Body Mass Index Calculator
Solve BMI = m / h² for any of its three quantities — body mass index, body mass, or height — with step-by-step math, a live BMI-scale diagram with WHO classification bands, and companion body-composition metrics.
A population screening tool, not a diagnosis
BMI was devised in the 1830s by Adolphe Quetelet as a way to describe the "average man" — it was never intended as an individual diagnostic. Its strength is that it requires only two easily-measured quantities and correlates reasonably well with body fat at the population level. Its weakness is that it treats all mass as equivalent: muscle, bone, fat, and water all count the same. A competitive rower and a sedentary office worker can have the same BMI and completely different metabolic health. This is why modern clinical practice combines BMI with waist circumference, blood pressure, lipid panel, fasting glucose, and body composition measurements.
Why athletes are "overweight" on the BMI scale
Skeletal muscle has a density of about 1.06 kg/L, while adipose tissue has a density of about 0.90 kg/L. A muscular athlete can therefore have a BMI of 27 or 28 while carrying very little body fat. Many professional rugby players, sprinters, and Olympic weightlifters fall into the WHO "overweight" category by BMI while having body fat percentages in the single digits or low teens. This is the single most common false positive of BMI. Conversely, someone with a "normal" BMI can have a high body-fat percentage and low muscle mass and be at elevated metabolic risk.
The squared-height dependence matters
BMI = m / h². Because height enters squared, a 10% difference in height corresponds to about a 21% difference in BMI at the same mass. This is why BMI must be interpreted relative to population norms: the same mass that is normal at 190 cm is obese at 155 cm. It is also why the formula itself has been criticised — the squared exponent assumes body mass scales with the square of height, but isometric scaling theory and empirical data suggest mass actually scales closer to h³ in many mammals, giving rise to alternative indices such as the Ponderal Index (m/h³) and the "New BMI" (1.3 · m / h²·⁵).
Ethnic and age adjustments
The WHO classification was derived primarily from European and American populations. Many health authorities now use lower thresholds for people of South Asian, Chinese, and other Asian ancestries, because the same BMI is associated with higher metabolic risk at lower body-fat levels. The WHO expert consultation of 2004 recommended that for Asian populations "overweight" begin at BMI 23 and "obese" at BMI 27.5. Similarly, BMI thresholds for the elderly are sometimes relaxed, because a slightly higher BMI (22–27) is associated with lower mortality in people over 65.
How to Use This Calculator
The BMI relation links three quantities: BMI, body mass, and height. Pick which one you want the tool to solve, then fill in the other two — or click a sample profile to load all three.
1. Start with a sample profile
The pills at the top load representative mass-height combinations spanning the full BMI range from underweight through obese class III. Click one to see the BMI and classification instantly.
2. Choose what to solve for
Pick BMI, m, or h from the toggle. Solving for BMI takes mass and height as inputs; solving for mass takes BMI and height; solving for height takes BMI and mass. The derived quantities are locked with a "SOLVED" badge.
3. Enter consistent units
Mass in kilograms, height in centimetres — the calculator converts to metres internally before squaring. The hints below each field show the value in imperial units (pounds, stones, feet-and-inches) so you can cross-check without a separate conversion step.
4. Remember what BMI does not measure
BMI does not distinguish muscle from fat, does not capture fat distribution (visceral vs subcutaneous), does not account for frame size or ethnicity, and is not a diagnostic tool. Use it as a starting point for a conversation with a healthcare provider, not as a final verdict on anyone's health.
5. Read the result and classification verdict
The result card shows the solved value plus the BMI, mass, and height chips side by side. A colour-coded verdict classifies the result using the WHO categories: underweight, normal, overweight, obese class I, class II, and class III.
6. Switch to Advanced for depth
Advanced mode adds a chart of BMI vs. height at fixed mass, a sensitivity check on +1% input changes, and a full table of companion body metrics including ideal weight range, BMI prime, Ponderal index, body surface area, and mass needed to reach a target BMI.
What This Tool Offers
Built around the classic BMI relation BMI = m / h², the world's most widely-used anthropometric screening formula.
Three-way solving
Solve for body mass index, body mass, or height. The calculator rearranges the formula for whichever quantity you choose.
Annotated BMI scale diagram
A horizontal color-coded scale with all WHO classification bands labelled, the current position marked, reference weights at each boundary, and a mass-position axis showing where the current mass sits.
Sample profile presets
Seven one-click profiles spanning mass 50–100 kg and height 150–200 cm, so you can see how BMI moves across the full population range.
Body-composition companion metrics
Ideal weight range, BMI prime, Ponderal index, body surface area, mass to reach a target BMI, and the WHO class boundaries in kilograms for the current height.
