Press Fit Calculator — Contact Pressure & Transmitted Torque Validator
Calculate press-fit and interference-fit contact pressure, torque and axial holding capacity across tolerance limits, with hollow-shaft, surface roughness, yield and combined-load checks.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Geometry
Fit (ISO / custom deviations)
Material
Surface correction (optional)
Friction
Applied load check (optional)
Results
Calculation tools Save, export and manage your results
Save your calculation, export available results, or store a finalized engineering artifact in your account.
Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
This calculator evaluates a cylindrical press fit (interference fit) over the minimum, nominal and maximum interference defined by the entered hole and shaft deviations.
Interference from hole and shaft deviations
Δraw,min = eishaft − EShole
Δraw,max = esshaft − EIhole
Δraw,nom = (Δraw,min + Δraw,max) / 2
The deviations are diametral deviations. ES and EI are the hole upper and lower deviations, while es and ei are the shaft upper and lower deviations.
Optional surface smoothing allowance
s = 0.8 · (Rzshaft + Rzhub)
Δmin = Δraw,min − s
Δnom = Δraw,nom − s
Δmax = Δraw,max − s
If no Rz values are entered, the surface allowance is zero. The implemented roughness correction is a simplified smoothing estimate and is not a complete standard-based interference-fit calculation.
Elastic compliance and contact pressure
khub = (D² + d²) / (D² − d²)
kshaft = (d² + di²) / (d² − di²)
chub = (khub + νhub) / Ehub
cshaft = (kshaft − νshaft) / Eshaft
C = d · (chub + cshaft)
p = Δ / C
For a solid shaft, di = 0 and kshaft = 1, so:
cshaft = (1 − νshaft) / Eshaft
The calculator evaluates pmin, pnom and pmax. If an effective interference is zero or negative, the corresponding contact pressure is taken as zero.
Axial holding force and torque capacity
A = π · d · L
F = μ · p · A
T = F · d / 2
Therefore:
T = μ · p · π · d² · L / 2
Minimum, nominal and maximum axial holding capacities and torque capacities are calculated from pmin, pnom and pmax. The minimum values represent the weakest tolerance condition predicted by the model.
Stress check at maximum interference
σr,hub = −pmax
σθ,hub = pmax · khub
σvM,hub = pmax · √(khub² + khub + 1)
For a solid shaft:
σvM,shaft = pmax
For a hollow shaft, the maximum shaft equivalent stress is evaluated at the shaft bore using:
σvM,shaft = pmax · 2d² / (d² − di²)
SFshaft = Reshaft / σvM,shaft
SFhub = Rehub / σvM,hub
SFyield = min(SFshaft, SFhub)
Yield utilization = 1 / SFyield
Combined torque and axial-load check
When a required torque or required axial force is entered, the calculator determines the minimum interface pressure required to resist both loads:
pF = Freq / (μ · A)
pT = 2 · Treq / (μ · A · d)
preq = √(pF² + pT²)
Load utilization = preq / pmin
Combined slip safety factor = pmin / preq
Symbols
- d — shaft / fit diameter
- di — shaft inner diameter; zero for a solid shaft
- D — hub outer diameter
- L — effective fit length
- Δ — effective diametral interference
- p — interface contact pressure
- μ — friction coefficient used for load capacity
- E — Young’s modulus
- ν — Poisson ratio
- Re — yield strength
- Rz — surface roughness depth
- F — frictional axial holding capacity
- T — frictional torque capacity
When to use this calculator
Use this press fit calculator to evaluate a cylindrical shaft-hub interference fit when the fit is defined by hole and shaft limit deviations and the joint is intended to transmit load through interface friction.
- Calculate minimum, nominal and maximum diametral interference from hole and shaft upper and lower deviations.
- Calculate minimum, nominal and maximum contact pressure using the elastic compliance of both the shaft and hub.
- Evaluate solid or hollow shafts with different shaft and hub materials.
