Enter the load and contact radius into the calculator to determine the (maximum) Hertz contact pressure.

Hertzian Contact Pressure Calculator

Contact Pressure
Known Radius

Calculate maximum Hertzian contact pressure from load, geometry, and material properties.

Sphere on Flat
Cylinder on Flat
Sphere on Flat Inputs
Typical use: ball bearing or spherical contact on a flat elastic surface.
Cylinder on Flat Inputs
Typical use: roller or cylindrical line contact on a flat elastic surface.

Enter any two values to calculate the third using the point-contact peak pressure relation.

This tab is best when the contact radius is already known from another source.

Hertz Pressure Formula

The following formula is used to calculate the maximum Hertz (Hertzian) contact pressure for a circular contact area of radius a when the contact radius is known.

p_0 = (3F) / (2\pi a^2)

Variables:

  • p0 is the maximum Hertz contact pressure (Pa)
  • F is the load (N)
  • a is the contact radius (m)

To calculate the maximum Hertz pressure, multiply the load by 3 and divide the result by 2π times the square of the contact radius. (Note: material properties such as Young’s modulus and Poisson’s ratio affect the contact radius predicted by Hertz theory, but once a is known they do not appear in the pressure formula above.)

What is Hertz Pressure?

Hertz pressure is a measure of the contact pressure between two elastic bodies in contact. It is named after the German physicist Heinrich Hertz, who developed the theory of contact mechanics. Hertz pressure is used to describe the stress distribution in the contact area of two bodies, such as a ball and a flat surface, or two spheres. This concept is important in various fields, including mechanical engineering, materials science, and tribology, as it helps in understanding the behavior of materials under load and in designing components that can withstand high contact pressures without failure.

How to Calculate Hertz Pressure?

The following steps outline how to calculate the Hertz Pressure.

  1. First, determine the load (F) applied to the contact.
  2. Next, determine the contact radius (a) for the contact patch.
  3. Finally, calculate the maximum Hertz Pressure using the formula p0 = (3F) / (2πa²).
  4. After inserting the values 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.

Load (F) = 1000 N

Maximum Hertz Pressure (p0) = ?

Contact Radius (a) = 0.05 m

Answer: p0 ≈ 1.91×105 Pa (≈ 27.7 psi)