Hertz Contact Stress Calculator (Sphere)
Peak pressure where a ball meets a flat — bearings, balls, cam followers.
100 N on a 10 mm ball ≈ 1.9 GPa — far past 'yield', yet fine: contact stress is triaxially confined. Bearing steel shrugs at 4 GPa. p_max grows only with F^⅓ — contacts are forgiving.
Formula
Hertz Contact Stress Calculator (Sphere) is a free hertz contact stress for design engineers, metallurgists and QA inspectors — instant, accurate and 100% client-side, with the governing formula and reference shown next to the result so the number can be defended, not just quoted.
About Hertz Contact Stress Calculator (Sphere)
Peak pressure where a ball meets a flat — bearings, balls, cam followers. The calculation implements a = (3FR/4E*)^⅓; p_max = 3F/2πa² (Hertz (1882); Johnson, Contact Mechanics). 100 N on a 10 mm ball ≈ 1.9 GPa — far past 'yield', yet fine: contact stress is triaxially confined. Bearing steel shrugs at 4 GPa. p_max grows only with F^⅓ — contacts are forgiving.
How to use Hertz Contact Stress Calculator (Sphere)
- 1Enter Normal force in N.
- 2Enter Ball diameter in mm.
- 3Enter Effective modulus E* in GPa (Steel-on-steel E* ≈ 110 GPa).
- 4Read Peak contact pressure, Contact patch radius instantly — no submit button needed.
- 5Need US units? Flip the SI/Imperial toggle and every field converts.
Why use Hertz Contact Stress Calculator (Sphere)?
- ✓Implements the standard formula — a = (3FR/4E*)^⅓; p_max = 3F/2πa²
- ✓Reference cited on-page: Hertz (1882); Johnson, Contact Mechanics
- ✓One-click SI ⇄ Imperial toggle — values convert in place, physics stays in SI
- ✓Live worked example: the substitution recomputes from your numbers
- ✓Runs entirely in your browser — nothing uploaded, free forever
Frequently asked questions
What formula does the Hertz Contact Stress Calculator (Sphere) use?+
It computes a = (3FR/4E*)^⅓; p_max = 3F/2πa², per Hertz (1882); Johnson, Contact Mechanics. The formula is displayed under the result along with a worked example substituted with your own inputs.
What should I keep in mind when using this calculator?+
100 N on a 10 mm ball ≈ 1.9 GPa — far past 'yield', yet fine: contact stress is triaxially confined. Bearing steel shrugs at 4 GPa. p_max grows only with F^⅓ — contacts are forgiving.
Where do the material property defaults come from?+
Defaults are standard handbook values (ASM, manufacturer datasheets, the cited standard). Always substitute certified values from your material's test certificate for critical work.
Is the Hertz Contact Stress Calculator (Sphere) free to use?+
Yes — completely free, no sign-up, no limits. It runs client-side in your browser, so inputs stay private and results are instant even on slow connections.
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