New BMI Calculator (Trefethen Formula)

Calculate your BMI using the updated formula proposed by Oxford University mathematician Nick Trefethen in 2013. The New BMI formula (1.3 × weight / height^2.5) corrects a known height bias in the traditional BMI calculation, giving slightly higher values for shorter people and slightly lower values for taller people. Use our standard BMI calculator for the traditional formula, or read on to understand the differences and why this alternative was proposed. For background on how BMI was developed, see our history of BMI guide.

Key Takeaways

New BMI formula: 1.3 × weight(kg) / height(m)^2.5 — replaces the exponent of 2 with 2.5
Corrects height bias — traditional BMI overestimates BMI for short people and underestimates it for tall people
Short people get slightly higher New BMI — typically +0.5 to +2 points compared to traditional BMI
Tall people get slightly lower New BMI — typically -0.5 to -2 points compared to traditional BMI
NOT adopted by WHO or major health organizations — the traditional formula remains the clinical standard
Same BMI categories apply — 18.5-24.9 is still considered normal weight

Formula Comparison: Traditional vs New BMI

Traditional BMI

height²

Exponent: 2.0

New BMI (Trefethen)

height^2.5

Exponent: 2.5

Key Difference

+0.5 exponent = better height scaling

The 1.3 multiplier normalizes values to match traditional BMI at average height

How Height Affects the Difference

5'0" (152cm)

+1.5 to +2.1

5'4" (163cm)

+0.4 to +0.8

5'7" (170cm)

~0.0 (baseline)

6'0" (183cm)

-0.7 to -1.1

6'4" (193cm)

-1.3 to -1.8

Short peopleHigher New BMI

Average heightNo change

Tall peopleLower New BMI

Height (feet)

Height (inches)

Weight (lbs)

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Under

Normal

Over

Obese I

Obese II+

1518.525303540

New BMI vs Traditional BMI Comparison

New BMI (Trefethen)

—

Traditional BMI

—

Difference

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Category Impact

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Healthy Min

—

Healthy Max

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Medical Disclaimer: This calculator provides estimates for informational purposes only. BMI is a screening tool, not a diagnostic measure. The New BMI (Trefethen) formula has not been adopted by major health organizations. Always consult a healthcare professional for medical advice. See the WHO obesity fact sheet for global guidelines.

Traditional vs New BMI Formula

The Body Mass Index was first devised by Belgian mathematician Adolphe Quetelet in the 1830s. For nearly two centuries, the formula has remained unchanged: divide weight by the square of height. In 2013, Oxford University mathematician Nick Trefethen proposed an updated version that he argued better accounts for the relationship between height and body volume. This proposal addressed one of the key limitations of BMI that researchers have long recognized. Here is how the two formulas compare:

Traditional BMI Formula

BMI = weight(kg) / height(m)²

Devised by Adolphe Quetelet in the 1830s
Uses an exponent of 2 (height squared)
Adopted by WHO, CDC, and all major health organizations
Clinically validated in thousands of studies

New BMI Formula (Trefethen)

BMI = 1.3 × weight(kg) / height(m)^2.5

Proposed by Nick Trefethen in 2013
Uses an exponent of 2.5 (height to the power of 2.5)
Not adopted by any major health organization
Designed to correct height bias in the traditional formula

Why the Exponent Changed from 2 to 2.5

The traditional BMI formula divides weight by height squared. However, human bodies are three-dimensional objects, and as a person grows taller, their volume (and therefore mass) scales more closely with height cubed than height squared. The traditional exponent of 2 was originally chosen as a compromise that worked well for average-height individuals, but it introduces systematic errors at the extremes of height. This is one reason why BMI accuracy varies across different populations.

Trefethen argued that the ideal exponent should be somewhere between 2 (pure area scaling) and 3 (pure volume scaling). After analyzing population data and the dimensional relationship between height and mass, he settled on 2.5 as the best fit. The factor of 1.3 is a scaling constant that ensures the New BMI produces values in the same range as the traditional BMI for people of average height (around 5'7" or 170 cm), so the existing BMI category thresholds (18.5, 25, 30) remain applicable without modification.