Dual comparison charts
BMI vs. mass at three heights, plus an advanced chart of BMI vs. height at three masses — showing the characteristic inverse-square curves.
Reference tables
The full WHO classification table with weights for common heights, the ethnic-adjustment table, the alternative indices table, and a variable reference.
Reference Tables & Conversions
An ideal-weight calculator, the WHO classification table, alternative body indices, and a full variable reference.
Ideal weight range for a given height
WHO BMI Classification and Weight Ranges
Standard adult classification (WHO 1995, 2000). Weight ranges shown for three common heights.
| Class | BMI range | Weight at 160 cm | Weight at 175 cm | Weight at 190 cm | Notes |
|---|---|---|---|---|---|
| Severe thinness | < 16.0 | < 41.0 kg | < 49.0 kg | < 57.8 kg | Clinical intervention typically indicated |
| Moderate thinness | 16.0 – 16.9 | 41.0 – 43.2 kg | 49.0 – 51.7 kg | 57.8 – 61.0 kg | Nutritional assessment advised |
| Mild thinness | 17.0 – 18.4 | 43.5 – 47.1 kg | 52.1 – 56.3 kg | 61.4 – 66.4 kg | Lower end of population distribution |
| Normal weight | 18.5 – 24.9 | 47.4 – 63.7 kg | 56.7 – 76.3 kg | 66.8 – 89.9 kg | Lowest all-cause mortality in most studies |
| Overweight (pre-obese) | 25.0 – 29.9 | 64.0 – 76.5 kg | 76.6 – 91.6 kg | 90.3 – 107.9 kg | Elevated metabolic risk at population level |
| Obese class I | 30.0 – 34.9 | 76.8 – 89.3 kg | 91.9 – 106.9 kg | 108.3 – 126.0 kg | Substantially elevated risk |
| Obese class II | 35.0 – 39.9 | 89.6 – 102.1 kg | 107.2 – 122.2 kg | 126.4 – 144.0 kg | Severe obesity |
| Obese class III | ≥ 40.0 | ≥ 102.4 kg | ≥ 122.5 kg | ≥ 144.4 kg | Very severe obesity; bariatric evaluation common |
Alternative Body Indices
BMI is not the only anthropometric index. Several alternatives were developed to address its weaknesses — particularly the fact that m/h² does not scale isometrically and that BMI cannot distinguish muscle from fat.
| Index | Formula | Units | Typical normal range | Notes |
|---|---|---|---|---|
| BMI | m / h² | kg/m² | 18.5 – 24.9 | The standard; simple but ignores composition |
| BMI Prime | BMI / 25 | — | 0.74 – 1.00 | Ratio to upper normal limit; ≤1 is "normal" |
| Ponderal Index | m / h³ | kg/m³ | 11 – 15 (adults) | More isometric; sometimes used in paediatrics |
| New BMI (Trefethen) | 1.3 · m / h²·⁵ | kg/m²·⁵ | ~18.5 – 25 | Adjusts for the non-quadratic scaling of mass |
| Body Surface Area (Mosteller) | √(h · m / 3600) | m² | 1.6 – 2.0 | Used for drug dosing and cardiac index |
| Waist-to-Height Ratio | waist / h | — | < 0.5 | Captures fat distribution; better than BMI for CV risk |
| Waist-to-Hip Ratio | waist / hip | — | < 0.90 (M) · < 0.85 (F) | Captures visceral fat distribution |
| Body Fat Percentage | various (DEXA, BIA, skinfold) | % | 10–20 (M) · 18–28 (F) | The most direct measure of adiposity |
Variable Reference
| Symbol | Meaning | Typical range | Notes |
|---|---|---|---|
| BMI | Body mass index | 10 – 50 kg/m² | = m / h²; the primary output of this calculator |
| m | Body mass | 20 – 200 kg | Total mass; does not distinguish fat from lean |
| h | Height | 1.4 – 2.1 m | Standing height; decreases with age after 40 |
| BMI Prime | BMI / 25 | 0.74 – 1.00 (normal) | A ratio: how close to the upper normal limit |
| Ponderal Index | m / h³ | 11 – 15 kg/m³ | Alternative to BMI; less height-biased |
| BSA | Body surface area | 1.6 – 2.0 m² | Used for drug dosing and cardiac output index |
What Does BMI = m / h² Measure?
The body mass index connects three quantities: body mass (m), height (h), and their ratio (BMI). It answers the question that Quetelet first posed in the 1830s — given a person's mass and height, how do they compare to the population average? The answer is a single dimensionless number that correlates reasonably well with body fat at the population level, and which has become the most widely used anthropometric screening tool in the world.
