Press Fit and Interference Fit Calculator (ISO 286 Fits, Pressure, Stress, Torque)
Choose an ISO 286 fit such as H7/p6, or enter the four limit deviations yourself, then give the shaft and hub geometry and materials. The calculator returns the minimum, mean and maximum interference, the contact pressure from Lamé thick-cylinder theory (hollow shafts and dissimilar materials included), the hub and shaft stresses with safety factors on yield, the axial holding force and torque capacity, the press-in force, the hub heating or shaft cooling temperature for a shrink fit, and the interference left at the operating temperature. Values are SI by default (mm, µm, MPa, kN, N·m, °C) with an inch toggle for in, thou, psi, lbf, lbf·ft and °F. The inputs are stored in the page URL so a case can be shared, exported as CSV or printed as a report.
Fit
Geometry
Materials and surfaces
Assembly and temperature
Results
Fit
| Result | Min | Mean | Max |
|---|---|---|---|
| Fit | H7/p6 | ||
| Fit type | Interference fit | ||
| Hole limits, EI / ES (µm) | 0 / +25 | ||
| Shaft limits, ei / es (µm) | +26 / +42 | ||
| Interference (µm) | 1 | 21.5 | 42 |
Pressure and stresses
| Result | Min | Mean | Max |
|---|---|---|---|
| Contact pressure (MPa) | 1.575 | 33.862 | 66.150 |
| Hub hoop stress at bore (MPa) | 2.625 | 56.438 | 110.250 |
| Hub radial stress at bore (MPa) | −1.575 | −33.862 | −66.150 |
| Hub von Mises (MPa) | 3.675 | 79.013 | 154.350 |
| Shaft hoop stress at surface (MPa) | −1.575 | −33.862 | −66.150 |
| Shaft radial stress at surface (MPa) | −1.575 | −33.862 | −66.150 |
| Shaft von Mises (MPa) | 1.575 | 33.862 | 66.150 |
| Hub safety factor on yield | 96.60 | 4.49 | 2.30 |
| Shaft safety factor on yield | 225.40 | 10.48 | 5.37 |
Transmission
| Result | Min | Mean | Max |
|---|---|---|---|
| Axial holding force (kN) | 1.48 | 31.91 | 62.34 |
| Torque capacity (N·m) | 37.11 | 797.87 | 1558.62 |
Assembly
| Press-in force (kN) | 62.34 |
|---|---|
| Assembly clearance (mm) | 0.020 |
| Hub heating, temperature rise (K) | 107.8 |
| Hub temperature (°C) | 127.8 |
| Or shaft cooling, temperature drop (K) | 107.8 |
| Shaft temperature (°C) | −87.8 |
Hub heating to the maximum interference plus the assembly clearance.
Operating temperature
| Result | Min | Mean | Max |
|---|---|---|---|
| Operating temperature (°C) | 20.0 | ||
| Interference at operating temperature (µm) | 1 | 21.5 | 42 |
| Contact pressure at operating temperature (MPa) | 1.575 | 33.862 | 66.150 |
| Torque at operating temperature (N·m) | 37.11 | 797.87 | 1558.62 |
Every value below uses the inputs above and updates as you edit them. The lines work in mm, MPa and N (1 MPa × 1 mm² = 1 N), so each product closes without hidden factors.
1. Limits and interference
Each tolerance class is a fundamental deviation (the letter, from ISO 286-1) plus a tolerance width (the grade, ITn). The interference is the shaft size minus the hole size: least when the shaft is smallest and the hole largest, most the other way round.
Tolerance grades: at d = 50.000 mm: IT7 = 25 µm, IT6 = 16 µm
Hole H7: EI = 0 µm (fundamental deviation H), ES = EI + IT7 = 0 + 25 = +25 µm
Shaft p6: ei = +26 µm (fundamental deviation p), es = ei + IT6 = +26 + 16 = +42 µm
Minimum interference: δ_min = ei − ES = +26 − +25 = 1 µm
Maximum interference: δ_max = es − EI = +42 − 0 = 42 µm
Mean interference: δ_mean = (1 + 42) / 2 = 21.5 µm
2. Contact pressure
The interference is shared between the hub growing and the shaft shrinking. Each part's flexibility depends on its wall (the Lamé factor K) and its material, and the pressure is the one that makes the two deflections add up to δ.
Hub factor: K_h = (D² + d²) / (D² − d²) = (100.000² + 50.000²) / (100.000² − 50.000²) = 1.6667
Shaft factor: K_s = 1 for a solid shaft (dᵢ = 0)
Maximum contact pressure: p = δ / (d × [(K_h + ν_h) / E_h + (K_s − ν_s) / E_s]) = 0.0420 / (50.000 × [(1.6667 + 0.300) / 210,000 + (1.0000 − 0.300) / 210,000]) = 66.150 MPa
Minimum and mean: δ 1 and 21.5 µm give p = 1.575 and 33.862 MPa (pressure is proportional to δ; zero when δ ≤ 0)
3. Stresses
The hub bore is in hoop tension and radial compression; the shaft is compressed both ways. Von Mises combines the two principal stresses into one value to compare with the yield strength.
