Free Testosterone Calculator — Vermeulen Formula
Most testosterone in blood is bound to SHBG or albumin and is biologically inactive. This calculator estimates the small free fraction — the hormonally active portion — from your total testosterone, SHBG and albumin using the Vermeulen 1999 formula.
nmol/L
nmol/L
g/dL
Calculated by the Vermeulen 1999 quadratic formula (estimated, not a direct assay)
- 1
Albumin (nmol/L)
4.3 × 10 ÷ 66,500 × 10⁹ = 646,617 - 2
Albumin binding factor (a)
1 + 0.000036 × 646,617 = 24.28 - 3
Quadratic coefficient B
24.28 + 0.597 × (35 − 20) = 33.233 - 4
Discriminant (B² + 4·A·TT)
33.233² + 4 × 14.494 × 20 = 2,263.97Since C = −TT the term −4AC equals +4·A·TT, so the discriminant is always positive. - 5
Free testosterone (nmol/L)
(−33.233 + √2,263.97) ÷ (2 × 14.494) = 0.495 - 6
Free testosterone (pg/mL)
0.495 × 288.43 = 142.8
How does this calculator work?
Free testosterone is estimated from total testosterone, SHBG and albumin using the Vermeulen 1999 quadratic formula. The association constants Ka_SHBG = 5.97×10⁸ L/mol and Ka_alb = 3.6×10⁴ L/mol yield a free fraction of ~1–3 % in typical adult males. Results are validated surrogates for equilibrium dialysis and should be interpreted by a clinician.
Formula
How this is calculated
Only about 1–3 % of circulating testosterone is unbound (free) and able to enter cells and exert biological effects. The remainder is tightly bound to sex hormone-binding globulin (SHBG) — which holds roughly 50–70 % of total testosterone in an essentially non-dissociable manner — or loosely bound to albumin (about 30–40 %), which dissociates readily and is therefore considered bioavailable along with free testosterone.
The Vermeulen 1999 model (Vermeulen A, Verdonck L, Kaufman JM, J Clin Endocrinol Metab) uses known association constants: Ka_SHBG = 5.97 × 10⁸ L/mol and Ka_alb = 3.6 × 10⁴ L/mol. Because SHBG binding follows a saturable Langmuir isotherm while albumin binding is linear at physiological concentrations, the mass-balance equation is quadratic in free testosterone. The positive root gives the estimated free fraction. Bioavailable testosterone is the sum of free plus albumin-bound testosterone.
The formula assumes a standard albumin of 4.3 g/dL when not measured; entering your actual lab value improves accuracy. This method is a validated surrogate for equilibrium dialysis (the gold-standard direct assay) and is used in clinical practice when direct measurement is unavailable. Reference ranges vary by age, sex and laboratory — always interpret results with a qualified healthcare professional.
Frequently asked questions
Only unbound (free) testosterone enters cells and binds androgen receptors. Men with elevated SHBG can have a normal total testosterone but low free testosterone and symptoms of hypogonadism. Conversely, low SHBG can give a low total T but an adequate free T. Free testosterone reconciles this discordance.
Reference ranges depend on the assay and laboratory. A commonly cited range for adult males aged 20–49 is approximately 50–210 pg/mL (174–729 pmol/L) by equilibrium dialysis. These values decline with age. This calculator uses 50–210 pg/mL as a broadly cited reference — always check your laboratory's age-specific reference range.
The Vermeulen 1999 method correlates well with equilibrium dialysis (r ≈ 0.93–0.97 in published studies) and is endorsed by the Endocrine Society as an acceptable alternative when direct assay is not available. However, it can deviate in patients with very abnormal albumin levels, liver or kidney disease, or extreme SHBG values. A direct assay by equilibrium dialysis is preferred for clinical decisions in borderline cases.
Also known as
TG we-Calculate Editorial Team. (2026). Free Testosterone Calculator — Vermeulen Formula [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/free-testosterone-calculator
TG we-Calculate Editorial Team. "Free Testosterone Calculator — Vermeulen Formula." TG we-Calculate. 2026. https://we-calculate.com/calculator/free-testosterone-calculator.
TG we-Calculate Editorial Team, "Free Testosterone Calculator — Vermeulen Formula," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/free-testosterone-calculator
@misc{wecalculate_free_testosterone_calculator, title = {Free Testosterone Calculator — Vermeulen Formula}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/free-testosterone-calculator}}, year = {2026}, note = {TG we-Calculate} }
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