Clinical Medicine & Physiology
Bioelectrical Impedance (BIA) Formula: Height^2 / R Index, Kushner TBW & Lukaski FFM
Calculate Resistive Impedance Index H^2 / R_50 (cm^2/Ohm), Kushner-Schoeller Total Body Water (TBW, L), and Fat-Free Mass (FFM = TBW / 0.732) from 50-kHz tetrapolar Bioelectrical Impedance Analysis.
Why conductor volume V = rho * L^2 / R turns Height^2 / Resistance into Total Body Water!
Adipose fat tissue is anhydrous and electrically insulating, whereas Lean Soft Tissue (~73.2% water rich in Na+, K+, and Cl- electrolytes) conducts a harmless 50-kHz tetrapolar alternating micro-current from wrist to ankle! By Ohm’s Law for a cylindrical ionic conductor of length L (~= Stature Height H in cm), cross-sectional area A, and ionic resistivity rho, electrical resistance is R = rho * L / A = rho * (L^2) / (A * L) = rho * (L^2) / Volume — rearranged as Volume = rho * ((H^2) / R)!
Validated against deuterium-oxide (D_2O) isotope dilution and hydrodensitometry by Henry C. Lukaski et al. (1985, 1986, Am. J. Clin. Nutr.) and Robert F. Kushner, D. A. Schoeller et al. (1986, 1992, Am. J. Clin. Nutr.), the 50-kHz Resistive Impedance Index RI = (Height_cm^2) / R_50_Ohm (cm^2/Ohm) predicts Total Body Water cleanly via Kushner (1992) Adult Equation: TBW (L) = 0.593 * ((Height_cm^2) / R_50) + 0.065 * Weight_kg + 0.04, yielding Pace-Rathbun Fat-Free Mass FFM (kg) = TBW / 0.732 and Percent Body Fat %BF = 100 * (Weight_kg - FFM) / Weight_kg!
| 50-kHz Tetrapolar BIA Profile (Height = 175 cm -> H^2 = 30,625 cm^2) | Measured Resistance R_50 (Ohm) | Impedance Index H^2 / R | Kushner TBW & Pace-Rathbun FFM |
|---|---|---|---|
| Muscular Athlete (82 kg) | 430 Ohm (Low Resistance) | 71.22 cm^2/Ohm | TBW = 47.61 L -> FFM = 65.04 kg (20.7% BF) |
| Average Adult (76 kg) | 510 Ohm | 60.05 cm^2/Ohm | TBW = 40.59 L -> FFM = 55.45 kg (27.0% BF) |
| Sarcopenic / Low Lean Mass (68 kg) | 625 Ohm (High Resistance) | 49.00 cm^2/Ohm | TBW = 33.52 L -> FFM = 45.79 kg (32.7% BF) |
Kushner (1992) 50-kHz BIA Total Body Water TBW (Liters)
Evaluates 0.593 * ((Height_cm^2) / R_50_Ohm) + 0.065 * Weight_kg + 0.04 across Height B2 (cm), Body Weight B3 (kg), and 50-kHz wrist-to-ankle Resistance R_50 B4 (Ohm in 150..1,200).
=IF(OR(B2 < 100, B2 > 230, B3 < 25, B3 > 250, B4 < 150, B4 > 1200), "Invalid Height (cm), Weight (kg), or 50-kHz Resistance R (150–1,200 Ohm)", ROUND(0.593 * ((B2 ^ 2) / B4) + 0.065 * B3 + 0.04, 2))BIA Fat-Free Mass FFM (kg) = TBW / 0.732 (Pace-Rathbun Euhydrated Constant)
Divides unrounded Kushner TBW (L) by standard mammalian lean-tissue hydration fraction 0.732 (73.2% water in fat-free mass).
=IF(OR(B2 < 100, B2 > 230, B3 < 25, B3 > 250, B4 < 150, B4 > 1200), "Invalid BIA Inputs", ROUND((0.593 * ((B2 ^ 2) / B4) + 0.065 * B3 + 0.04) / 0.732, 2))Try the example
Use the original values or change them to test your understanding.