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MachineCalcs

Press Fit & Interference Fit Calculator

Contact pressure, press-in force, torque capacity and hub hoop stress from the interference and geometry — Lamé thick-cylinder theory for a solid shaft in a same-material hub. Metric and imperial.

Inputs

mm
mm
mm
mm
MPa

Results

Contact pressure(p)
48.75 MPa

Interface pressure between shaft and hub.

Assembly force(F)
45 950 N

45.95 kN · 4.69 t

Axial force to press the shaft in (F = π·μ·p·d·L).

Torque capacity(T)
1 149 N·m

Torque the friction joint can transmit before slipping.

Hub hoop stress(σ) ✓
111.3 MPa

Peak tangential stress at the hub bore.

  • Lamé thick-cylinder result for a solid shaft pressed into a same-material hub; contact pressure p = (E·δ)/(2·d) · (d₀²−d²)/d₀².
  • Press-in force and torque capacity use the friction coefficient μ — pick it conservatively, as it is the largest source of uncertainty.
  • Ignores surface-roughness flattening (which reduces the effective interference), temperature and centrifugal effects; check the hub hoop stress against its yield strength.

How it works

An interference fit holds by the contact pressure created when the shaft is forced into a slightly smaller hole. For a solid shaft pressed into a hub of the same material, Lamé thick-cylinder theory gives that pressure from the diametral interference δ: p = (E · δ) / (2 · d) · (d₀² − d²) / d₀² where d is the interface diameter, d₀ the hub outside diameter and E Young's modulus. The hub's stiffness — set by the (d₀² − d²)/d₀² wall-thickness term — controls how much pressure a given interference produces.

From the contact pressure the axial assembly force is F = π · μ · p · d · L (μ the friction coefficient, L the engagement length), and the friction joint's torque capacity is T = F · d / 2. The pressure also loads the hub: the peak tangential (hoop) stress at the bore is σ = p · (d₀² + d²) / (d₀² − d²), which must stay below the hub material's yield strength.

Worked example

A 50 mm shaft pressed into an 80 mm-OD hub with 0.04 mm diametral interference, 40 mm of engagement, μ = 0.15, both steel (E = 200,000 MPa). The contact pressure is p ≈ 48.8 MPa, the press force is F = π × 0.15 × 48.8 × 50 × 40 ≈ 45.9 kN, and the joint transmits up to T ≈ 1149 N·m before slipping. The hub hoop stress is σ ≈ 111 MPa — comfortably below mild-steel yield. The calculator returns exactly these numbers.

Frequently asked questions

How do you calculate an interference fit?
Start from the diametral interference δ (shaft diameter minus hole diameter) and use Lamé thick-cylinder theory to get the contact pressure: p = (E·δ)/(2·d) · (d₀²−d²)/d₀², for a solid shaft in a same-material hub. From p you get the press-in force F = π·μ·p·d·L, the torque capacity T = F·d/2, and the hub hoop stress σ = p·(d₀²+d²)/(d₀²−d²).
How much interference do I need for a press fit?
A common rule of thumb is about 0.001–0.002 × the interface diameter of diametral interference for a steel-on-steel press fit — so roughly 0.05–0.10 mm on a 50 mm shaft. Use the calculator to convert your chosen interference into actual pressure, force and hub stress, then back off if the hub hoop stress approaches yield.
How much force does it take to press it together?
The axial assembly force is F = π·μ·p·d·L, where p is the interface pressure, μ the friction coefficient, d the interface diameter and L the engagement length. Friction μ is the biggest unknown — pick it conservatively (dry steel-on-steel is typically 0.1–0.2).
Will the hub yield?
Check the hub hoop stress σ = p·(d₀²+d²)/(d₀²−d²) — the peak tangential stress at the bore — against the hub material yield strength. The calculator flags it when it climbs past about 250 MPa, near the yield of mild steel; a thinner hub (smaller d₀) raises this stress quickly.
Can I use a shrink (thermal) fit instead of pressing?
Yes — heat the hub so its bore grows by at least the interference, drop it onto the shaft, and let it cool. The required temperature rise is ΔT = δ/(α·d), where α is the coefficient of thermal expansion (≈ 12×10⁻⁶ /°C for steel) and d the interface diameter. A shrink fit avoids galling the surfaces during assembly.
Does this work in metric and imperial?
Yes — enter the diameters, interference and length in mm or inches and the modulus in MPa or ksi; results show in metric or imperial. The physics runs in fixed internal units, so the unit toggle never changes the answer.

Method & assumptions

  • Lamé (elastic) thick-cylinder theory for a solid shaft in a hub of the same material; both parts stay below yield.
  • Ignores surface-roughness flattening — real assemblies lose part of the nominal interference, so the actual pressure and force are usually a little lower.
  • Ignores temperature differentials and centrifugal (rotational) effects, both of which change the effective fit in service.
  • Press force and torque capacity scale directly with the friction coefficient μ, the largest source of uncertainty — choose it conservatively.
  • Always check the hub hoop stress against the hub material's yield strength; a thin hub can yield well before the shaft does.

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