An interference fit holds two parts together with nothing but their own elasticity. The shaft is made a few hundredths of a millimetre larger than the hole; pressing them together squeezes the shaft and stretches the hub, and the contact pressure that results is what grips them. Multiply that pressure by the friction and the contact area and you get the holding force and the torque the joint can carry. The catch is the hub: the same interference stretches its bore in tension, so you must check the hoop stress stays below yield.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Lamé thick-cylinder theory (same-material solid shaft).
The interference-fit equations
Work in consistent units: with E in MPa, δ and the diameters in millimetres, p comes out in MPa, and forces follow in newtons. Pressure is proportional to interference, so doubling δ doubles the pressure, the holding force and the torque. The hub stress amplifies the pressure by a factor that grows sharply as the hub wall gets thin — the reason a thin hub can crack from a fit that a thick one shrugs off.
Worked example — a gear on a shaft
Scenario: A 50 mm steel shaft in an 80 mm-OD steel hub, 40 mm long, with 0.04 mm diametral interference (E = 210 GPa, μ = 0.12).
The fit grips with about 38.6 kN axially and can transmit ~965 N·m of torque — plenty for most gear or pulley mounts without a key. The hub bore hoop stress works out to ~117 MPa, comfortably below the yield of typical machine steel. If you needed more torque, raising the interference to 0.06 mm would push the pressure to ~77 MPa and the torque past 1,400 N·m, but always re-check the hub stress when you do.
Frequently Asked Questions
The shaft is slightly oversize; forcing it in compresses the shaft and stretches the hub, creating contact pressure that grips the parts by friction.
Same-material solid shaft: p = (E·δ)/(2d)×(D²−d²)/D². Pressure scales with interference and falls as the hub gets thinner.
F = π·d·L·μ·p; torque T = F·d/2. More length, pressure or friction = more grip.
Same interference, different assembly: press = forced cold; shrink = heat hub / chill shaft, slip on, grip on cooling. Shrink avoids galling.
Possibly — bore hoop stress σ = p(D²+d²)/(D²−d²). Keep it below hub yield; thicken the hub or cut interference if it's close.