Press Fit Interference Calculator
Calculate contact pressure, hub hoop stress, and press-in force/torque for a shaft-hub interference (press/shrink) fit using the Lamé thick-cylinder equations — including the hub outer diameter and Poisson's ratio the simplified version of this calculator skips, plus an optional von Mises safety-factor check against the hub's yield strength.
Input
Geometry (mm)
The shaft's measured (oversized) diameter before assembly. A solid shaft is assumed.
The hub's measured (undersized) bore diameter before assembly.
A thinner hub concentrates more stress at the same interference — this is what the simplified 4-field version of this calculator skips.
Materials
Steel ≈ 200 GPa, aluminium ≈ 69 GPa, bronze ≈ 110 GPa, titanium ≈ 114 GPa.
Axial length of contact. Leave blank to skip the press-in force / torque estimate.
Dry steel-on-steel ≈ 0.15; lubricated assembly ≈ 0.10. Only used if an engagement length is given.
Leave blank to skip the safety-factor check.
Output
Press Fit Result
| Metric | Value |
|---|---|
| No data yet | |
Guides
Estimate the contact pressure, stresses, and assembly force for a shaft pressed into a hub with an interference (press or shrink) fit — using the full thick-cylinder (Lamé) equations, not a back-of-envelope approximation.
How to use it
- Enter the shaft outer diameter and hub bore diameter — the actual measured values before assembly. The shaft should be slightly larger than the bore; that difference is the interference.
- Enter the hub outer diameter. This matters more than it looks: a thin-walled hub concentrates far more stress at the same interference than a thick one, and it's the field a "simplified" press-fit calculator usually leaves out.
- Enter each part's modulus of elasticity and Poisson's ratio — defaults are set for steel-on-steel (200 GPa, 0.30).
- Optionally enter an engagement length and coefficient of friction to get an estimated press-in force and torque capacity, and a hub yield strength to get a safety factor against yielding.
The formula
Contact pressure at the interface, for a solid shaft pressed into a finite-thickness hub:
p = δ / [ (d/E₀)·((d₀² + d²)/(d₀² − d²) + ν₀) + (d/Eᵢ)·(1 − νᵢ) ]
where d is the nominal interface diameter, δ the diametral interference, d₀ the hub outer diameter, and the i/0 subscripts mark the shaft (inner) and hub (outer) properties. This is the standard thick-cylinder shrink/press-fit equation used in mechanical design references (e.g. Shigley's Mechanical Engineering Design) — a solid shaft is assumed, so if your shaft is hollow, the fit will be slightly looser than this estimate.
From that pressure, the calculator also reports the hub's hoop (tangential) stress at the bore — always higher than the contact pressure, and the number that actually governs whether the hub cracks or yields.
Press-in force and torque capacity
If you give an engagement length, the axial force needed to press the parts together, and the torque the fit can transmit before slipping, both follow from Coulomb friction at the contact surface:
- Force ≈ π · d · L · p · μ
- Torque ≈ π · d² · L · p · μ / 2
These are estimates from a simplified friction model — actual press-in force is also affected by chamfer lead-in geometry, lubrication, and surface finish, so treat it as a sizing check for your press, not a spec.
Safety factor
If you give the hub's yield strength, the calculator computes the von Mises stress at the hub bore (combining the hoop stress with the radial contact pressure) and divides the yield strength by it. A safety factor below 1 means the fit is tight enough to yield the hub — worth knowing before you press two expensive parts together and find out the hard way.
Limits
This models the classic axisymmetric two-cylinder case: a solid, uniform shaft and a hub that's a simple ring (no keyways, flanges, or stepped bores). Real parts with local stress concentrations, non-uniform wall thickness, or a hollow shaft will differ from this estimate. It also doesn't model thermal shrink-fit assembly (heating the hub, cooling the shaft) — the interference and resulting pressure are the same either way, but the assembly force/torque section assumes a room-temperature press.
Privacy
Everything runs in your browser — no dimensions or material data leave your machine.
Related tools
To work out how much interference a chain of toleranced dimensions actually produces, see the Tolerance Stackup Calculator. For the weight of the parts involved, use the Plate Weight Calculator.
Use it from code
From 3 credits per callREST API
curl -X POST https://api.iotools.cloud/v1/tool/press-fit-interference-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"shaftDiameter": "25.040",
"holeDiameter": "25.000",
"hubOuterDiameter": "50.000",
"shaftModulus": "200",
"shaftPoisson": "0.30",
"hubModulus": "200",
"hubPoisson": "0.30",
"engagementLength": "25",
"frictionCoefficient": "0.15",
"hubYieldStrength": "250"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `press-fit-interference-calculator` tool (Press Fit Interference Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.