Enter the molecular weight and the shape factor of a protein into the calculator to determine its hydrodynamic radius. The hydrodynamic radius is a measure of how a molecule behaves in solution and can be used to infer the size and shape of proteins.

Protein Hydrodynamic Radius Formula

The following formula is used to calculate the hydrodynamic radius of a protein.

Rh = (3 * MW) / (4 * π * f))^{(1/3)}

Variables:

  • Rh is the hydrodynamic radius (nm)
  • MW is the molecular weight of the protein (Da)
  • f is the shape factor (dimensionless), which accounts for the protein’s shape and is typically between 1.1 (for a sphere) and 2.5 (for an elongated particle)

To calculate the hydrodynamic radius, use the molecular weight of the protein and the shape factor to compute the radius using the formula above.

What is a Protein Hydrodynamic Radius?

The hydrodynamic radius is a parameter that describes the size of a molecule in solution. It is the radius of a hard sphere that diffuses at the same rate as the molecule of interest. For proteins, the hydrodynamic radius can provide insights into the protein’s tertiary and quaternary structure and is important for understanding protein behavior in different environments.

How to Calculate Protein Hydrodynamic Radius?

The following steps outline how to calculate the Protein Hydrodynamic Radius.


  1. First, determine the molecular weight (MW) of the protein in Daltons (Da).
  2. Next, determine the shape factor (f) of the protein, which is dimensionless.
  3. Next, gather the formula from above = Rh = (3 * MW) / (4 * π * f))^(1/3).
  4. Finally, calculate the Protein Hydrodynamic Radius (Rh) in nanometers (nm).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Molecular Weight (MW) = 50000 Da

Shape Factor (f) = 1.5