Clinical Medicine & Physiology
A Body Shape Index (ABSI) Calculator: Krakauer Allometric Waist-BMI-Height Formula
Calculate Nir Y. Krakauer and Jesse C. Krakauer’s (2012) BMI-independent allometric A Body Shape Index ABSI = WC_m / ((BMI^(2/3)) * (Height_m^(1/2))) and standardized ABSI z-score for premature mortality risk.
Orthogonalize Waist Circumference from BMI and Height via allometric scaling!
Raw Waist Circumference correlates strongly with BMI (r ~= 0.85–0.90), making it hard to tell whether waist size adds independent hazard beyond body mass! Performing log-log allometric regression across 14,105 US NHANES adults, Nir Y. Krakauer and Jesse C. Krakauer (2012, PLOS ONE) found that expected waist circumference scales as BMI^(2/3) * Height^(1/2), defining A Body Shape Index (in SI units m^(11/6) kg^(-2/3)) as ABSI = WC_m / ((BMI^(2/3)) * (Height_m^(1/2)))!
Because raw ABSI values cluster near ~0.075 to ~0.086 m^(11/6) kg^(-2/3) (often reported × 1,000 as ~75 to ~86), Krakauer & Krakauer convert ABSI against age- and sex-specific population mean ABSI_mean and standard deviation ABSI_SD into ABSI_z = (ABSI - ABSI_mean) / ABSI_SD — where each +1.0 SD increase in ABSI_z raises all-cause mortality hazard by ~33%, completely independent of BMI!
| ABSI Standardized Z-Score Band | Relative Mortality Risk Tier (Krakauer 2012) | Body Habitus Interpretation |
|---|---|---|
| ABSI_z < -0.868 | Very Low Risk (~0.80x Hazard) | Slender waist relative to BMI & Height |
| -0.272 <= ABSI_z < +0.229 | Average Population Risk (1.00x) | Age/sex-typical abdominal contour |
| ABSI_z >= +0.798 | High Risk (~1.35x+ Hazard) | Disproportionate central visceral adiposity / sarcopenic obesity |
Scaled ABSI * 1000 (1000 * WC_m / (BMI^(2/3) * Height_m^(1/2)))
Computes BMI = Weight_kg / (Height_m^2) from Height B2 (cm) and Weight B3 (kg), then evaluates 1000 * (B4 / 100) / ((BMI^(2/3)) * ((B2 / 100)^(1/2))) for Waist B4 (cm).
=IF(OR(B2 < 120, B2 > 230, B3 < 30, B3 > 300, B4 < 45, B4 > 200), "Invalid Height, Weight, or Waist Inputs", ROUND(1000 * (B4 / 100) / ((((B3 / ((B2 / 100) ^ 2)) ^ (2 / 3)) * SQRT(B2 / 100))), 4))Standardized ABSI Z-Score (ABSI - ABSI_mean) / ABSI_SD
Standardizes raw ABSI against age/sex NHANES reference mean B5 (e.g., 0.0808) and SD B6 (e.g., 0.0042).
=IF(OR(B2 < 120, B2 > 230, B3 < 30, B3 > 300, B4 < 45, B4 > 200, B5 <= 0, B6 <= 0), "Invalid Anthropometric or Reference Mean/SD Inputs", ROUND((((B4 / 100) / ((((B3 / ((B2 / 100) ^ 2)) ^ (2 / 3)) * SQRT(B2 / 100)))) - B5) / B6, 2))Try the example
Use the original values or change them to test your understanding.