ENGINEERING CALCULATOR
Interference Calculator
An interference calculator finds the contact pressure between a shaft and a hub pressed or shrunk together. Enter the interference, shaft and hub sizes, and materials — the Lamé equation returns contact pressure, press-in force, torque capacity, and hub stress. One number, the diametral interference, drives all four outputs.
Built for engineers and machinists who need a defensible fit spec. This is a mechanical interference fit, not a wave interference calculator. The contact pressure from the overlap is what holds bearings, bushings, and gear hubs on shafts. The press fit calculator handles assembly force; the shrink fit calculator handles thermal assembly. This calculator owns the contact pressure and the stress.
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Free Online Tool
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Lamé Equation Results
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Pressure & Stress Outputs
Interference Calculator
Enter shaft and hub geometry, interference, and materials to calculate contact pressure and stress.
Contact Pressure
77.6 MPa
Press Force
58.5 kN
Hub Stress
129 MPa
Formula
p = E·δ·(D²−d²) / (2·d·D²)
Engineering Calculator
Interference Calculator
Enter shaft and hub geometry, interference, and materials to calculate contact pressure, force, torque, and stress.
Contact Pressure p
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Press Force F
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Torque Capacity Mt
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Hub Hoop Stress σ
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Safety Factor
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Status
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Formula
Enter values and press Calculate.
HOW IT WORKS
How to Use the Interference Calculator
Enter shaft diameter, hub diameter, interference, and material properties to get contact pressure, press force, torque capacity, and hub stress. The tool also works with tolerance limits or target force.
Lamé Contact Pressure
p = E·δ·(D²−d²) / (2·d·D²)
δ = Diametral interference
d = Shaft diameter (hub bore)
D = Hub outer diameter
Press Force & Torque Capacity
F = μ·p·π·d·L T = μ·p·π·d²·L/2
F = Axial press-in force
T = Torque before slipping
μ = Friction coefficient
Worked Example
Steel shaft 50 mm, steel hub 100 mm outer, 0.05 mm interference, E = 207 GPa, μ = 0.12, hub length 40 mm.
p = 77.6 MPa
Contact pressure
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F = 58.5 kN
Press force
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T = 1,463 N·m
Torque capacity
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σ = 129 MPa
Hub hoop stress
Contact Pressure
77.6 MPa
Press‑in Force
58.5 kN
Torque Capacity
1,463 N·m
Three Solve Modes
01
Pressure from Interference
Given shaft, hub diameters, and interference, compute contact pressure using Lamé.
p = f(δ, d, D, E)
02
Force & Torque
From pressure and friction, calculate axial press force and torque capacity.
F, T = f(p, μ, d, L)
03
Hub Stress & Safety
Check hoop stress at the hub bore and compare with material yield.
σhub = p·(D²+d²)/(D²−d²)Key Concepts & Applications
Interference Fit Types
Press fit (force assembly), shrink fit (thermal assembly), and force fit share the same pressure math. The overlap sets contact pressure, which determines torque capacity.
Tolerance & Surface Finish
ISO 286 fit classes (H7/p6, H7/r6) define min/max interference. Rough surfaces lose up to 13 μm when peaks crush; grinding preserves the designed interference.
Hub Strength & Safety
Hub hoop stress peaks at the bore: σ = p·(D²+d²)/(D²−d²). Compare with yield strength using a safety factor ≥2.0 to avoid splitting thin walls.
MACHINE DESIGN APPLICATIONS
Hub & Shaft Stress: Is the Fit Safe?
The contact pressure loads the hub like internal pressure, and a thin hub can split before the fit ever sees service. Check stress against yield with a safety factor.
The hub hoop stress peaks at the bore: σhub = p · (D² + d²) / (D² − d²). Compare it against the material yield strength with a safety factor of at least 2.0. In the worked example, 77.6 MPa of contact pressure produces 129 MPa of hoop stress — comfortably under common steel yield, but the same fit in cast aluminum would need a close check.
Hoop Stress Formula
σhub = p · (D² + d²) / (D² − d²)
Where p is contact pressure, D is hub outer diameter, and d is shaft/bore diameter. This is the maximum tangential stress at the hub bore — the most strained location.
