Free Testosterone Calculator (Vermeulen Equation): Free and Bioavailable Testosterone
Calculate free and bioavailable testosterone from total testosterone, SHBG and albumin with the Vermeulen equation, in pg/mL, ng/dL and pmol/L, with lab reference ranges by age.
How it works
N = 1 + Ka × [albumin] · N·Kt·[FT]² + (N + Kt·([SHBG] − [TT]))·[FT] − [TT] = 0 → [FT] = (−b + √(b² + 4·N·Kt·[TT])) ÷ (2·N·Kt) · Bioavailable T = [FT] × N · Kt = 1.0 × 10⁹ L/mol (SHBG), Ka = 3.6 × 10⁴ L/mol (albumin), all concentrations in mol/L
Only 1–4% of the testosterone in blood is free. Roughly half is bound tightly to SHBG and the rest loosely to albumin. Free testosterone plus the albumin-bound part is called bioavailable testosterone, because albumin lets go of it easily in tissues. Measuring free testosterone directly by equilibrium dialysis is slow and expensive, so labs such as LabCorp calculate it with the equation of Vermeulen, Verdonck and Kaufman (1999), which agreed closely with equilibrium dialysis in their study. It applies the law of mass action with fixed binding constants for SHBG (10⁹ L/mol) and albumin (3.6 × 10⁴ L/mol) and solves a quadratic for the free fraction. Enter total testosterone and SHBG from the same blood test. If albumin was not measured, the standard 4.3 g/dL works well for healthy people, but use a measured albumin in liver or kidney disease, pregnancy or acute illness. The result is compared with LabCorp’s age- and sex-specific reference range for calculated free testosterone, and a table shows how much free testosterone changes with SHBG at your total level. This site had no testosterone or SHBG tool before; the Absolute Neutrophil Count and other lab calculators cover different blood tests. Some online calculators use an albumin molar mass of 66,500 g/mol instead of Vermeulen’s 69,000, which gives free values about 2% lower.
Worked example
Total testosterone 600 ng/dL, SHBG 35 nmol/L and albumin 4.3 g/dL. Total T = 600 ÷ 28.842 = 20.803 nmol/L. Albumin = 43 g/L ÷ 69,000 = 6.232 × 10⁻⁴ mol/L, so N = 1 + 36,000 × 0.0006232 = 23.435. Solving the quadratic gives free testosterone 0.4350 nmol/L = 125.5 pg/mL (435 pmol/L, 12.55 ng/dL), 2.09% of the total. Bioavailable testosterone is 0.4350 × 23.435 = 10.19 nmol/L (294 ng/dL, 49.0%), albumin-bound 9.76 nmol/L and SHBG-bound 10.61 nmol/L. For a 40-year-old man LabCorp’s range is 42.3–190.0 pg/mL, so the result is within the reference range.
Sources: Lab Medicine Blog: Tackling the testosterones (Vermeulen equation, albumin 40–50 g/L = 5.8–7.2 × 10⁻⁴ mol/L) · LabCorp: Testosterone, Free, Profile I (calculated by Vermeulen; reference intervals) · Best-Calculators: Free testosterone calculator (constants and 600 ng/dL worked example) · ISSAM: Free and bioavailable testosterone calculator
Frequently asked questions
What is a normal free testosterone level for men?
Ranges depend on the lab and age. LabCorp’s calculated free testosterone range is 47.7–173.9 pg/mL for men aged 18–30, 42.3–190.0 pg/mL at 31–40, falling to 31.7–120.8 pg/mL at 71–80. As a share of total testosterone, free testosterone is usually about 1.5–3%.
What is the difference between free and bioavailable testosterone?
Free testosterone is the 1–4% not bound to any protein. Bioavailable testosterone is free testosterone plus the part loosely bound to albumin, typically 30–60% of the total. Only the SHBG-bound part, which is held tightly, is excluded.
Why is my total testosterone normal but free testosterone low?
A high SHBG binds more testosterone, leaving less free. SHBG rises with age, hyperthyroidism, liver disease, low body weight and some drugs. With total testosterone at 600 ng/dL, raising SHBG from 35 to 80 nmol/L drops calculated free testosterone from about 125 to 68 pg/mL. Obesity and type 2 diabetes do the opposite: low SHBG can make total testosterone look low while free testosterone is normal.
Is calculated free testosterone accurate?
The Vermeulen equation tracks equilibrium dialysis closely in most men, though later studies found it can read somewhat higher than dialysis. It is less reliable when albumin is very low, in pregnancy, with drugs that bind SHBG, and at the very low levels seen in women and children.
How do I convert testosterone from nmol/L to ng/dL?
Multiply nmol/L by 28.84 to get ng/dL (and divide to go back). For free testosterone, nmol/L × 288.4 = pg/mL, and pmol/L ÷ 3.467 = pg/mL. For example 0.435 nmol/L = 125.5 pg/mL = 12.55 ng/dL.
Should albumin be measured or can I use 4.3 g/dL?
Vermeulen showed that a fixed 4.3 g/dL (43 g/L) gives almost the same result as measured albumin in healthy people. Use the measured value when albumin is likely abnormal, for example with nephrotic syndrome, cirrhosis, malnutrition or pregnancy.
Related calculators
Educational estimate, not a diagnosis. Calculated free testosterone depends on the lab’s total testosterone and SHBG assays, and reference ranges differ between labs. Low testosterone should be confirmed with repeat early-morning fasting tests and assessed by a clinician; do not start, stop or change hormone treatment based on this calculator.