Worked Examples

To illustrate the practical difference, consider two individuals of different heights who both weigh 150 lbs (68 kg):

Short Person: 5'2" (157 cm), 150 lbs (68 kg)

Traditional BMI: 68 / 1.57² = 27.6 (Overweight)
New BMI: 1.3 × 68 / 1.57^2.5 = 28.6 (Overweight)
Difference: +1.0 — New BMI is higher for this short person, suggesting the traditional formula was slightly underestimating their BMI

Tall Person: 6'2" (188 cm), 150 lbs (68 kg)

Traditional BMI: 68 / 1.88² = 19.2 (Normal)
New BMI: 1.3 × 68 / 1.88^2.5 = 18.3 (Underweight)
Difference: -0.9 — New BMI is lower for this tall person, suggesting the traditional formula was slightly overestimating their BMI

Notice that in the tall person example, the difference is enough to change the BMI category from Normal to Underweight. This illustrates why Trefethen argued the height bias in the traditional formula is not merely academic but can have real classification consequences, particularly for people at the extremes of height. For a comprehensive explanation of the standard formula, see our BMI formula guide.

New BMI vs Traditional BMI Comparison Table

The table below compares both BMI calculations across a range of heights and weights. Cells highlighted in green indicate that both formulas agree on the BMI category, while cells in yellow indicate a category disagreement. All values are rounded to one decimal place.

Height	Weight	Traditional BMI	New BMI	Difference
5'0" (152 cm)	120 lbs	23.4	24.6	+1.2
	150 lbs	29.3	30.8	+1.5
	180 lbs	35.2	36.9	+1.7
	210 lbs	41.0	43.1	+2.1
5'4" (163 cm)	120 lbs	20.6	21.0	+0.4
	150 lbs	25.7	26.3	+0.6
	180 lbs	30.9	31.5	+0.6
	210 lbs	36.0	36.8	+0.8
5'8" (173 cm)	120 lbs	18.2	18.1	-0.1
	150 lbs	22.8	22.6	-0.2
	180 lbs	27.4	27.1	-0.3
	210 lbs	31.9	31.7	-0.2
6'0" (183 cm)	120 lbs	16.3	15.6	-0.7
	150 lbs	20.3	19.5	-0.8
	180 lbs	24.4	23.5	-0.9
	210 lbs	28.5	27.4	-1.1
6'4" (193 cm)	120 lbs	14.6	13.6	-1.0
	150 lbs	18.3	17.0	-1.3
	180 lbs	21.9	20.4	-1.5
	210 lbs	25.6	23.8	-1.8

Traditional BMI = weight(kg) / height(m)². New BMI = 1.3 × weight(kg) / height(m)^2.5. Categories: Underweight < 18.5, Normal 18.5-24.9, Overweight 25-29.9, Obese 30+. The most notable category disagreements occur at 6'4" where the New BMI drops the 150 lbs reading from Normal to Underweight and the 210 lbs reading from Overweight to Normal. Compare your personal values with the standard BMI calculator. Learn more about what the numbers mean in our healthy BMI range guide.

Why Was the New BMI Formula Proposed?

In January 2013, Nick Trefethen published a letter in The Economist arguing that the traditional BMI formula was mathematically flawed. His critique centered on what he called the "height bias problem" — a systematic error that causes the traditional BMI to give misleading results for people who are significantly shorter or taller than average. Here is a breakdown of his argument:

The Height Bias Problem

The traditional BMI divides weight by height squared. If human bodies scaled uniformly in all three dimensions (like a cube), weight would scale with height cubed, and dividing by height squared would systematically overestimate the BMI of tall people and underestimate the BMI of short people. The actual scaling is between squared and cubed, but closer to cubed for typical human proportions. The result is that a 6'6" person may be classified as overweight by traditional BMI even at a healthy body composition, while a 5'0" person may be given a false sense of security at the same BMI value.

Trefethen's Mathematical Reasoning

Trefethen examined how body mass scales with height across population data and through dimensional analysis. He found that an exponent of approximately 2.5 provides the best fit: it sits between the area-based scaling of 2 (where we imagine people are flat) and the volume-based scaling of 3 (where people are perfect cubes). The 2.5 exponent better captures how human bodies actually grow taller — we get proportionally wider and deeper, but not as fast as a perfect cube would predict.

