Enter values
Formula used
1) Average pressure
Average contact pressure assumes the load spreads uniformly across the chosen area.
| Quantity | Expression |
|---|---|
| Average pressure | P = F / A |
2) Hertz contact (sphere on flat)
This model estimates a circular contact patch for elastic bodies.
| Quantity | Expression |
|---|---|
| Reduced modulus | 1/E* = (1−ν1²)/E1 + (1−ν2²)/E2 |
| Contact radius | a = (3FR / 4E*)^(1/3) |
| Mean pressure | p̄ = F / (πa²) |
| Maximum pressure | p₀ = 3F / (2πa²) |
3) Hertz contact (cylinder on flat)
This model estimates a line contact with a finite contact length.
| Quantity | Expression |
|---|---|
| Half-width | b = √(4FR / (πLE*)) |
| Approx. area | A ≈ 2bL |
| Mean pressure | p̄ = F / (2bL) |
| Maximum pressure | p₀ = 2F / (πbL) |
Notes: These Hertz equations assume smooth, elastic contact, small deformations, and no plastic yielding. If surfaces yield, real pressures and contact areas can differ.
How to use this calculator
- Select a calculation mode that matches your contact type.
- Enter the applied force and choose the correct force unit.
- For average pressure, enter the effective load-carrying area.
- For Hertz models, enter radius, material moduli, and Poisson’s ratios.
- Set the output unit, then press Calculate.
- Use CSV or PDF buttons to save the displayed result tables.
Example data table
| Case | Inputs | Key outputs |
|---|---|---|
| Average (F/A) | F = 1000 N, A = 200 mm² | P = 5 MPa |
| Hertz sphere | F = 500 N, R = 10 mm, E1 = 210 GPa, ν1 = 0.30, E2 = 70 GPa, ν2 = 0.33 | a ≈ 0.400 mm, p̄ ≈ 995 MPa, p₀ ≈ 1.49 GPa |
| Hertz cylinder | F = 2000 N, R = 25 mm, L = 50 mm, E1 = 210 GPa, ν1 = 0.30, E2 = 70 GPa, ν2 = 0.33 | b ≈ 0.147 mm, p̄ ≈ 136 MPa, p₀ ≈ 173 MPa |
These examples are illustrative and rounded for readability.
Contact pressure guide
1) Why contact pressure matters
Contact pressure is the local stress transmitted across an interface where two parts touch. It influences wear, indentation, sealing performance, rolling resistance, and fatigue life. Designers track it because failure often begins at the surface, even when bulk stresses appear acceptable.
2) Average pressure versus peak pressure
Average pressure uses P = F/A and is appropriate when you can justify an effective load-carrying area, such as a gasket land or a bonded pad. Hertz models estimate peak pressure when contact is curved and the real area forms from elastic deformation.
3) Typical magnitudes you will see
Soft interfaces (elastomers, foams, thin coatings) often operate from a few kPa to tens of MPa depending on thickness and support. Hardened metal contacts in bearings and gears can reach hundreds of MPa and may exceed 1 GPa under heavy load. Use these as order-of-magnitude checks, not limits.
4) Material stiffness drives the Hertz result
The reduced modulus E* combines both materials through 1/E*. A stiffer pair (higher E*) produces a smaller contact patch, which raises the maximum pressure. A softer counterface increases the patch size and lowers the peak, but can introduce creep or permanent set over time.
5) Geometry controls contact size
For sphere contact, the contact radius a grows roughly with the cube root of load and radius. Larger radii spread load and reduce peak pressure. For cylinder contact, the half-width b increases with the square root of load, radius, and reduced compliance, and decreases with contact length.
6) Surface finish and lubrication shift reality
Hertz theory assumes smooth elastic bodies. Roughness concentrates load on asperities, raising local micro-pressures above the reported peak. Lubrication can redistribute load and reduce wear, but it may also change the effective contact conditions at high speed or temperature.
7) Compare against yield, indentation, and fatigue
When maximum pressure approaches the material’s yield or hardness-related limits, plastic deformation can occur and the contact patch may grow beyond the elastic prediction. For repeated loading, compare peak pressures against fatigue contact criteria and apply conservative safety factors for uncertainty in load, alignment, and finish.
8) Documenting calculations for reviews
Report the mode used, units, and assumptions about area, radius, and material properties. Include both mean and maximum pressure for Hertz cases, plus the computed contact size. The export buttons help attach consistent tables to design notes, test plans, and maintenance documentation.
FAQs
1) What is the difference between mean and maximum contact pressure?
Mean pressure is load divided by the contact area. Maximum pressure is the peak value at the center of a Hertz contact patch. Peak is typically higher and is important for surface damage checks.
2) Which mode should I use: average or Hertz?
Use average pressure when you know an effective load-carrying area, such as a gasket land. Use Hertz modes for curved elastic contacts where the patch forms from deformation, such as ball or roller contact.
3) Why does Poisson’s ratio affect the result?
Poisson’s ratio changes elastic compliance in the reduced modulus E*. Higher ν increases the term (1−ν²) reduction, altering stiffness and therefore contact size and peak pressure, especially for softer materials.
4) Can I use this for plastic deformation or indentation?
The Hertz models assume elastic behavior. If peak pressure is near yield or hardness-related thresholds, plasticity may occur and real contact areas change. Use the result as a screening value, then apply a plastic contact model if needed.
5) How accurate is the cylinder contact area shown?
It uses an approximate area A ≈ 2bL from the Hertz half-width and effective length. It is useful for quick mean-pressure estimates, but edge effects and misalignment can reduce effective length in practice.
6) What if my surface is rough or coated?
Roughness and coatings can concentrate load on small asperities, creating higher local pressures than the smooth-body prediction. Treat Hertz outputs as baseline values and use surface measurements or correction factors for critical designs.
7) Why do my results look extremely high?
Small areas, small radii, short contact lengths, or very stiff material pairs can produce high peaks. Double-check unit selections, radius and length inputs, and whether the chosen mode matches your real contact geometry.