How to use this calculator
- Enter the geometry. Enter the interface diameter, the hub outside diameter and the engagement length.
- Enter the interference. Enter the diametral interference (shaft diameter minus hole diameter).
- Set friction and material. Enter the friction coefficient, Young’s modulus and thermal expansion coefficient for the same-material fit.
- Read the results. Read the contact pressure, press-in force, torque capacity, hub hoop stress and shrink-fit temperature rise.
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.
Use this as an interference fit pressure calculator, a press fit force calculator or a first-pass shrink fit calculator once the diametral interference is known. In query terms, the interface pressure formula is the same contact-pressure formula; the press fit assembly force comes afterward from friction over the engaged surface.
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.
If you assemble it as a shrink fit instead of pressing at room temperature, the hub
bore needs to grow by roughly the same diametral interference. The first-pass
temperature rise is
ΔT = δ / (α · d)
where α is the hub material's linear thermal expansion coefficient. For a
broader heat-growth check, use the thermal
expansion calculator; for ISO tolerance-zone limits before the pressure check, use
the hole and shaft fit calculator.
Worked example
Verified against the live calculator
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. With steel's
α = 12 µm/m·°C, the shrink-fit temperature rise is
ΔT ≈ 66.7°C before adding a handling margin. 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). For tolerance-based fit limits first, use the hole and shaft fit calculator.
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. For shaft/hub retention details around the same joint, the keyway dimension calculator is a useful companion.
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. This calculator reports that rise directly; use the thermal expansion calculator for more general length-growth checks.
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.
- Shrink-fit temperature rise expands only the hub bore by the nominal diametral interference; add process margin for heat loss, transfer time and handling clearance.
- Always check the hub hoop stress against the hub material's yield strength; a thin hub can yield well before the shaft does.