- Estimate frictional axial holding capacity and transmissible torque over the full interference range.
- Check hub and shaft stresses at the maximum interference condition and compare the calculated von Mises stress with the entered yield strengths.
- Estimate the contact pressure and interference required to resist an entered torque, axial force, or simultaneous torque and axial force.
- Include an optional simplified surface-roughness smoothing allowance using the entered shaft and hub Rz values.
- Evaluate ISO-style hole and shaft tolerance deviations when suitable deviation data are selected or entered.
Do not use the axial holding-force result as the required press installation force. This calculator evaluates resistance to axial slip after assembly; it does not calculate press tonnage, insertion-force variation during assembly, shrink-fit temperature, thermal operating effects, or galling.
The model is intended for preliminary analysis of concentric cylindrical interference fits operating predominantly in the elastic range. More detailed analysis may be required for short joints, stepped hubs, strongly non-uniform geometry, plastic deformation, high rotational speed, fatigue, fretting, significant temperature changes or other conditions that make interface pressure non-uniform.
How to interpret the result
The primary results are the minimum contact pressure pmin and the corresponding minimum predicted torque capacity Tmin. They describe the weakest effective interference condition obtained from the entered tolerance limits and surface correction.
The calculator also returns nominal and maximum contact pressures and the corresponding axial and torque capacities. Minimum interference governs the friction-capacity check, while maximum interference governs the shaft and hub yield check.
A larger effective interference generally increases contact pressure and friction capacity, but it also increases hub and shaft stress. A larger hub outer diameter reduces hub compliance and changes both the developed pressure and hub stress state. A hollow shaft is more compliant than an otherwise equivalent solid shaft.
Torque and axial holding capacity are directly proportional to the entered friction coefficient. The result should therefore be treated as reliable only to the extent that the selected friction coefficient represents the actual materials, surface condition, lubrication and assembly process.
Result status
- Safe — the calculated maximum-interference stress does not exceed the entered yield strength of either component, the minimum effective interference is positive, and any entered torque/axial load does not exceed the calculated minimum friction capacity.
- Warning — the maximum-interference yield criterion is not exceeded, but the minimum effective interference is zero or negative. The selected tolerance range therefore does not guarantee positive interference at its minimum condition.
- Unsafe — the maximum-interference condition predicts first yield in the shaft or hub, or an entered required load exceeds the minimum friction capacity of the fit.
- Invalid — the entered geometry, deviations, material data, friction coefficient or other required values do not satisfy the calculator input requirements, or the selected tolerances do not produce any positive interference condition.
The yield safety factor is Re divided by the calculated von Mises stress. The current status logic uses first predicted yield, corresponding to a safety factor of 1.0, as the limit between the elastic and predicted-yield condition. It does not automatically apply a project-specific design safety factor.
A Safe result confirms only the criteria evaluated by this calculator. It does not establish complete component safety and does not check fatigue, fretting, thermal effects, centrifugal unloading, stress concentrations, assembly damage, surface failure or other possible failure modes.
Calculation example
A solid steel shaft is press-fitted into a steel hub. The fit is defined by hole and shaft deviations rather than by one nominal interference. The joint must also resist 500 N·m of torque and 5 kN of axial load.