Body Mass Index Formula
The defining relation, in SI units:
where mass is in kilograms and height is in metres. Rearranged to solve for the other two unknowns:
h = √( m / BMI )
In imperial units (mass in pounds, height in inches), the formula gains a conversion factor of 703:
The BMI prime — the ratio of BMI to the upper normal limit — is simply:
Body Mass Index Variables
| Symbol | Meaning | Notes |
|---|---|---|
| BMI | Body mass index | The screening index; units kg/m² |
| m | Body mass | Total mass in kilograms; not lean mass |
| h | Height | Standing height in metres |
| h² | Height squared | The scaling term that BMI normalises against |
| BMI Prime | BMI / 25 | Ratio to upper limit; easy to interpret |
| PI | Ponderal Index | Alternative index = m / h³ |
How Each Variable Affects BMI
The relation is linear in mass and inverse-square in height. This means small height differences have a larger impact on BMI than the same fractional mass differences. If you increase mass by 10% at fixed height, BMI rises 10%. But if you increase height by 10% at fixed mass, BMI falls by about 17% — because height enters as h². This is why the same mass can classify as "normal" at 190 cm and "overweight" at 175 cm, and why height errors of a few centimetres shift BMI by more than most people expect.
The inverse-square dependence also explains the historical criticism of BMI: the formula assumes that body mass scales with the square of height, but in real populations mass scales closer to h²·⁵ or h³ because taller people are not just scaled-up shorter people. This is why the "New BMI" of Trefethen uses an exponent of 2.5 and why the Ponderal Index uses h³. For adults in the typical height range of 1.5–1.9 m, however, the difference between these indices is modest and BMI remains the standard for its simplicity and its vast reference base.
BMI Calculation Examples
BMI = 70 / (1.75)² = 70 / 3.0625 = 22.86 kg/m² — normal weight
BMI = 90 / 3.0625 = 29.39 kg/m² — overweight (near the obesity boundary)
BMI = 100 / 2.89 = 34.60 kg/m² — obese class I
m = 22 × 1.75² = 22 × 3.0625 = 67.4 kg
h = √(70 / 22) = √3.182 = 1.784 m = 178.4 cm
BMI Prime = 22.86 / 25 = 0.914
Frequently Asked Questions
BMI was devised in the 1830s by the Belgian mathematician, astronomer, and statistician Adolphe Quetelet, who was studying the statistical distribution of human physical traits. He observed that in adults, body mass tended to scale with the square of height, and he proposed the ratio m/h² as a way to compare people of different sizes — he called it the "social physics" of the average man. The formula was rediscovered and renamed "body mass index" by the American physiologist Ancel Keys in a landmark 1972 paper that compared several anthropometric indices and concluded that m/h² was the best simple proxy for body fat. Since then, the WHO and most national health authorities have adopted BMI as the standard population-level screening tool.
The World Health Organization classification for adults (18–65 years) defines the following categories: severe thinness below 16.0, moderate thinness 16.0–16.9, mild thinness 17.0–18.4, normal weight 18.5–24.9, overweight (pre-obese) 25.0–29.9, obese class I 30.0–34.9, obese class II 35.0–39.9, and obese class III (sometimes called "extreme" or "morbid" obesity) at 40.0 and above. These thresholds were derived primarily from studies of European and American populations and correlate with all-cause mortality in a U-shaped curve — the lowest mortality is generally in the 20–25 range, with elevated risk at both extremes.
No — BMI has well-known limitations that make it unreliable as an individual diagnostic. It does not distinguish fat from muscle, so athletes and heavily-muscled people are often misclassified as "overweight" or "obese" despite having low body fat. It does not capture fat distribution, and visceral fat (which surrounds the organs and is more metabolically active) is more harmful than subcutaneous fat at the same BMI. It does not account for frame size, age-related height loss, or ethnic differences in body composition and metabolic risk. For all of these reasons, clinicians typically combine BMI with waist circumference, blood pressure, lipid panel, fasting glucose, and where available, body composition measurements.
Multiple studies have shown that for a given BMI, people of South Asian, Chinese, Japanese, and other Asian ancestries tend to carry a higher percentage of body fat and more visceral fat than people of European ancestry, and they develop type 2 diabetes and cardiovascular disease at lower BMI values. To account for this, the WHO convened an expert consultation in 2004 that recommended additional "action points" for Asian populations: overweight begins at BMI 23 and obesity at BMI 27.5, rather than the standard 25 and 30. Many national health authorities in Asia — including Japan, China, India, Singapore, and Taiwan — have adopted these or even lower thresholds into their clinical guidelines.
