Engineering Tools
Press-Fit / Interference Fit Calculator
Enter shaft and hub geometry, materials, and the diametral interference, and get the contact pressure, assembly (press) force, transmissible torque, and stresses — from Lamé thick-wall cylinder theory.
Fit inputs
Dimensions in mm. Interference is diametral (on diameter, not radius) — e.g. a Ø20 H7/p6 fit gives roughly 0.02–0.04 mm. Shaft bore = 0 for a solid shaft.
Reference
How the numbers are derived
Contact pressure from the elastic ring equations, then friction converts pressure into holding force and torque.
Equations
| p | Contact pressure = δ / [ d·( Cₚ/Eₚ + Cₛ/Eₛ ) ] where Chub = (Dₜ²+d²)/(Dₜ²−d²) + νhub and Cshaft = (d²+dᵢ²)/(d²−dᵢ²) − νshaft. |
| F | Assembly / axial holding force = μ·p·π·d·l. |
| T | Transmissible torque = F·d/2 = μ·p·π·d²·l/2. |
| σhub | Hoop stress at hub bore = p·(Dₜ²+d²)/(Dₜ²−d²) (tensile — the governing stress). |
| σshaft | Hoop stress in shaft = −p (solid) or −2p·d²/(d²−dᵢ²) at the bore (hollow), compressive. |
Watch-outs
- Take the minimum interference from your tolerance stack for holding capacity, and the maximum for stress and press force — the same fit must pass both.
- Surface finish smooths on assembly: subtract roughly 3–6 µm of effective interference for machined surfaces (embedding loss).
- Dissimilar metals + temperature changes the fit: aluminum hub on steel shaft loses interference when hot.
- Friction scatter is large. For torque-critical joints test the actual parts, or add a key or spline.
- Repeated press cycles, knurls, and adhesives all change the picture — this tool covers the plain elastic fit.
Fits that must survive assembly, temperature, and time?
A press fit is a system: tolerances, finishes, thermal cycles, and the press process itself. If a bearing seat, gear, or insert is holding your product together, bring the drawing to a consultation.
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