BMI Formula and Calculations

Review the metric and U.S. BMI formulas, adult thresholds, healthy-weight equation, BMI Prime, Ponderal Index, and CDC BMI-for-age methods.

How do the BMI Calculator formulas work?

This formula page defines the variables used by the BMI Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Formula Overview

Body mass index is weight divided by height squared. The core equation is the same for adults, children, and teens. What changes is the interpretation: adults use fixed categories, while ages 2-19 use CDC age- and sex-specific reference data.

Variable Definitions

Symbol	Meaning	Unit
BMI	Body mass index	kg/m²
W_kg	Body weight	Kilograms
W_lb	Body weight	Pounds
H_m	Height	Meters
H_in	Total height	Inches
L, M, S	CDC growth-chart parameters for the selected age and sex	Reference values
P₉₅	Age- and sex-specific 95th-percentile BMI	kg/m²
Φ	Standard normal cumulative distribution function	Probability

Metric BMI Formula

BMI=\frac{W_{kg}}{H_m^2}

Divide weight in kilograms by height in meters squared. When height is entered in centimeters, divide it by 100 before squaring.

BMI=\frac{W_{kg}}{(H_{cm}/100)^2}

U.S. Customary BMI Formula

BMI=\frac{703\,W_{lb}}{H_{in}^2}

Total height in inches equals feet multiplied by 12 plus the remaining inches. The direct factor 703 is rounded. The production engine instead converts pounds and inches with exact conversion constants before applying the metric equation.

Adult BMI Categories

CDC adult categories apply from age 20 and do not change by age, sex, or race.

Category	BMI range
Underweight	Below 18.5
Healthy weight	18.5 to below 25
Overweight	25 to below 30
Obesity class 1	30 to below 35
Obesity class 2	35 to below 40
Obesity class 3	40 or higher

Adult Healthy-Weight Screening Range

W_{min}=18.5H_m^2\qquad W_{boundary}=25H_m^2

The lower value corresponds to BMI 18.5. The upper displayed value is the weight at BMI 25, the boundary where the adult overweight category begins. This is a mathematical screening range, not an individualized weight goal.

CDC BMI-for-Age Method

For ages 2-19, the calculator first computes BMI and then compares it with the CDC reference for age in months and sex.

At or Below the 95th Percentile

z=\frac{(BMI/M)^L-1}{LS}

percentile=100\Phi(z)

L, M, and S come from the CDC growth-chart data. The calculator interpolates the reference at the entered age in months.

Above the 95th Percentile

percentile=90+10\Phi\left(\frac{BMI-P_{95}}{\sigma}\right)

The extended method uses the age- and sex-specific P₉₅ value and the dispersion parameter sigma. For finer age intervals, the CDC gives these sigma regressions:

\sigma_{girls}=0.8334+0.3712a-0.0011a^2

\sigma_{boys}=0.3728+0.5196a-0.0091a^2

Here, a is age in years. Severe obesity is classified at 120% of P₉₅ or BMI 35 kg/m² or higher.

Worked Adult Metric Calculation

For 75 kg and 1.80 m:

BMI=\frac{75}{1.80^2}=23.1481\ldots

Displayed BMI	23.1
Category	Healthy weight
BMI Prime	0.93
Ponderal Index	12.86 kg/m³
Healthy-weight screening range	59.9-81.0 kg

Precision, Rounding, and Assumptions

The engine keeps full available precision through the calculation.
Classification uses the unrounded BMI, even when the displayed value is rounded.
Adults are age 20 and older; ages 2-19 use the pediatric reference.
Entered age, height, and weight are assumed to be current and accurate.
BMI does not directly measure body fat, muscle, bone density, or fat distribution.
The adult healthy-weight result is not shown as a pediatric recommendation.

Use the BMI examples to reproduce adult and pediatric cases.

References

These references support the calculation method, assumptions, or current program guidance.

Centers for Disease Control and Prevention - Adult BMI Categories
United States. Effective: Published 2024-03-19. Verified: 2026-08-01.
Centers for Disease Control and Prevention - Child and Teen BMI Categories
United States. Effective: Published 2024-06-28. Verified: 2026-08-01.
Centers for Disease Control and Prevention - Data file for the Extended CDC BMI-for-age Growth Charts
United States. Effective: Reviewed 2024-09-02. Verified: 2026-08-01.
National Institute of Diabetes and Digestive and Kidney Diseases - Am I at a Healthy Weight?
United States. Effective: Reviewed 2023-05. Verified: 2026-08-01.

Corrections and Review

Report an issue or error in the calculator using the Contact Us page.

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