What the 2.5 Exponent Means Physically

The exponent in the BMI formula describes how body mass scales with height. An exponent of 2 assumes mass scales with the square of height (as if people were two-dimensional). An exponent of 3 assumes mass scales with the cube of height (as if people were perfectly proportioned three-dimensional objects). Trefethen's exponent of 2.5 is a compromise that acknowledges human bodies are three-dimensional but do not scale perfectly isometrically — taller people tend to be relatively slimmer in proportion to their height.

The 1.3 Scaling Factor

The constant 1.3 in the New BMI formula is a normalizing factor. Because the exponent changed from 2 to 2.5, the raw output of weight / height^2.5 would produce numbers in a different range than what people are accustomed to seeing. The factor of 1.3 was chosen so that for a person of average height (approximately 5'7" or 170 cm), the New BMI and traditional BMI produce nearly identical values. This means the existing BMI category thresholds (18.5, 25, 30) can be applied directly without modification. For more detail, visit Trefethen's original BMI page at Oxford University.

Who Is Affected Most by the New BMI?

The difference between New BMI and traditional BMI depends almost entirely on your height. For people of average height, the two formulas produce nearly identical results. The further you are from average height, the larger the discrepancy. Here is a breakdown of how the change affects different height groups:

Short People (under 5'4" / 163 cm)

New BMI is typically +0.5 to +2 points higher than traditional BMI. The traditional formula was slightly flattering short individuals, and the New BMI corrects this by increasing their score. For someone at 5'0", the difference can be as much as +2.1 points at higher weights. This could push a person from "normal" to "overweight" or from "overweight" to "obese" in some cases.

Average Height (5'6" - 5'10" / 168-178 cm)

New BMI is within -0.5 to +0.5 points of traditional BMI. At average height, both formulas produce essentially identical results because the 1.3 scaling factor was calibrated to this range. Most people in this group will see no change in their BMI category. The formulas are designed to agree at approximately 5'7" (170 cm).

Tall People (over 6'0" / 183 cm)

New BMI is typically -0.5 to -2 points lower than traditional BMI. The traditional formula was slightly penalizing tall individuals, and the New BMI corrects this by decreasing their score. For someone at 6'4", the difference can be as much as -1.8 points. This could move a person from "overweight" to "normal" or from "obese" to "overweight."

BMI Difference by Height

The following table shows the approximate difference between New BMI and Traditional BMI at various heights, assuming a weight of 160 lbs (73 kg). Positive values mean the New BMI is higher; negative values mean it is lower.

Height	Traditional BMI	New BMI	Difference	Direction
4'10" (147 cm)	33.6	36.1	+2.5	New BMI higher
5'0" (152 cm)	31.2	32.8	+1.6	New BMI higher
5'4" (163 cm)	27.4	28.0	+0.6	Slightly higher
5'7" (170 cm)	25.1	25.1	0.0	No difference
5'10" (178 cm)	23.0	22.5	-0.5	Slightly lower
6'0" (183 cm)	21.7	20.9	-0.8	New BMI lower
6'4" (193 cm)	19.5	18.2	-1.3	New BMI lower
6'8" (203 cm)	17.7	16.1	-1.6	New BMI lower

All values calculated for a weight of 160 lbs (72.6 kg). The crossover point where both formulas agree is approximately 5'7" (170 cm). For sex-specific analysis, see our BMI calculator for women and BMI calculator for men.

Should You Use the New BMI?

The New BMI formula raises an important question: if the traditional formula has a known height bias, should we all switch to the updated version? The answer is nuanced. Here is a balanced look at the pros and cons, according to researchers and health organizations:

Pros of the New BMI

Corrects a real mathematical flaw: The height bias in the traditional formula is well-documented and undeniable. The New BMI addresses this directly.
More accurate for very short and very tall people: If you are under 5'2" or over 6'2", the New BMI gives a less biased result.
Mathematically sound: The 2.5 exponent is supported by dimensional analysis and empirical data on height-weight relationships.
Uses the same categories: No new thresholds to learn or remember. 18.5-24.9 is still normal weight.

