Interference Fit Pressure & Torque Calculator

Estimate interface pressure and friction-driven transmittable torque for a solid shaft pressed into a same-material hub, from the diametral interference.

PRESS-FIT MECHANICS · LAMÉ THICK-CYLINDER EQUATIONS

Interference Fit Pressure & Torque Calculator

Estimates interface pressure and friction-driven transmittable torque for a solid shaft pressed into a same-material hub, from the diametral interference.

Shaft / Interface Diameter (d)
[Inches]

Hub Outer Diameter (Do)
[Inches]

Diametral Interference (Δ)
[Inches]

Difference between shaft OD and hub bore ID before assembly (shaft slightly larger).

Material (Same for Shaft & Hub)
Modulus of Elasticity

Friction Coefficient
Static, Dry-Fit Assumption

Engagement Length (L)
[Inches]

Interface Pressure

15,000 psi

Transmittable torque: 2,237 in-lbf (186.4 ft-lbf)

✔
Same-material, solid-shaft assumption — verify against your material’s yield strength before finalizing.

Engineering Model (classical Lamé thick-cylinder theory)

Standard Reference
Derived from the Lamé equations for thick-walled cylinders under interference fit, documented in references such as Shigley’s Mechanical Engineering Design and Roark’s Formulas for Stress and Strain — not itself an ISO/SAE-issued formula. IT-grade tolerance widths (reference table) follow the ISO 286-1 standard-tolerance-unit formula.

Calculation Method
p = Δ·E·(Do²−d²) / (2·d·Do²) · T = f·p·π·d²·L / 2
Valid for a solid shaft (no bore) pressed into a hub of the same material. Δ is diametral interference.

Assumptions & Limitations

Assumes shaft and hub are the same material — dissimilar materials (e.g. steel shaft in aluminum hub) require the general two-material Lamé formula, not implemented here.
Assumes a solid shaft (no bore); a hollow shaft reduces the achievable pressure for the same interference.
Does not check whether the resulting pressure exceeds either material’s yield strength — always verify against your material’s yield/allowable stress.
Does not account for thermal effects during shrink-fit assembly, or stress concentration at the hub’s edge.

STATIC REFERENCE DATA

Reference: ISO 286-1 IT Grade Tolerance Widths

Precomputed values from the exact formula used above — useful as a quick lookup without re-entering inputs.

Nominal Size Range	IT6	IT7	IT8
18–30 mm	13.1 μm	20.9 μm	32.7 μm
30–50 mm	15.6 μm	25.0 μm	39.0 μm
50–80 mm	18.6 μm	29.7 μm	46.4 μm

Computed from the ISO 286-1 standard-tolerance-unit formula i = 0.45·D^(1/3) + 0.001·D (D = geometric mean of the size range, in mm). This gives the tolerance width only — fundamental deviation letters (H, g, k, p, s…) that set where the zone sits are not covered by this reference table.

WORKED EXAMPLE

Pressing a Bushing onto a 0.75″ Shaft

A steel bushing (1.5″ OD) is pressed onto a 0.75″ steel shaft with 0.001″ diametral interference, 1″ engagement length.

p = Δ·E·(Do²−d²) / (2·d·Do²) = 0.001 × 30×10⁶ × (2.25−0.5625) / (2 × 0.75 × 2.25) ≈ 15,000 psi interface pressure.
Transmittable torque (f=0.15): T = f·p·π·d²·L/2 ≈ 1,988 in-lbf (165.7 ft-lbf).
Before finalizing, verify 15,000 psi is comfortably below both parts’ yield strength — this tool does not check that automatically.
Assembly method matters: a hydraulic press assembly (f≈0.10–0.15) vs. a dry force-fit (f≈0.15–0.20) changes the achievable torque capacity even at the same interference.

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