Free Testosterone Calculator (Vermeulen equation from total T, SHBG and albumin)

Understanding the free testosterone calculator — concept and principle

This calculator estimates free and bioavailable testosterone from total testosterone, sex hormone-binding globulin (SHBG) and albumin using the Vermeulen equation. Doctors use it when total testosterone is borderline or when SHBG is unusually high or low, for example with ageing, obesity or thyroid disease.

Most testosterone is bound: with the default inputs the result is 323 pmol/L (free = 1.86% of total).

How it is calculated

N = 1 + K_alb × albumin (mol/L), with K_alb = 3.6 × 10⁴ L/mol and albumin molar mass 69,000 g/mol.

Free testosterone (FT) is the positive root of: N × K_SHBG × FT² + (N + K_SHBG × (SHBG − TT)) × FT − TT = 0, with K_SHBG = 1.0 × 10⁹ L/mol and all concentrations in mol/L.

Bioavailable testosterone = FT × N (free plus albumin-bound).

Conversions: 1 nmol/L = 28.842 ng/dL; 1 pmol/L = 0.28842 pg/mL.

The principle

In blood, testosterone is partly bound tightly to SHBG, partly loosely to albumin and only about 1–3% is free. Free and albumin-bound hormone can reach tissues, so together they are called bioavailable. Each binding follows the law of mass action: bound = constant × free hormone × free binding sites. Writing the balance for total testosterone gives a quadratic equation in FT, which has one positive solution.

Worked example

Default inputs: total testosterone 500 ng/dL, SHBG 40 nmol/L, albumin 4.3 g/dL.

Total = 500 ÷ 28.842 = 17.34 nmol/L.
N = 1 + 36,000 × 43 ÷ 69,000 = 23.43.
Solving the quadratic gives FT = 0.323 nmol/L = 323 pmol/L = 93.2 pg/mL.
Free share = 0.323 ÷ 17.34 = 1.86%.
Bioavailable = 0.323 × 23.43 = 7.57 nmol/L = 218 ng/dL.

Each point is the calculator re-run with only “Total testosterone” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Total testosterone	Free testosterone (pmol/L)
125	71
250	149
375	233
500	323
625	420
750	523
1,000	749

How to read the result

Reference ranges for free testosterone depend on the laboratory, age and sex, so compare with the range your lab or doctor uses. Low SHBG raises the free share and high SHBG lowers it, which is why total testosterone alone can mislead. Testosterone should be measured in the morning and confirmed on a second sample.

Common mistakes

Entering total testosterone in nmol/L while the unit is set to ng/dL.
Entering albumin in g/L (43) instead of g/dL (4.3).
Comparing calculated free testosterone with a range meant for a direct immunoassay method.

Keep in mind: This is not a diagnosis. Low or high testosterone should be assessed by a doctor together with symptoms and repeat tests.

Frequently asked questions

Is calculated free testosterone accurate?

It agrees well with equilibrium dialysis in most people, but less so in pregnancy, liver disease or nephrotic syndrome.

Why does SHBG matter?

SHBG binds testosterone tightly; the more SHBG, the less is free to act on tissues.

Can I use a typical albumin value?

Yes. 4.3 g/dL is a common default and changes the result only modestly within the normal range.

Sources: 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):3666–3672

Checked 9 Nov 2026. 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):3666–3672; equation steps and constants as written in the statistical analysis plan of trial NCT01554618 (section 3.6.7, ClinicalTrials.gov); fixed albumin 43 g/L discussion: Lab Medicine Blog, “Tackling the Testosterones: Total, Free, and Bioavailable” (2019).

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