Input data
- d — Shaft / fit diameter = 50 mm
- di — Shaft inner diameter = 0 mm
- D — Hub outer diameter = 80 mm
- L — Effective fit length = 40 mm
- ES — Hole upper deviation = 0 µm
- EI — Hole lower deviation = −20 µm
- es — Shaft upper deviation = +40 µm
- ei — Shaft lower deviation = +20 µm
- Eshaft = 210 GPa
- Ehub = 210 GPa
- νshaft = 0.30
- νhub = 0.30
- Reshaft = 250 MPa
- Rehub = 250 MPa
- μ = 0.15
- Rzshaft = 0 µm
- Rzhub = 0 µm
- Treq = 500 N·m
- Freq = 5 kN
1. Interference range
Δmin = eishaft − EShole = 20 − 0 = 20 µm
Δmax = esshaft − EIhole = 40 − (−20) = 60 µm
Δnom = (20 + 60) / 2 = 40 µm
2. Elastic compliance
khub = (80² + 50²) / (80² − 50²) = 2.2821
For the solid shaft: kshaft = 1
Using the shaft and hub elastic properties, the combined diametral compliance is:
C = 7.8144 × 10−13 m/Pa
3. Contact-pressure range
pmin = 20 µm / C = 25.59 MPa
pnom = 40 µm / C = 51.19 MPa
pmax = 60 µm / C = 76.78 MPa
4. Axial and torque capacity
A = π · 0.05 · 0.04 = 0.006283 m²
At minimum interference:
Faxial,min = 0.15 · 25.59 MPa · 0.006283 = 24.12 kN
Tmin = 24.12 kN · 0.025 m = 603.04 N·m
The nominal torque capacity is approximately 1206.08 N·m and the maximum-condition torque capacity is approximately 1809.12 N·m.
5. Maximum-interference yield check
At pmax = 76.78 MPa, the calculated hub von Mises stress is approximately 223.72 MPa. The solid-shaft von Mises stress is approximately 76.78 MPa.
The hub governs with:
SFyield = 250 / 223.72 = 1.12
The model therefore remains below first predicted yield, but with only a relatively small yield margin at the maximum interference condition.
6. Combined required-load check
For Treq = 500 N·m and Freq = 5 kN, the required contact pressure is approximately:
preq = 21.87 MPa
The combined load utilization is:
21.87 / 25.59 = 0.855
and the combined slip safety factor is approximately 1.17.
The entered load therefore remains below the minimum predicted friction capacity. This confirms only the interference-fit slip and elastic yield criteria evaluated by the calculator; other design checks may still be required.
Assumptions and limitations
- The shaft and hub are modeled as concentric cylindrical elastic bodies connected by a uniform interference-fit interface.
- Materials are treated as homogeneous, isotropic and linearly elastic up to the first predicted yield condition.
- Contact pressure is calculated using Lamé-type thick-cylinder compliance. A solid or hollow shaft may be evaluated.
- Hole and shaft deviations define diametral interference. Minimum and maximum interference correspond to the extreme combinations of the entered tolerance limits.
- The optional surface correction uses the implemented relation s = 0.8 · (Rzshaft + Rzhub). It is a simplified smoothing allowance and should not be interpreted as a complete implementation of DIN 7190-1:2017.
- If the calculated effective interference is zero or negative, the corresponding contact pressure is taken as zero because tensile interface pressure is not modeled.
- Friction is represented by one constant coefficient μ over the complete cylindrical contact area. Local variations in lubrication, surface finish, coatings and contamination are not modeled.
- Axial holding force and torque capacity assume uniform interface pressure and Coulomb-type friction over the full effective fit length.
- When torque and axial force are entered together, the calculator combines the required interface tractions using a resultant-friction criterion rather than allowing both individual capacities to be used independently at 100%.
- The yield check uses the maximum effective interference and compares calculated von Mises stress with the entered shaft and hub yield strengths.
- The calculator does not automatically apply a design safety factor above first yield. Required project or code safety factors must be assessed separately.
- Finite-length edge effects, shoulders, grooves, keyways, splines, local stress concentrations, form errors and non-uniform contact pressure are not included.
- Plastic redistribution after yield, residual stresses from manufacturing, creep, fatigue, fretting and wear are not modeled.
- Thermal expansion, operating-temperature changes, centrifugal effects at rotational speed and shrink-fit assembly temperatures are not calculated.
- The axial holding-force result is not a calculation of the press force or machine tonnage required during assembly.
- Material properties and friction coefficients should correspond to the actual material condition, temperature, surface state and assembly method.