For people over 65, the relationship between BMI and health outcomes is more complicated than for younger adults. A number of large epidemiological studies have found that the BMI associated with the lowest mortality shifts upward with age — to roughly 22–27 for people over 65, compared with 20–24 for younger adults. Part of the explanation is that some extra weight in older age provides a reserve to draw on during illness or recovery from surgery. Part is that the normal BMI range in old age partly reflects muscle mass, which is protective. Part is a statistical artefact — smoking-related and illness-related weight loss inflates mortality in the "normal" range.
Not directly. Children's bodies change composition rapidly as they grow, and the standard adult thresholds do not apply. Instead, paediatric BMI is expressed as a percentile for age and sex, using growth reference data from the CDC (in the US) or the WHO (internationally). A child is typically classified as underweight below the 5th percentile, normal weight between the 5th and 85th percentile, overweight between the 85th and 95th, and obese above the 95th. The raw BMI number that corresponds to these percentiles changes dramatically with age: a healthy 5-year-old might have a BMI of 15, while a healthy 15-year-old might have a BMI of 20. This is why the calculator here is designed for adults.
Several alternatives exist, each addressing one or more of BMI's limitations. The BMI Prime (BMI / 25) is simply a rescaling that makes it easy to see how close someone is to the upper normal limit. The Ponderal Index (m / h³) uses a cubic exponent, which is theoretically more correct for isometric scaling but is less widely used in adults. Trefethen's "New BMI" (1.3 · m / h²·⁵) adjusts for the empirical scaling exponent of 2.5. Body surface area (usually Mosteller's formula, √(h · m / 3600)) is used for drug dosing and cardiac index. The waist-to-height ratio (WHtR) captures central adiposity and has been shown in multiple studies to predict cardiovascular risk better than BMI; the widely-quoted rule is "keep your waist to less than half your height".
Yes — both numerator and denominator change with age in ways that make raw BMI harder to interpret in older adults. Height decreases with age, typically by 1–2 cm per decade after 40, due to compression of the spinal discs and loss of vertebral bone density. Because height enters the formula squared, a 3 cm height loss at 175 cm raises apparent BMI by about 4% — meaning that an individual's BMI can increase by nearly a full point without any change in body mass. At the same time, body composition shifts: lean mass declines by 1–2% per year after age 50 (sarcopenia), while fat mass tends to increase and redistribute toward the visceral compartment.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| BMI | Body mass index | kg/m2 |
| mass | Body mass | kg |
| height | Height | m |
What it means
Body Mass Index (BMI) is a widely used screening tool that categorises individuals based on their weight relative to height. It is calculated as mass (kg) divided by the square of height (m). While it does not directly measure body fat, it correlates with adiposity and is associated with health risks. WHO categories: underweight <18.5, normal 18.5‑24.9, overweight 25‑29.9, obesity ≥30. BMI is used in clinical practice, epidemiological studies, and public health. However, it has limitations: it may misclassify athletes or older adults. Despite this, it remains a practical first‑line measure. Understanding BMI is essential for healthcare professionals to initiate weight‑management discussions and to assess risk.
Worked example
Body Mass Index – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| mass (kg) | 70 |
| height (m) | 1.75 |
| Parameter | Value |
|---|---|
| mass | 60 |
| height | 1.6 |
Common mistakes
- Units: mass in kilograms, height in metres. Using pounds and inches gives a wrong result.
- Height squared: Divide by h², not h – a common error.
- Interpretation: BMI is a screening tool, not a diagnostic measure – does not account for muscle mass.
- Categories: Underweight <18.5, normal 18.5‑24.9, overweight 25‑29.9, obese ≥30.
- Children: Use age‑ and sex‑specific percentiles, not adult cut‑offs.
Applications
Body Mass Index (BMI) is a simple anthropometric index that classifies individuals into underweight, normal weight, overweight, or obesity categories based on weight and height. Despite its limitations (it does not distinguish between muscle and fat), it is widely used in clinical practice, public health, and epidemiological research. Healthcare professionals use BMI to screen for weight‑related health risks, to guide counselling, and to monitor population health trends. Public health agencies use it for surveillance and to evaluate intervention programmes. By calculating BMI, clinicians can identify patients at risk for cardiovascular disease, diabetes, and other metabolic conditions. Understanding BMI is essential for promoting healthy lifestyles and for designing effective public health strategies.
- Clinical screening for obesity and underweight
- Risk assessment for metabolic and cardiovascular diseases
- Public health surveillance and epidemiological studies
- Guidance for dietary and exercise interventions
- Entry criteria in clinical trials and research
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