How does a press fit (interference fit) work?

In a press or interference fit the shaft is made slightly larger than the hole. Forcing them together elastically compresses the shaft and stretches the hub, generating a contact pressure at the interface. That pressure, times the friction coefficient and the contact area, is what grips the parts together — holding them with no key, pin or adhesive.

How much holding force does a press fit give?

The axial force to push the parts apart equals the friction over the contact area: F = π·d·L·μ·p, where μ is the friction coefficient (around 0.1–0.15 for dry steel). The torque the joint can transmit is that force times the shaft radius, T = F·d/2. Longer engagement, higher pressure or more friction all raise the grip.

What is the difference between a press fit and a shrink fit?

They produce the same interference; only the assembly method differs. A press fit forces the parts together cold with an arbor press. A shrink fit heats the hub (or chills the shaft) so it slips on freely, then grips as temperatures equalise. Shrink fitting avoids galling on large interferences and gives a cleaner, often stronger joint, but needs heating or cooling equipment.

Will a press fit overstress the hub?

It can. The interference puts the hub bore into tension — the hoop (tangential) stress at the bore is σ = p × (D²+d²)/(D²−d²), and a thin hub multiplies the pressure into a large stress. Keep that hoop stress below the hub material's yield strength with a sensible safety factor, and increase the hub wall or reduce the interference if it gets too close.

Press Fit Calculator — Interference Fit Pressure & Force

Interference δ	Pressure	Torque
0.02 mm	25.6 MPa	482 N·m
0.04 mm	51.2 MPa	965 N·m
0.06 mm	76.8 MPa	1447 N·m

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

Interface pressure (same material, solid shaft)

p = (E·δ)/(2d) × (D² − d²)/D²

Holding force & torque

F_axial = π·d·L·μ·p · T = F_axial · d/2

Hub bore hoop stress

σ_θ = p × (D² + d²)/(D² − d²)

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).

Pressure

p = (210000 × 0.04)/(2×50) × (80²−50²)/80² = 84 × 0.609 ≈ 51.2 MPa

Holding force & torque

F = π×50×40×0.12×51.2 ≈ 38.6 kN · T = 38,600 × 0.025 ≈ 965 N·m

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.

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Frequently Asked Questions

How does a press fit work?⌄

The shaft is slightly oversize; forcing it in compresses the shaft and stretches the hub, creating contact pressure that grips the parts by friction.

How do you calculate interference fit pressure?⌄

Same-material solid shaft: p = (E·δ)/(2d)×(D²−d²)/D². Pressure scales with interference and falls as the hub gets thinner.

How much holding force does it give?⌄

F = π·d·L·μ·p; torque T = F·d/2. More length, pressure or friction = more grip.

Press fit vs shrink fit?⌄

Same interference, different assembly: press = forced cold; shrink = heat hub / chill shaft, slip on, grip on cooling. Shrink avoids galling.

Will it overstress the hub?⌄

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.

Press Fit Calculator

Press fit — Quick answer