Clinical Medicine & Physiology
Siri (1956) & Brozek (1963) Body Density to Body Fat % Formula: Hydrostatic & BodPod
Convert two-compartment whole-body density D_b (g/cm^3) from hydrostatic underwater weighing, air-displacement plethysmography (BodPod), or skinfold equations into Percent Body Fat (%BF) and Fat-Free Mass using Siri (495/D_b - 450) and Brozek (457/D_b - 414.2).
How two-compartment densitometry separates 0.900 g/cm^3 lipid from ~1.100 g/cm^3 fat-free mass!
Underwater hydrostatic weighing and Air-Displacement Plethysmography (BodPod) measure whole-body volume V_body (corrected for residual lung volume and thoracic gas), dividing body mass by volume to obtain Whole-Body Density D_b (g/cm^3)! Modeling the human body as anhydrous triglyceride fat (density d_FM = 0.9007 g/cm^3 at 37°C) plus hydrated Fat-Free Mass (density d_FFM = 1.1000 g/cm^3), William E. Siri (1956, Adv. Biol. Med. Phys.) derived the classic hyperbola: %BF_Siri = (495 / D_b) - 450!
Analyzing direct human cadaver chemical composition, Josef Brozek et al. (1963, Ann. N.Y. Acad. Sci.) established a reference body with slightly higher fat-free density weighting, yielding %BF_Brozek = (457 / D_b) - 414.2 — preferred in very lean or obese extremes and certain ethnic cohorts where Siri slightly overestimates fat change per density increment!
| Whole-Body Density D_b (g/cm^3) | Siri (1956) %BF = 495/D_b - 450 | Brozek (1963) %BF = 457/D_b - 414.2 | Fat-Free Mass on 80.0 kg Adult (Siri) |
|---|---|---|---|
| D_b = 1.075 g/cm^3 (Athletic) | 10.47% | 10.92% | 71.63 kg FFM |
| D_b = 1.055 g/cm^3 (Fitness) | 19.19% | 18.98% | 64.64 kg FFM |
| D_b = 1.030 g/cm^3 (Elevated Adiposity) | 30.58% | 29.49% | 55.53 kg FFM |
Siri (1956) Two-Compartment Percent Body Fat (%BF)
Evaluates (495 / D_b) - 450 across physiological whole-body density B2 (0.92 <= D_b <= 1.11 g/cm^3).
=IF(OR(B2 < 0.92, B2 > 1.11), "Unphysiological Body Density D_b (Requires 0.92–1.11 g/cm^3)", ROUND((495 / B2) - 450, 2))Brozek (1963) Percent Body Fat & Siri Fat-Free Mass (kg)
Computes Brozek %BF = (457 / D_b) - 414.2 for comparison across two-compartment densitometry reports.
=IF(OR(B2 < 0.92, B2 > 1.11), "Unphysiological Body Density D_b (Requires 0.92–1.11 g/cm^3)", ROUND((457 / B2) - 414.2, 2))Try the example
Use the original values or change them to test your understanding.