Clinical Medicine & Physiology
Conicity Index (Valdez) & Waist-to-Height Ratio (WHtR) Calculator: Cylinder vs Bicone
Calculate Roberto Valdez’s (1991) Abdominal Conicity Index C_index = WC_m / (0.109 * SQRT(Weight_kg / Height_m)) and Margaret Ashwell’s universal Waist-to-Height Ratio WHtR = WC / Height (< 0.50 healthy threshold).
Measure geometric progression from a uniform cylinder (C = 1.00) toward a central bicone (C -> 1.73)!
Assuming constant mean human tissue density rho = 1,050 kg/m^3, an adult of mass W_kg and height H_m modeled as a uniform circular cylinder has theoretical circumference 2 * SQRT(PI() * W_kg / (1050 * H_m)) = 0.109 * SQRT(W_kg / H_m) meters! Dividing actual measured Waist Circumference WC_m by that equal-mass cylinder circumference yields Roberto Valdez’s (1991, J. Clin. Epidemiol.) dimensionless Conicity Index: C_index = WC_m / (0.109 * SQRT(Weight_kg / Height_m))!
A perfectly cylindrical torso gives C_index = 1.00, whereas redistributing mass toward the abdomen transitions the silhouette into a double-cone (bicone, theoretical limit 1.73; clinical cardiovascular elevation typically >= 1.25 in men and >= 1.18 in women)! Complementing Conicity Index is Margaret Ashwell’s universal public-health rule ("Keep your waist to less than half your height"): Waist-to-Height Ratio WHtR = WC_cm / Height_cm < 0.50 across both sexes and ethnicities!
| Adult Profile (Height cm, Weight kg, Waist cm) | Valdez Conicity Index C_index | Ashwell WHtR = WC / H | Central Risk Screening |
|---|---|---|---|
| Lean Athletic (H = 180 cm, W = 75 kg, WC = 78 cm) | 1.1086 | 0.4333 (< 0.50) | Low Central Cardiometabolic Risk |
| Borderline Gain (H = 175 cm, W = 82 kg, WC = 91 cm) | 1.2194 | 0.5200 (>= 0.50) | Exceeds WHtR 0.50 Boundary |
| Biconic Central Obesity (H = 172 cm, W = 86 kg, WC = 106 cm) | 1.3753 | 0.6163 (>= 0.60) | High Visceral / Biconic Risk |
Valdez (1991) Dimensionless Abdominal Conicity Index C_index
Evaluates (WC_cm / 100) / (0.109 * SQRT(Weight_kg / (Height_cm / 100))) across Height B2 (cm), Weight B3 (kg), and Waist B4 (cm).
=IF(OR(B2 < 100, B2 > 240, B3 < 25, B3 > 300, B4 < 40, B4 > 200), "Invalid Height, Weight, or Waist Inputs", ROUND((B4 / 100) / (0.109 * SQRT(B3 / (B2 / 100))), 4))Ashwell Waist-to-Height Ratio (WHtR) & 0.50 Screening Rule
Computes ROUND(WC_cm / Height_cm, 4) across identical centimeter units.
=IF(OR(B2 < 100, B2 > 240, B4 < 40, B4 > 200), "Invalid Height or Waist Inputs", ROUND(B4 / B2, 4))Try the example
Use the original values or change them to test your understanding.