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
Engineering Pro Save, document and continue this calculation
Turn this result into a reusable engineering record with saving, PDF export and reporting workflows.
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.
Frequently asked questions
the unassembled shaft is larger than the mating bore over at least part of the
tolerance range. Assembly elastically compresses the shaft and expands the hub,
producing interface contact pressure that can transmit axial load and torque
through friction.
minus the hole upper deviation ES. Maximum interference is the shaft upper
deviation es minus the hole lower deviation EI. The calculator also evaluates
the midpoint of these two limits as the nominal interference condition.
by the combined elastic compliance of the shaft and hub. The compliance depends
on shaft diameter, shaft bore diameter, hub outer diameter, Young’s modulus and
Poisson ratio. The calculator uses separate shaft and hub properties and supports
both solid and hollow shafts.
one exact value. Minimum interference gives the lowest predicted contact pressure
and therefore the lowest friction capacity. Maximum interference gives the
highest contact pressure and is used for the shaft and hub yield check.
the cylindrical contact area using F = μ · p · π · d · L. Torque capacity is
then T = F · d / 2. The minimum predicted torque capacity uses the minimum
effective contact pressure.
converts each load into a required interface-pressure component and combines them
using the square root of the sum of their squares. The resulting pressure is
compared with the minimum available contact pressure.
the loosest possible assembly condition. The calculator assigns zero minimum
contact pressure in that condition. Without an entered required load this produces
a Warning; with a positive required load the fit cannot satisfy the minimum-load
check because no guaranteed minimum friction capacity remains.
after assembly. It is not the force or press tonnage required to install the
shaft into the hub. Assembly force can depend on maximum interference, sliding
friction, lead-in geometry, surface condition, lubrication and the progress of
engagement during pressing.
fit selections or entered manually. ISO 286 defines the tolerance and deviation
system; the contact-pressure, stress and friction-capacity calculations are
separate mechanical calculations. A result from this calculator should therefore
not be interpreted as certification of compliance with a complete design standard.
0.8 times the sum of the shaft and hub Rz values. This allowance is subtracted
from the raw interference before contact pressure is calculated. If Rz values
are left blank, no surface correction is applied. This is a simplified model,
not a complete surface or standard-based analysis.
bearing ring can reasonably be represented by the shaft-hub model. It is not a
bearing-specific fit-selection calculator and does not evaluate bearing internal
clearance change, raceway geometry, manufacturer fit recommendations, mounting
load paths or bearing-life effects.
entered shaft and hub yield strengths, the minimum effective interference is
positive, and any entered required torque or axial force remains within the
minimum predicted friction capacity. It does not prove that the complete
component or assembly is safe against every failure mode.