Cons of the New BMI

Not clinically validated: The category thresholds (18.5, 25, 30) were established using the traditional formula. They have not been re-validated for the New BMI.
No health outcome studies: Decades of epidemiological research link traditional BMI values to disease risk. This evidence base does not exist for the New BMI.
Not adopted by any major health organization: The WHO, CDC, NHS, and all major medical bodies still use the traditional formula.
Confusion potential: Having two competing BMI numbers in circulation could cause confusion among patients and healthcare providers.

The Bottom Line

The New BMI is an interesting mathematical improvement that highlights a real flaw in the traditional formula. However, the traditional BMI remains the clinical standard because it has been validated against health outcomes over decades of research. If you are significantly shorter or taller than average, the New BMI can provide useful additional perspective, but you should continue to use the traditional BMI for any medical or clinical purposes. Both formulas share the same fundamental limitation: they cannot distinguish between muscle and fat. For a more complete health assessment, combine your BMI with body composition analysis and waist circumference measurement.

New BMI Adoption Status

Despite generating media attention when it was first proposed in 2013, the Trefethen New BMI formula has not been adopted by any major health organization. Here is the current status across the world's leading health authorities:

Organization	Formula Used	New BMI Status	Notes
World Health Organization (WHO)	Traditional	Not Adopted	Continues to use weight/height² for global obesity monitoring
CDC (United States)	Traditional	Not Adopted	Uses traditional BMI for all adult and pediatric screening
NHS (United Kingdom)	Traditional	Not Adopted	Standard BMI used in all NHS health checks
American Medical Association (AMA)	Traditional	Not Adopted	Recognizes BMI limitations but has not endorsed the New BMI
Academic Researchers	Varies	Mixed Interest	Some researchers advocate for the New BMI; others argue for different approaches entirely

The primary reason for non-adoption is practical rather than mathematical. The traditional BMI formula has been used in clinical research for decades, and all the evidence linking BMI to health outcomes (such as heart disease, diabetes, and mortality risk) is based on the traditional formula. Switching to a new formula would require re-validating all of this research. Additionally, some health experts argue that the effort to refine the BMI formula is misplaced — they believe the focus should instead be on developing better body composition metrics that go beyond any BMI calculation, such as body fat percentage, waist-to-hip ratio, or metabolic health markers. For more on BMI limitations, see our complete BMI guide.

Frequently Asked Questions

The New BMI formula is BMI = 1.3 × weight(kg) / height(m)^2.5. It was proposed in 2013 by Oxford University mathematician Nick Trefethen as an improvement to the traditional formula (weight/height²). The key changes are raising the height exponent from 2 to 2.5 and adding a 1.3 scaling factor to keep the output in the same familiar range. You can read Trefethen's original explanation at his Oxford University page. To compare both calculations side by side, use the calculator at the top of this page or try our standard BMI calculator.

The New BMI was created by Nick Trefethen, a professor of numerical analysis at the Mathematical Institute of the University of Oxford. He proposed the formula in a letter to The Economist published in January 2013. Trefethen is a Fellow of the Royal Society and has made significant contributions to applied mathematics. His BMI proposal was not a formal academic paper but rather a public observation about a mathematical error in a widely-used health metric. Despite this informal origin, the proposal received significant media coverage and sparked widespread debate about the accuracy of the traditional BMI formula.

The difference comes down to how height is accounted for. The traditional BMI divides weight by height squared (exponent of 2), while the New BMI divides by height raised to 2.5. Since human bodies are three-dimensional objects, their mass scales closer to height cubed than height squared. The exponent of 2 was a convenient simplification when Quetelet devised the formula in the 1830s, but it causes systematic errors: short people get artificially low BMI values and tall people get artificially high values. The 2.5 exponent is a better approximation of how mass actually scales with height in humans. See the comparison table above for specific examples, or check our BMI formula guide for the complete mathematical derivation.

