Hertz Sphere Plane Contact Calculator
Calculate elastic circular contact radius, peak pressure and approach for a sphere against a flat half-space.
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Result
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Calculation steps
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How to calculate
Use frictionless nonadhesive Hertz sphere/plane elasticity with the combined reduced modulus.
1/E*=(1−ν1²)/E1+(1−ν2²)/E2; a=(3FR/(4E*))^(1/3); p0=3F/(2πa²); approach=a²/R
Worked example
Multiplying load by eight doubles contact radius under this elastic model; peak pressure doubles and approach quadruples.
Assumptions and input details
Require contact radius≤0.1 sphere radius. Isotropic linear elasticity, small deformation, smooth sphere and flat half-space; no adhesion, friction, plasticity, yield check, thin coatings or permissible load claim.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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