Free Testosterone Level Calculator

A Free Testosterone Level Calculator is an advanced clinical tool used to estimate the concentration of biologically active testosterone in the bloodstream. While a standard blood test measures your "Total Testosterone," a significant portion of this hormone is bound to proteins—primarily Sex Hormone-Binding Globulin (SHBG) and, to a lesser extent, Albumin. When bound, testosterone is inactive. This calculator uses a scientifically validated formula, known as the Vermeulen equation, to account for these binding proteins. By inputting your Total Testosterone, SHBG, and Albumin levels from a lab report, it calculates an estimate of your "Free Testosterone"—the unbound, active portion that is available for your body's cells to use. This provides a more accurate and clinically relevant picture of your androgen status, which is crucial for healthcare professionals investigating hormonal imbalances, such as hypogonadism in men or hyperandrogenism and Polycystic Ovary Syndrome (PCOS) in women.

formula of Free Testosterone Level Calculator

The calculation of free testosterone is based on the law of mass action and involves solving a quadratic equation to find the concentration of unbound testosterone. The standard quadratic formula, ax² + bx + c = 0, is used where 'x' represents the Free Testosterone concentration.

1. Formula to find Free Testosterone (FT)

Free Testosterone = (-b + sqrt(b² - 4ac)) / (2*a)

The components a, b, and c are derived from the binding constants and the total concentrations of Testosterone, Albumin, and SHBG.

2. Calculating the Components (a, b, c)

Before you can solve for Free Testosterone, you must first calculate the values of a, b, and c using the following formulas.

2.1. Variable 'a'

The 'a' component is simply the binding constant of testosterone to SHBG.
Formula:
a = K_shbg

2.2. Variable 'b'

The 'b' component incorporates the binding constants and the concentrations of SHBG and Albumin.
Formula:
b = 1 + (K_alb * [Albumin]) + (K_shbg * [SHBG]) - (K_shbg * [Total Testosterone])

2.3. Variable 'c'

The 'c' component is the negative of the Total Testosterone concentration.
Formula:
c = -[Total Testosterone]

3. Required Inputs and Constants

You will need values from a blood test and standard constants to perform the calculation. Crucially, all concentrations must be converted to the same unit, typically moles per liter (mol/L), before being used in the formulas.

3.1. Lab Results (Input Variables)

• Total Testosterone [Total Testosterone]: The total concentration of testosterone in the blood.
• Sex Hormone-Binding Globulin [SHBG]: The concentration of the SHBG protein.
• Albumin [Albumin]: The concentration of the albumin protein.

3.2. Standard Binding Constants

These are generally accepted average values for the affinity of testosterone to its binding proteins.

• K_shbg (SHBG-Testosterone association constant): 1 x 10⁹ L/mol
• K_alb (Albumin-Testosterone association constant): 3.6 x 10⁴ L/mol

Reference Tables for Calculation

For an accurate calculation, your lab values must be in the correct units. The following tables provide necessary conversion factors and general reference ranges for free testosterone.

Table 1: Unit Conversion Factors

Lab Test	Common Unit	Conversion to Scientific Unit (mol/L)
Total Testosterone	ng/dL	Value in ng/dL * 0.0347 = value in nmol/L, then / 10⁹
SHBG	nmol/L	Value in nmol/L / 10⁹ = value in mol/L
Albumin	g/dL	Value in g/dL * 1.449 * 10⁻⁴ = value in mol/L

Table 2: Typical Free Testosterone Reference Ranges

These ranges are general guidelines. Laboratory reference ranges may vary, and results should be interpreted by a healthcare professional.

Population	Typical Free Testosterone Range (pmol/L)
Adult Males	200 - 600 pmol/L
Adult Females	5 - 40 pmol/L

Example of Free Testosterone Level Calculator

Let's calculate the free testosterone for a male patient with the following lab results.

• Total Testosterone: 450 ng/dL
• SHBG: 35 nmol/L
• Albumin: 4.2 g/dL

Step 1: Convert all lab results to mol/L.

• Total Testosterone (mol/L) = (450 ng/dL * 0.0347) / 10⁹ = 15.615 nmol/L / 10⁹ = 1.56 x 10⁻⁸ mol/L
• SHBG (mol/L) = 35 nmol/L / 10⁹ = 3.5 x 10⁻⁸ mol/L
• Albumin (mol/L) = 4.2 g/dL * 1.449 * 10⁻⁴ = 6.086 x 10⁻⁴ mol/L

Step 2: Calculate the components a, b, and c.

• a = K_shbg = 1 x 10⁹
• b = 1 + (K_alb * [Albumin]) + (K_shbg * [SHBG]) - (K_shbg * [Total Testosterone])
  b = 1 + (3.6e4 * 6.086e-4) + (1e9 * 3.5e-8) - (1e9 * 1.56e-8)
  b = 1 + 21.91 + 35 - 15.6
  b = 42.31
• c = -[Total Testosterone] = -1.56 x 10⁻⁸

Step 3: Solve for Free Testosterone using the quadratic formula.
FT = (-42.31 + sqrt(42.31² - 4 * 1e9 * -1.56e-8)) / (2 * 1e9)
FT = (-42.31 + sqrt(1852.3)) / (2e9)
FT = 0.73 / (2e9)
FT = 3.65 x 10⁻¹⁰ mol/L

Step 4: Convert the result to a common unit (pmol/L).
Free Testosterone (pmol/L) = 3.65 x 10⁻¹⁰ * 10¹² = 365 pmol/L

The calculated free testosterone is 365 pmol/L, which falls within the typical reference range for adult men.

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