Analyze contact using load, radius, modulus, and Poisson inputs. Get peak, mean, and size instantly. Export results, inspect curves, and validate examples with confidence.
These examples show typical elastic contact outputs for quick checking.
| Case | Mode | Force (N) | R1 (mm) | R2 (mm) | Length (mm) | Peak Pressure (MPa) | Contact Size (mm) | Approach (µm) |
|---|---|---|---|---|---|---|---|---|
| Steel sphere on flat steel | Point | 500.00 | 20.00 | 0.00 | 0.00 | 1476.734721 | 0.402073 | 8.083118 |
| Steel sphere on aluminum sphere | Point | 1500.00 | 12.50 | 30.00 | 0.00 | 2317.286456 | 0.555938 | 35.027616 |
| Parallel steel cylinders | Line | 2000.00 | 25.00 | 25.00 | 20.00 | 542.055818 | 0.117445 | 0.551737 |
This calculator uses classical Hertz elastic contact relations for smooth bodies under normal load.
Effective modulus: 1 / E* = (1 - ν21) / E1 + (1 - ν22) / E2
Equivalent radius: 1 / R = 1 / R1 + 1 / R2. If radius 2 is zero, the second body is treated as flat.
Point contact: a = ((3FR) / (4E*))1/3, p0 = 3F / (2πa2), pmean = F / (πa2), δ = a2 / R
Line contact: b = √((4FR) / (πLE*)), p0 = 2F / (πbL), pmean = F / (2bL), δ = b2 / (2R)
The graph plots the Hertz pressure distribution. Point mode shows pressure from the center to the contact edge. Line mode shows pressure across the full strip width.
Hertzian contact pressure is a standard way to estimate stress where curved solid bodies touch under a normal load. It is widely used in physics, tribology, rolling contact studies, machine elements, bearings, gears, and material comparison work. The method assumes the contact stays elastic, the surfaces are smooth, and the contact region remains small compared with the body dimensions.
The key idea is that two bodies do not touch at an ideal mathematical point or line after loading. They deform slightly and create a finite contact patch. Once that patch size is known, the pressure field can be estimated. Higher loads usually increase both the contact area and the maximum pressure. Larger effective radius often spreads the load more gently, while higher effective modulus usually keeps the contact smaller and the pressure higher.
This calculator supports two common Hertz cases. Point mode suits ball and spherical contacts that form a circular footprint. Line mode suits parallel cylinders or rollers that form a narrow rectangular strip with a semi elliptical pressure profile across the width. In both cases, the calculator combines the two materials into one effective modulus and combines the curvatures into one equivalent radius.
The results help with quick engineering judgment. Peak pressure is useful for checking surface stress limits. Mean pressure helps compare average loading. Contact size reveals how concentrated the load is, and elastic approach shows how much the bodies move together under force. These values are often the first step before more detailed fatigue, wear, lubrication, or finite element analysis.
Hertzian contact pressure is the elastic stress distribution created where curved bodies touch under load. It assumes smooth surfaces, small contact regions, and no permanent yielding.
Use point contact for spheres or near circular contacts. Use line contact for parallel cylinders, rollers, or narrow contacts extended along a measurable length.
Both bodies deform. The effective modulus combines each elastic modulus and Poisson ratio into one value that controls contact size, pressure, and elastic approach.
It is the peak stress at the center of the contact patch. It is larger than the mean pressure and is often used for allowable contact stress checks.
A blank or zero second radius is treated as a flat partner. The calculator then uses the first body radius as the effective curvature for the Hertz model.
No. Hertz theory is mainly elastic. If stresses exceed yield strength, roughness matters strongly, or contact areas become large, use a more advanced model.
Line contact pressure depends on load distributed along a contact length. A longer roller spreads force more and lowers peak pressure for the same load.
Enter force in newtons, radii and length in millimeters, elastic modulus in gigapascals, and Poisson ratio as unitless. Outputs are shown in millimeters, micrometers, gigapascals, and megapascals.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.