
Calculate My New BMI →Free · No signup · Both formulas side by side
What Is the New BMI Formula?
Professor Nick Trefethen of Oxford University proposed a corrected BMI formula in 2013:
The original 1832 Quetelet formula uses height² — which overstates BMI for tall people and understates it for short people. Trefethen's exponent of 2.5 changes this height relationship because body volume scales with height at a power between 2 and 3, not exactly 2.
Old vs New BMI Formula
| Old BMI (Quetelet, 1832) | New BMI (Trefethen, 2013) | |
|---|---|---|
| Formula | weight ÷ height² | 1.3 × weight ÷ height²·⁵ |
| Proposed | Lambert Quetelet, 1832 | Nick Trefethen, Oxford, 2013 |
| Bias for tall adults | Overstates BMI ↑ | Corrected |
| Bias for short adults | Understates BMI ↓ | Corrected |
| WHO Standard? | ✅ Yes | Not yet — academic use |
| Best for | Average heights (5'3″–5'9″) | All adult heights |
Worked Examples
5'4" (163cm)
65 kg
Average height — small difference
6'2" (188cm)
85 kg
Tall adult — old formula overstates by 2.1 points
5'0" (152cm)
55 kg
Short adult — old formula understates by 1.7 points
New BMI vs Old BMI — Results Across Heights
All examples use 75 kg (165 lb) to isolate the height effect. The gap widens at extreme heights.
| Height | Old BMI (÷h²) | New BMI (÷h²·⁵) | Difference | Verdict |
|---|---|---|---|---|
| 4'11" (150 cm) | 33.3 | 35.4 | +2.0 | New formula produces a higher BMI for this short-height example |
| 5'7" (170 cm) | 26.0 | 25.9 | −0.1 | Closest match between formulas |
| 6'3" (190 cm) | 20.8 | 19.6 | −1.2 | Old formula produces a higher BMI for this tall-height example |
* New BMI = 1.3 × 75 ÷ height(m)^2.5. Old BMI = 75 ÷ height(m)². Categories: Underweight <18.5, Normal 18.5–24.9, Overweight 25–29.9, Obese ≥30. See 5 fully worked examples with step-by-step math →
Why the Old Formula Falls Short
The 1832 Quetelet formula (weight ÷ height²) was never designed as a medical measure — it was a convenient constant for people of average height. Body volume actually scales with height at a power between 2 and 3, not exactly 2, which is why the old formula overstates BMI for tall adults and understates it for short adults.
Want the full derivation, the population studies behind the 2.5 exponent, Nick Trefethen's original 2013 argument, and the formula's known criticisms? Read the complete deep dive →
Limitations of BMI — Both Old and New
The Trefethen formula changes how height affects the result, but both formulas share the fundamental limitation of all BMI calculations: they measure weight relative to height, not actual body fat. Neither formula accounts for age, sex, ethnicity, or muscle mass.
Athletes and muscular individuals
Muscle weighs more than fat. A competitive athlete or bodybuilder can have a BMI of 28–30 (overweight by BMI) while carrying very low body fat. Neither formula can distinguish muscle from fat.
Older adults
After age 60, people typically lose muscle and gain fat even at a stable weight. A 70-year-old with a Normal BMI may carry more visceral fat than a 30-year-old with the same BMI — neither formula captures this.
Ethnic body composition differences
Asian populations tend to carry more visceral fat at lower BMI values. The WHO has published separate BMI cut-points for Asian adults (overweight at ≥23 rather than ≥25). The Trefethen formula does not address this.
Pregnancy
BMI is not a valid health measure during pregnancy. Expected weight gain varies by trimester and starting BMI.
Children and adolescents
BMI-for-age percentiles (not fixed cut-points) apply to people under 20. Neither adult formula should be applied to children.
Very short and very tall adults
The Trefethen formula improves accuracy but still breaks down at extreme heights (under 4'8" or over 6'10") where body proportions differ significantly from the average adult used to calibrate the exponent.
When to Go Beyond BMI for Body Composition
BMI — even the improved Trefethen version — is a screening tool, not a diagnostic one. If your BMI falls outside the Normal range, or if you are athletic, older, or from a population with different body composition norms, consider these more direct measures:
Body Fat Percentage
DEXA scan (gold standard), hydrostatic weighing, Bod Pod, bioelectrical impedance, or the Navy tape method (waist + neck circumference)
Healthy ranges
Men: 10–20% | Women: 18–28% (general fitness ranges)
Why it matters
Directly measures fat mass vs lean mass. A muscular person with BMI 28 may have 15% body fat — perfectly healthy.
Waist Circumference
Measure at the navel (or at the narrowest point of the torso) with a flexible tape
Healthy ranges
Men: <40 in (102 cm) | Women: <35 in (88 cm)
Why it matters
Strongly predicts visceral (abdominal) fat and metabolic risk. Waist-to-height ratio (waist ÷ height < 0.5) is another simple marker.
Waist-to-Hip Ratio
Measure waist at narrowest, hip at widest, divide
Healthy ranges
Men: <0.90 | Women: <0.85 (WHO thresholds)
Why it matters
Apple-shaped fat distribution (high W:H ratio) carries more metabolic risk than pear-shaped (low W:H). BMI cannot distinguish these.
Bottom line: Use the new BMI as a quick first screen. If your result is borderline, or if you are particularly tall, short, muscular, older, or of Asian descent, pair it with waist circumference and — if possible — a body fat measurement. For any clinical decision, consult a healthcare provider.
Try the Full BMI Calculator
Our BMI calculator shows both the old Quetelet result and the new Trefethen result side by side — with WHO category, healthy weight range, and metric/imperial support.
Calculate My BMI →Frequently Asked Questions
What is the new BMI formula?▼
What is a healthy range on the new BMI?▼
Why does the new BMI matter for tall people?▼
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