BMI Formula

The BMI formula in metric units

In the International System of Units (SI), the formula is: BMI = mass (kg) / height (m)². Take your weight in kilograms and divide it by your height in meters, squared. This is the formula the World Health Organization uses as its reference definition, and it is the same formula used worldwide outside the US.

Worked example: a person weighing 72 kg who is 1.75 m tall: BMI = 72 / (1.75 x 1.75) = 72 / 3.0625 = 23.5, which falls in the Normal weight band on the BMI chart.

The BMI formula in imperial units (US)

In US customary units, the formula is: BMI = 703 x mass (lb) / height (in)². The 703 is not an arbitrary number, it is a unit-conversion constant that makes the imperial formula produce the exact same BMI value as the metric formula would for the same person. It comes from converting pounds to kilograms (1 lb = 0.453592 kg) and inches to meters (1 in = 0.0254 m), then simplifying: 0.453592 / (0.0254)² works out to approximately 703.07, rounded to 703 in practice.

Worked example: a person weighing 160 lb who is 5'10" (70 inches) tall: BMI = 703 x 160 / (70 x 70) = 703 x 160 / 4900 = 112,480 / 4900 = 23.0. Converting the same person to metric (72.57 kg, 1.778 m) gives BMI = 72.57 / (1.778 x 1.778) = 72.57 / 3.161 = 23.0, the identical result, confirming the two formulas are truly equivalent.

A third worked example, on a category boundary

One more example, this time landing right on a category line so you can see how close the boundaries actually are: a person weighing 203 lb who is 6'0" (72 inches) tall. BMI = 703 x 203 / (72 x 72) = 703 x 203 / 5184 = 142,709 / 5184 = 27.5, which is Overweight, not Obese, but only 2.5 BMI points below the Obese Class I line at 30. This is exactly why the BMI chart page notes that a result close to a boundary is worth re-checking with an accurately measured height and weight rather than treated as a firm cutoff.

Solving the formula backwards: healthy weight for a given height

The same formula can be rearranged to answer a different, often more useful question: "what weight would give me a specific BMI at my height?" Multiplying both sides of the metric formula by height squared gives: weight (kg) = BMI x height (m)². Plugging in 18.5 and 25, the lower and upper edges of the WHO Normal weight band, for a specific height produces the low and high ends of a healthy weight range for that height, exactly what the calculator's "healthy weight for your height" result and the height-to-healthy-weight lookup table both do automatically.

BMI Prime

BMI Prime is a simple derived ratio: BMI Prime = BMI / 25, where 25 is the upper edge of the WHO Normal weight range. Because it is a ratio of two BMI values, BMI Prime has no unit at all, it is just a number. A BMI Prime under 1.0 means a person's BMI sits below the normal-weight ceiling; exactly 1.0 means their BMI is exactly 25; and above 1.0 means their BMI exceeds 25. For the 23.0 BMI example above, BMI Prime = 23.0 / 25 = 0.92. It is mainly a convenience for quickly comparing how far two different BMI values sit from that 25 line, without doing the division by hand each time.

Rather than doing this arithmetic by hand every time, the BMI calculator works out your BMI Prime automatically alongside your BMI and healthy weight range.

What the formula does not account for

BMI is deliberately a simple two-variable formula, and that simplicity is both its strength (fast, free, needs no special equipment) and its main limitation. It cannot distinguish between muscle, bone, organ tissue and fat, all of which contribute to total body weight differently. It does not adjust for age, sex, ethnicity or body frame size in the standard adult formula. A bodybuilder with very low body fat and a sedentary person carrying the same weight and height can show the identical BMI number despite very different actual health profiles. According to the CDC, older adults tend to carry more body fat than younger adults at the same BMI, and women tend to carry more body fat than men at an equivalent BMI. None of that is visible in the formula itself, which is exactly why BMI is described as a screening tool rather than a diagnostic one; a result outside the normal range is a reason to look closer, not a conclusion on its own.

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• Cannot separate muscle mass from fat mass
• Does not adjust for age, sex or ethnicity in the standard adult formula
• Less reliable at the extremes of height (very tall or very short people)
• A single snapshot number; a trend over time is often more informative than one reading