Calculated Free Testosterone (Vermeulen): formula, worked example and cautions with the result
What free, bioavailable and total testosterone are
Total serum testosterone is divided into three fractions: bound to SHBG (sex hormone-binding globulin), with high affinity; bound to albumin, with low affinity; and free, not bound to proteins. Bioavailable testosterone is the sum of the free fraction and the albumin-bound fraction, because the albumin bond comes apart easily in tissues.
The reference method for the free fraction is equilibrium dialysis, which is laborious for routine use. In 1999, Vermeulen, Verdonck and Kaufman compared several simple methods and concluded that free testosterone calculated from total testosterone and measured SHBG was almost identical to that obtained by equilibrium dialysis, except in pregnancy. The free androgen index and the direct analog immunoassay did not prove reliable.
The albumin used in this calculation is the same one measured for albumin-corrected calcium. Metabolic abnormalities, assessed for example by HOMA-IR, are part of the clinical context of hormone testing.
How to use the calculator: inputs, units and outputs
The calculator asks for three values, with the units shown next to each field:
- Total testosterone, in nmol/L, greater than 0 and up to 200. Example: 15.
- Albumin, in g/L, between 10 and 60. Example: 43.
- SHBG, in nmol/L, greater than 0 and up to 500. Example: 40.
Values outside these ranges produce a message saying which field to correct. The albumin range prevents the most common error: entering 4.3 (g/dL) instead of 43 (g/L).
The tool returns five lines: free testosterone in nmol/L (three decimal places) and in pg/mL (one decimal place), free fraction as a percentage of total, bioavailable testosterone in nmol/L and bioavailable fraction as a percentage. A note reminds you that there is no single range for calculated free testosterone and that the valid interval is the laboratory's.
Useful conversions: testosterone in ng/dL divided by 28.84 gives nmol/L, based on the molar mass of 288.4 g/mol; albumin in g/dL multiplied by 10 gives g/L.
Vermeulen formula with the published constants
The Vermeulen model treats the binding of testosterone to SHBG and albumin as chemical equilibria with fixed association constants. The published constants are Kalb = 3.6 × 10⁴ L/mol for albumin and KSHBG = 1 × 10⁹ L/mol for SHBG. All concentrations are entered in mol/L.
N = 1 + Kalb × [Alb]
KSHBG × N × FT² + [N + KSHBG × ([SHBG] − [TT])] × FT − [TT] = 0
Bioavailable = N × FT
FT is free testosterone, the positive root of the quadratic equation; TT is total testosterone; [Alb] is albumin in mol/L, obtained by dividing g/L by the molar mass of 69,000 g/mol. N groups the free and albumin-bound fractions: with albumin of 43 g/L, N equals 23.43.
To display in pg/mL, the tool multiplies nmol/L by 288.42, the molar mass of testosterone. The percentage fractions divide free and bioavailable testosterone by total testosterone. The tool's test cases include a published worked example and others checked by an independent mass-balance calculation.
Step-by-step worked example
Didactic example (not an interpretation of a patient): total testosterone of 10 nmol/L, SHBG of 40 nmol/L and albumin of 43 g/L, the same case used to illustrate the method on the ISSAM page that cites Vermeulen.
- Albumin in mol/L: 43 ÷ 69,000 = 6.23 × 10⁻⁴.
- N = 1 + 3.6 × 10⁴ × 6.23 × 10⁻⁴ = 23.43.
- Coefficients: a = 10⁹ × 23.43 = 2.343 × 10¹⁰; b = 23.43 + 10⁹ × (40 − 10) × 10⁻⁹ = 53.43; c = −10 × 10⁻⁹.
- Positive root: FT = 1.739 × 10⁻¹⁰ mol/L, or 0.174 nmol/L.
- In pg/mL: 0.174 × 288.42 ≈ 50.2 pg/mL. Free fraction: 1.74%.
- Bioavailable: 23.43 × 0.174 = 4.07 nmol/L, or 40.7% of total.
With the example values in the fields (total testosterone 15, albumin 43 and SHBG 40 nmol/L), the tool shows free testosterone of about 0.27 nmol/L. Comparison with the reference interval is done by the physician, with the report.
How to understand free testosterone on the report
Free testosterone is used mainly when total testosterone alone can be misleading. The Endocrine Society guideline on male hypogonadism (Bhasin and colleagues, 2018) recommends the diagnosis only in men with compatible signs and symptoms and unequivocally and consistently low total testosterone, measured in the morning, fasting, by an accurate assay and confirmed on a second sample.
