Calculated Free Testosterone (Vermeulen)
Calculated Free Testosterone (Vermeulen)
Solve the Vermeulen equation for free testosterone from total testosterone, SHBG and albumin — the calculation validated against equilibrium dialysis.
Calculated Free Testosterone (Vermeulen)
Solves the SHBG/albumin binding equilibriumTotal testosterone 15 nmol/L, SHBG 30 nmol/L, albumin 4.3 g/dL
The Vermeulen equation
- T, S
- total testosterone and SHBG converted from nmol/L to mol/L (× 10⁻⁹)
- Calb
- albumin converted to mol/L: (g/dL × 10) ÷ 69,000, using an albumin molecular weight of 69,000 Da
- Ka
- 1 × 10⁹ L/mol — the testosterone–SHBG association constant
- Kalb
- 3.6 × 10⁴ L/mol — the testosterone–albumin association constant
- N
- 1 + Kalb·Calb — the albumin binding term
- result
- free testosterone in mol/L, converted to pmol/L by × 10¹²
Worked example
Total testosterone 15 nmol/L, SHBG 30 nmol/L, albumin 4.3 g/dL
T = 1.5 × 10⁻⁸ mol/L · S = 3.0 × 10⁻⁸ mol/L · Calb = 4.3 × 10 ÷ 69,000 = 6.232 × 10⁻⁴ mol/L
N = 1 + (3.6 × 10⁴ × 6.232 × 10⁻⁴) = 23.43
a = N × 10⁹ = 2.343 × 10¹⁰ · b = N + 10⁹ × (S − T) = 38.43
( −b + √(b² + 4aT) ) ÷ 2a = 3.256 × 10⁻¹⁰ mol/L = 325.6 pmol/L free testosterone
What moves SHBG independently of testosterone
| Direction | Causes |
|---|---|
| Raises SHBG | Ageing, hyperthyroidism, cirrhosis, oestrogen, anticonvulsants |
| Lowers SHBG | Obesity, insulin resistance, type 2 diabetes, hypothyroidism, glucocorticoids, nephrotic syndrome |
Why total testosterone can mislead
Total testosterone is only informative when SHBG is normal. Roughly 98% of circulating testosterone is bound — most of it tightly to SHBG, the rest loosely to albumin — and it is the small unbound fraction, together with the albumin-bound fraction that dissociates readily at the tissue capillary bed, that is biologically available. SHBG is raised by ageing, hyperthyroidism, cirrhosis, oestrogen and anticonvulsants, and lowered by obesity, insulin resistance, type 2 diabetes, hypothyroidism, glucocorticoids and nephrotic syndrome. An obese man with a low SHBG can have a low total testosterone and a perfectly normal free testosterone; treating the total number alone would misdiagnose him as hypogonadal.
The Vermeulen equation solves the binding equilibria between testosterone, SHBG and albumin simultaneously, using association constants of 1×10⁹ L/mol for SHBG and 3.6×10⁴ L/mol for albumin. It has been repeatedly validated against equilibrium dialysis, the reference method, and tracks it closely across the clinically relevant range.
Direct “free testosterone” analogue immunoassays are a different matter and are unreliable — they are distorted by the same SHBG abnormalities they are meant to bypass, and professional guidelines advise against using them. Sample between 08:00 and 10:00 fasting, when testosterone is at its diurnal peak, and confirm any low result on a second morning sample before making a diagnosis.
Frequently asked questions
Why not just measure total testosterone?
Because SHBG varies between individuals for reasons unrelated to gonadal function. Total testosterone can be low with a normal free level, or normal with a low free level, depending on SHBG — free testosterone is the biologically relevant fraction.
Is the Vermeulen equation accurate?
Yes. It has been validated repeatedly against equilibrium dialysis, the reference method, and correlates closely with it across the range seen in clinical practice.
Should I use a direct free testosterone immunoassay instead?
No. Direct analogue immunoassays for free testosterone are unreliable, particularly at abnormal SHBG, and are not recommended by endocrine guidelines. Calculate it instead.
When should I sample testosterone?
Between 08:00 and 10:00, fasting, when the diurnal peak gives the most representative result. Confirm any abnormal result on a second morning sample before acting on it.
Related calculators
References
- Vermeulen A, Verdonck L, Kaufman JM. A critical evaluation of simple methods for the estimation of free testosterone in serum. J Clin Endocrinol Metab. 1999;84(10):3666–72.
- Rosner W et al. Position statement: utility, limitations, and pitfalls in measuring testosterone. J Clin Endocrinol Metab. 2007;92(2):405–13.