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Lorentz Formula Ideal Weight Calculator

Enter your height and sex to get the Lorentz ideal weight and the BMI it corresponds to.

How it is calculated

Both versions start from height − 100 (height in cm) and then subtract a correction that grows with height above 150 cm. For men: ideal = (H − 100) − (H − 150) ÷ 4. For women: ideal = (H − 100) − (H − 150) ÷ 2.5. The smaller divisor for women means a larger correction, so women get a lower figure at the same height. The tool then shows the ideal weight in kg and in pounds (kg × 2.20462), and the BMI that weight would have at your height, BMI = kg ÷ height in m², rounded to one decimal. Heights of 100 cm or less return no result. Below 150 cm the correction turns negative and adds weight, so results for short heights should be read cautiously.

Worked example

A man is 180 cm tall. Base = 180 − 100 = 80. Correction = (180 − 150) ÷ 4 = 7.5. Ideal weight = 80 − 7.5 = 72.50 kg, which is 72.5 × 2.20462 = 159.83 lb. The matching BMI is 72.5 ÷ (1.80 × 1.80) = 22.4. A woman of 180 cm would get 80 − 30 ÷ 2.5 = 68 kg, because her correction is 12 instead of 7.5.

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Common mistakes

  • Entering the height in metres or feet instead of centimetres; any value of 100 or below returns nothing.
  • Choosing the wrong sex: at 180 cm the two formulas differ by 4.5 kg.
  • Applying it to a height under 150 cm, where the correction term becomes negative and the result stops matching the formula's design.
  • Reading the BMI in the result as your current BMI; it is the BMI you would have at the ideal weight, not at your real weight.
  • Expecting it to agree with Broca, Devine or Hamwi; every formula uses different constants and the answers can differ by several kilograms.

Sources

About this calculator

The Lorentz formula refines the older Broca index for estimating ideal body weight, correcting for the fact that Broca’s simple height-in-cm-minus-100 rule overestimates ideal weight for taller people. For men: Ideal Weight (kg) = (Height - 100) - ((Height - 150) / 4); for women: Ideal Weight (kg) = (Height - 100) - ((Height - 150) / 2.5). Both formulas only apply meaningfully above 150 cm, which is exactly the range Lorentz was designed to correct.

Developed in the early 20th century, the Lorentz formula predates BMI as a clinical shorthand and is still referenced in some European medical and nutrition contexts as a quick sex-specific ideal weight estimate, particularly because it (unlike a flat BMI target) scales its correction with how tall someone is rather than applying one formula uniformly. It’s most useful as a rough reference point alongside — not a replacement for — BMI and body composition measures, since neither Broca nor Lorentz accounts for frame size or muscle mass.

Your Lorentz ideal weight, along with the BMI that weight corresponds to, is returned from your height and sex.

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