The same guideline recommends measuring free testosterone, by equilibrium dialysis or by an accurate formula, when total testosterone is near the lower limit or when there is a condition that alters SHBG.
The calculator does not classify the result. Free testosterone intervals vary with the method, the reference population and the calculation approach, and we did not find a single published range for the calculated value in pg/mL. That is why the tool shows only the numbers, with a neutral note. The valid interval is the laboratory's, and interpretation is the responsibility of the attending physician.
Common errors, units and verification checklist
The most frequent errors in this calculation involve units, because each laboratory may report testosterone, SHBG and albumin in different units. Check before entering:
- Total testosterone in nmol/L: if it is in ng/dL, divide by 28.84 (for example, 432 ng/dL ≈ 15 nmol/L).
- Albumin in g/L: if it is in g/dL, multiply by 10 (4.3 g/dL = 43 g/L). Values below 10 produce an error message.
- SHBG in nmol/L: the usual unit of immunoassays.
- Collection: in the morning and fasting, as the Endocrine Society guideline recommends for total testosterone.
- Pregnancy: Vermeulen showed that the calculation underestimates the free fraction, because estradiol occupies part of the SHBG binding sites.
- Plausible result: with usual SHBG and albumin, the calculated free fraction is usually around 1% to 3% of total. A value far outside this range calls for checking the units.
For another calculation that uses albumin, see the anion gap.
Equilibrium dialysis, calculation, free androgen index and direct immunoassay
There are four ways to assess testosterone not bound to SHBG. Vermeulen and colleagues (1999) compared all of them, with the results summarized in the table.
| Method | How it works | Performance in the study |
|---|---|---|
| Equilibrium dialysis | Physically separates the free fraction | Reference |
| Calculated free testosterone | Equilibrium equation with total testosterone, SHBG and albumin | Almost identical to dialysis, except in pregnancy |
| Free androgen index (100 × TT ÷ SHBG) | Simple ratio | Not reliable as an index of the free fraction |
| Direct analog immunoassay | Direct measurement of the free fraction | Not reliable as an index of the free fraction |
Bioavailable testosterone can also be measured by ammonium sulfate precipitation, which Vermeulen used to validate the calculation. For the patient's cardiovascular context, the LDL calculator and BMI often accompany the assessment.
Frequently asked questions about calculated free testosterone
What is the difference between free and bioavailable testosterone?
Free testosterone is the fraction not bound to proteins. Bioavailable testosterone adds the free fraction to the albumin-bound fraction, which is released easily in tissues. The SHBG-bound fraction is included in neither.
What constants does the calculator use?
Those published by Vermeulen and colleagues (1999): 1 × 10⁹ L/mol for binding to SHBG and 3.6 × 10⁴ L/mol for albumin, with albumin converted to mol/L using the molar mass of 69,000 g/mol.
In what units should I enter the values?
Total testosterone and SHBG in nmol/L and albumin in g/L. To convert testosterone from ng/dL to nmol/L, divide by 28.84; for albumin from g/dL to g/L, multiply by 10.
How do I convert free testosterone from nmol/L to pg/mL?
Multiply by 288.42, the molar mass of testosterone. For example, 0.174 nmol/L corresponds to about 50 pg/mL. The calculator already shows both units.
Is calculated free testosterone valid in pregnancy?
No. In pregnancy, estradiol occupies part of the SHBG binding sites, and the calculation underestimates the free fraction, according to Vermeulen and colleagues (1999).
Why doesn't the calculator say whether the value is normal?
Because free testosterone intervals depend on each laboratory's method and reference population, and there is no single published range for the calculated value. Compare with the report and take the interpretation to the physician.
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. doi:10.1210/jcem.84.10.6079. View
- ISSAM (International Society for the Study of the Aging Male). Free & bioavailable testosterone calculator: explanation and examples (Vermeulen method, J Clin Endocrinol Metab 1999). View
- Bhasin S, Brito JP, Cunningham GR, Hayes FJ, Hodis HN, Matsumoto AM, et al. Testosterone therapy in men with hypogonadism: an Endocrine Society clinical practice guideline. J Clin Endocrinol Metab. 2018;103(5):1715-44. View
Updated . A support tool for educational purposes; it does not replace clinical assessment.