It depends on what you mean by "accurate." Mathematically, the New BMI is more accurate in the sense that it better accounts for the relationship between height and body mass. It reduces the systematic height bias that causes the traditional formula to overestimate BMI for tall people and underestimate it for short people. However, clinically, the traditional BMI has a much stronger evidence base. Decades of medical research have linked specific traditional BMI values to health outcomes like heart disease, diabetes, and mortality. This body of evidence has not been replicated using the New BMI. So the New BMI is mathematically better but clinically unproven. For a complete health assessment, consider supplementing any BMI reading with body composition analysis and waist circumference measurement.

For medical and clinical purposes, use the traditional BMI. This is what your doctor uses, what health organizations recommend, and what clinical research is based on. The New BMI is best used as a supplementary perspective, especially if you are significantly shorter or taller than average. If you are 5'0" and your traditional BMI says you are at the top of the normal range, it is worth noting that the New BMI would put you slightly into overweight territory. Similarly, if you are 6'4" and classified as overweight by traditional BMI, the New BMI may suggest you are actually in the normal range. Use both numbers to get a more complete picture, but defer to the traditional BMI for official health assessments. Compare your results using our standard BMI calculator.

It depends on your height and where your BMI falls relative to category boundaries. If you are of average height (5'5" to 5'10"), the difference is usually less than half a point, which is unlikely to change your category. If you are short (under 5'4"), the New BMI will be higher by 0.5 to 2+ points, which could push you from normal to overweight or from overweight to obese. If you are tall (over 6'0"), the New BMI will be lower by 0.5 to 2+ points, which could drop you from overweight to normal or from obese to overweight. Category changes are most likely for people whose traditional BMI is close to a threshold (18.5, 25, or 30) and who are significantly above or below average height. Use the calculator above to check your personal results and see the age-adjusted BMI calculator for additional context.

There are several practical reasons. First, the BMI category thresholds (18.5, 25, 30) were validated using the traditional formula. These numbers were not chosen arbitrarily; they are based on large epidemiological studies that linked specific traditional BMI values to disease risk and mortality. Re-validating these thresholds with a new formula would require extensive new research. Second, decades of clinical guidelines from organizations like the WHO and CDC reference the traditional formula. Changing would require updating thousands of clinical protocols and retraining healthcare providers worldwide. Third, many experts argue that the effort is better spent moving beyond BMI entirely toward metrics that directly measure body composition, such as body fat percentage or metabolic health markers. The height bias, while real, is considered a relatively minor issue compared to BMI's fundamental inability to distinguish between muscle and fat.

Yes, height does affect the accuracy of the traditional BMI formula. This is not controversial — it is a known mathematical property of the formula. Dividing by height squared when mass scales closer to height to the 2.5 power creates a systematic bias that becomes more pronounced at the extremes of height. Research published in the International Journal of Obesity has confirmed that tall people tend to have their body fatness overestimated by traditional BMI, while short people tend to have it underestimated. However, the magnitude of this effect is relatively small for most people — typically 1-2 BMI points for people who are 6 inches above or below average height. At average height, the bias is negligible. For most clinical purposes, this level of error is acceptable, which is why the traditional formula continues to be used. For a more detailed analysis, see Harvard Health's analysis of BMI usefulness and our BMI formula guide.

Other Calculators

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Trusted Sources and References

The information on this page is based on the following authoritative sources:

Nick Trefethen - New BMI (Oxford University) - Original proposal and explanation of the New BMI formula by its creator
The Economist - Body Mass Index Letter - Original 2013 letter from Trefethen proposing the New BMI formula
WHO Obesity and Overweight Fact Sheet - Global BMI classification standards and obesity statistics
CDC - BMI Information - U.S. federal guidance on BMI interpretation and screening
Harvard Health - How Useful Is BMI? - Critical analysis of BMI as a health metric including height bias discussion
Harvard Health - Muscle Mass and Health - Why body composition matters beyond BMI numbers
NHS BMI Calculator - UK National Health Service BMI guidance and healthy weight resources
Mayo Clinic - Obesity - Symptoms, causes, risk factors, and treatment options for obesity
PubMed - Database of peer-reviewed medical research on BMI and body composition
ACE Body Fat Calculator - Body fat percentage norms and categories for context beyond BMI