Skip to main content

Free vs Total Testosterone: How the Vermeulen Equation Computes the Active Fraction

Why total testosterone misses key information, how SHBG binding works, and how the Vermeulen equation estimates your biologically active free testosterone.

Why Total Testosterone Misses the Picture

When a laboratory measures “testosterone,” it typically reports total testosterone — the sum of all testosterone in the blood, regardless of whether it is biologically available or not. This number can be misleading, because most testosterone in the blood is tightly bound to proteins and unable to interact with androgen receptors.

Testosterone in blood exists in three fractions:

  1. SHBG-bound (~60–70% in healthy adults): Tightly bound to sex hormone-binding globulin (SHBG). This fraction is biologically inert — SHBG holds testosterone so tightly that it cannot enter cells and activate androgen receptors.

  2. Albumin-bound (~30–35%): Loosely bound to albumin, the most abundant protein in blood. This binding is weak enough that testosterone can dissociate and enter tissues. The albumin-bound fraction is considered biologically available.

  3. Free testosterone (~1–4%): Completely unbound. This is the most immediately active fraction.

Bioavailable testosterone = free + albumin-bound. It represents the total testosterone that your tissues can actually use.

Two people can have the same total testosterone level but very different bioavailable and free testosterone concentrations, simply because their SHBG levels differ.

The Problem with Measuring Free Testosterone Directly

The gold standard for measuring free testosterone is equilibrium dialysis — a laboratory technique that physically separates the free fraction by dialysing serum across a semi-permeable membrane. This is accurate but expensive, technically demanding, and rarely available in routine clinical laboratories.

Most clinical labs that offer “free testosterone” use analog immunoassay kits. These kits are designed to bind only the free fraction, but they are affected by immunoassay artefacts and have been shown in multiple studies to produce unreliable results — often over- or under-estimating free testosterone by 30–50% compared to equilibrium dialysis.

The Endocrine Society and the International Society for the Study of the Aging Male (ISSAM) both recommend against using analog immunoassay for free testosterone measurement and endorse the Vermeulen equation (or similar calculated methods) as the practical alternative.

The Vermeulen Equation

The Vermeulen equation, published by Alex Vermeulen and colleagues in the Journal of Clinical Endocrinology and Metabolism in 1999, models testosterone binding equilibria using mass-action equations.

The equation uses three binding constants:

  • Ka = 3.6 × 10⁴ L/mol (albumin–testosterone association constant)
  • Kb = 5.97 × 10⁸ L/mol (SHBG–testosterone association constant)
  • MW albumin = 66,500 g/mol (to convert albumin from g/dL to molar concentration)

The calculation proceeds as follows:

  1. Convert total testosterone to nmol/L (if in ng/dL, multiply by 0.03467)
  2. Convert albumin (g/dL) to molar concentration: (albumin_gdl × 10) / 66500
  3. Convert SHBG (nmol/L) to mol/L: shbg_nmoll × 1×10⁻⁹
  4. Compute the binding denominator: 1 + Ka × [Albumin] + Kb × [SHBG]
  5. Free testosterone (mol/L) = totalT_mol / denominator
  6. Bioavailable T = free T + albumin-bound T

The equation assumes equilibrium binding, standard temperature (37°C), and a mildly acidic pH (7.4). These are reasonable approximations for most fasting venous blood samples.

Worked Example (Vermeulen 1999 Reference Values)

Using the reference values from the Vermeulen 1999 paper:

  • Total T: 15 nmol/L
  • SHBG: 40 nmol/L
  • Albumin: 4.3 g/dL

Step-by-step:

  • [Albumin] = (4.3 × 10) / 66500 = 6.466 × 10⁻⁴ mol/L
  • [SHBG] = 40 × 10⁻⁹ = 4.0 × 10⁻⁸ mol/L
  • Denominator = 1 + (3.6×10⁴ × 6.466×10⁻⁴) + (5.97×10⁸ × 4.0×10⁻⁸) = 1 + 23.28 + 23.88 = 48.16
  • Free T = 15 × 10⁻⁹ / 48.16 ≈ 3.11 × 10⁻¹⁰ mol/L
  • Converting to pg/mL: 3.11 × 10⁻¹⁰ mol/L × 288.4 g/mol × 1×10⁹ = ~89.8 pg/mL

The calculator produces approximately 89.8 pg/mL free testosterone for these reference inputs.

How SHBG Affects the Result

SHBG has a far larger effect on free testosterone than albumin, because SHBG binds testosterone approximately 16,000 times more tightly than albumin does (compare Ka vs Kb).

If SHBG doubles from 40 to 80 nmol/L (all other values the same):

  • Denominator ≈ 1 + 23.28 + 47.76 = 72.04 (vs 48.16)
  • Free T drops by approximately 33%

Conditions that raise SHBG (and therefore lower free T): aging (SHBG rises with age in men), liver disease, hyperthyroidism, oral estrogen therapy.

Conditions that lower SHBG (and therefore raise free T): obesity, insulin resistance, hypothyroidism, exogenous androgens.

Reference Ranges

Reference ranges for calculated free testosterone vary by laboratory and the reference population used. Typical adult male ranges (using the Vermeulen equation or equilibrium dialysis):

  • Free testosterone: 50–210 pg/mL (commonly used range)
  • Bioavailable testosterone: 130–680 ng/dL

These ranges decrease substantially with age. A 65-year-old man will typically have a lower free T than a 30-year-old at the same total T, because SHBG increases with age.

For women, free testosterone reference ranges are much lower (typically 1–8.5 pg/mL in premenopausal women) and decline after menopause. Interpretation requires clinical context.

Important Caveats

The Vermeulen equation is the best available practical tool for estimating free testosterone, but it carries several caveats:

  • Albumin assumption: The equation performs best when albumin is near the normal range. In patients with hypoalbuminaemia (liver disease, nephrotic syndrome, malnutrition), albumin-bound testosterone will be low regardless of the Vermeulen output.
  • Non-standard temperatures or pH: The binding constants were derived at 37°C, pH 7.4. Clinical samples drawn under different conditions may deviate slightly.
  • Extreme SHBG values: At very high SHBG (>100 nmol/L), the equation may overestimate free T compared to equilibrium dialysis.

All interpretation should be done by a qualified clinician in the context of your complete clinical picture.