- Compare σhub with material yield strength
- Apply safety factor ≥ 2.0
- Thin walls amplify stress rapidly
Three Cautions
Keep the fit honest with these checks:
- Aluminum/brass yield before steel — the hub material usually limits the maximum interference; check the weaker part first.
- Thin hub wall amplifies stress — a wall much thinner than the shaft diameter pushes hoop stress up fast.
- Lamé is an idealization — real surfaces and local yielding can produce measured pressure ±20% from theory; keep the safety factor.
Material & Machining
Compare yield strengths and pick the material before you lock the fit. The hub material often sets the maximum interference, not the shaft.
- Baetro machines over 50 metals and plastics
- Holds interference tolerances to ±0.001″
- Grinding available to preserve surface finish (Ra 0.4–0.8 μm)
Interference Fit Questions
Interference Fit FAQ
An interference fit is a connection where the shaft is always larger than the hole, so the assembled parts grip by friction. The overlap creates contact pressure, which is what holds the joint together without keys or fasteners.
Use the Lamé equation. For a same-material steel joint, p = E·δ·(D²−d²)/(2·d·D²). For 50 mm and 100 mm parts with 0.05 mm of interference, the pressure is about 77.6 MPa.
The Lamé thick-cylinder equation. For a solid shaft of the same material as the hub, p = E·δ·(D²−d²)/(2·d·D²), where δ is the diametral interference, d the shaft diameter, D the hub diameter, and E the elastic modulus.
An interference fit is the general term for any fit where the shaft is larger than the hole. A press fit is an interference fit assembled by pushing the parts together with force. A shrink fit is an interference fit assembled with heat or cold. The contact pressure math is the same for all three.
The assembly method. A press fit is pushed together with force. A shrink fit is assembled by heating the hub, or cooling the shaft, so it grows, slides on, and locks as it returns to room temperature. Shrink fits suit large interferences and thin hubs, and the shrink fit calculator owns the heating number.
Enough that the contact pressure holds the service load. Typical values run from about 0.01 to 0.05 mm on 10 to 50 mm diameters, and the fit class sets the exact range. An H7/p6 fit at 25 mm gives 1 to 35 µm, and heavy fits run larger.
A light press fit defined by ISO 286: the H7 hole with the p6 shaft. At 25 mm it produces 1 to 35 µm of interference, enough to hold a bearing or bushing, and it can usually be assembled with an arbor press. H7/r6 is a medium fit, and H7/s6 is a heavy fit that needs heat.
Multiply the contact pressure by the contact area and the friction coefficient: F = μ·p·π·d·L. For 77.6 MPa on a 50 mm diameter over 40 mm of length with μ = 0.12, the press-in force is about 58.5 kN.
The allowed variation on the shaft and the hole that still produces interference. In tolerance mode, the maximum interference is the largest shaft minus the smallest hole, and the minimum is the smallest shaft minus the largest hole. The fit class on the drawing, such as H7/p6, sets these bounds.
No. This interference calculator is for mechanical interference fits, where a shaft and hub are pressed together. Wave interference, in optics and acoustics, is a different subject with different calculators.
Mostly from three causes: too little interference for the load, so the joint slips; too much interference for the hub, so it splits; and a poor surface finish that crushes away the designed interference. Grinding to Ra 0.4 to 0.8 μm and checking the safety factor avoid all three.
PRECISION MANUFACTURING SUPPORT
From Interference Spec to Machined Shaft & Hub
This interference calculator gives you the contact pressure, force, torque, and stress behind a shaft-hub joint — now you need the parts that make it real: a turned shaft, a bored hub, a bushing, or a bearing housing held to the right microns.
Baetro delivers precision CNC machining to ±0.001″, with interference-fit journals ground to Ra 0.4–0.8 μm. We machine 50+ metals and plastics, with CMM inspection and material certifications on every order. ISO 9001 and AS9100 certified, no minimum order, and standard parts ship in 3–7 days.
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Precision CNC machining to ±0.001″
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Ground journals to Ra 0.4–0.8 μm
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Free DFM feedback on every quote