Hub hoop at bore: σθ = p × K_h = 66.150 × 1.6667 = 110.250 MPa
Hub radial at bore: σr = −p = −66.150 MPa
Hub von Mises: σ_vm = √(σθ² + σr² − σθ σr) = √(110.250² + (−66.150)² − 110.250 × (−66.150)) = 154.350 MPa
Shaft hoop at surface: σθ = −p × K_s = −66.150 × 1.0000 = −66.150 MPa
Shaft radial at surface: σr = −p = −66.150 MPa
Shaft von Mises: σ_vm = 66.150 MPa (σθ = σr, so σ_vm = p)
Safety factors on yield: hub 355.000 /154.350 = 2.30, shaft 355.000 / 66.150 = 5.37
4. Force and torque
Friction on the contact area π d L carries the load. The same friction resists axial slip and rotation, so the torque is the axial force times the radius.
Force, minimum: F = μ p π d L = 0.150 × 1.575 × π × 50.000 × 40.000 = 1.48 kN
Torque, minimum: T = F d / 2 = 1.48 kN × 50.000 mm / 2 = 37.11 N·m
Force, mean: F = μ p π d L = 0.150 × 33.862 × π × 50.000 × 40.000 = 31.91 kN
Torque, mean: T = F d / 2 = 31.91 kN × 50.000 mm / 2 = 797.87 N·m
Force, maximum: F = μ p π d L = 0.150 × 66.150 × π × 50.000 × 40.000 = 62.34 kN
Torque, maximum: T = F d / 2 = 62.34 kN × 50.000 mm / 2 = 1558.62 N·m
5. Assembly temperature
For a shrink fit the hub is heated until its bore has grown by the maximum interference plus a clearance to slide it on. Cooling the shaft works the same way with the shaft's expansion coefficient.
Hub heating: ΔT = (δ_max + c) / (α_h d) = (0.0420 + 0.0200) / (11.50 × 10⁻⁶ /K × 50.000) = 107.8 K
Hub temperature: 20.0 + 107.8 = 127.8 °C
Or cool the shaft: ΔT = (δ_max + c) / (α_s d) = 107.8 K, shaft at −87.8 °C
Press-in force: F at maximum interference = 62.34 kN
At operating temperature: Δδ = d (α_s − α_h)(T − T₀) = 50.000 × (11.50 × 10⁻⁶ /K − 11.50 × 10⁻⁶ /K) × (20.0 − 20.0) = 0 µm; minimum δ becomes 1 µm
Tolerance zones
Cross-section
Method
Limits and interference. For a fit code the hole and shaft limit deviations come from ISO 286-1:2010 and ISO 286-2:2010: the standard tolerance ITn for the grade and size range, and the fundamental deviation for the letter. For holes F, G and H the lower deviation EI is fundamental and ES = EI + IT; for K, M, N, P, R and S the upper deviation ES is fundamental, including the Δ correction of ISO 286-1 for the finer grades, and EI = ES − IT. Shafts follow the same pattern with es fundamental for f, g and h, ei fundamental for k to u, and ±IT/2 for js and JS. The diametral interference is δ = shaft − hole, so δ_min = ei − ES and δ_max = es − EI, with the mean halfway between. A negative value is a clearance.
Surface smoothing. When the surfaces are pressed together the roughness peaks flatten and part of the measured interference is lost. DIN 7190-1:2017 gives the simplified loss 0.8 × (Rz_shaft + Rz_hub), which is subtracted from each interference before the pressure is worked out. It is off by default (Rz 0).
Contact pressure. Hub and shaft are treated as thick-walled cylinders of the same length in plane stress (Lamé; Budynas and Nisbett, Shigley’s Mechanical Engineering Design, eq. 3-56). With K_h = (D² + d²) / (D² − d²) for the hub of outside diameter D and K_s = (d² + dᵢ²) / (d² − dᵢ²) for a shaft with bore dᵢ, p = δ / (d × [(K_h + ν_h) / E_h + (K_s − ν_s) / E_s]). For a solid shaft and hub of one material this reduces to p = E δ (D² − d²) / (2 d D²).
Stresses. At the hub bore the hoop stress is σθ = p K_h (tension) and the radial stress σr = −p. At the shaft surface σθ = −p K_s and σr = −p; at the bore of a hollow shaft σθ = −2 p d² / (d² − dᵢ²) and σr = 0, which governs the shaft. Von Mises equivalent stress for plane stress is √(σθ² + σr² − σθ σr), and the safety factor is the yield strength divided by it.
Transmission and assembly. The axial holding force is F = μ p π d L and the torque capacity T = F d / 2, with μ the friction coefficient and L the engagement length. The press-in force is the holding force at maximum interference. For a shrink fit the hub must grow by the maximum interference plus an assembly clearance c (default 0.001 × d when left blank): ΔT = (δ_max + c) / (α_hub d), or the shaft can be cooled by (δ_max + c) / (α_shaft d). At an operating temperature T the interference changes by d (α_shaft − α_hub)(T − T_ambient), which matters for dissimilar materials such as a steel shaft in an aluminium hub.
Assumptions
- Hub and shaft are elastic thick cylinders of equal length in plane stress, with uniform pressure over the engagement.
- No end effects. The real pressure and stress peak at the hub edges, typically by a factor Kt of 1.5 to 2, which matters for fatigue.
- The friction coefficient is constant and the same for axial force and torque.
- Surface smoothing uses the simplified DIN 7190-1 factor 0.8 × (Rz_shaft + Rz_hub).
- Material properties are room-temperature typical values; the operating temperature changes only the interference, through thermal expansion.
- Grey cast iron has no yield point; its safety factor is taken against tensile strength and it should be checked as a brittle material.
- The fit is either an ISO 286 code within the listed letters and grades IT5 to IT11, or four limit deviations entered by hand.
Standards and references
| Standard | Note |
|---|---|
| ISO 286-1:2010, Geometrical product specifications (GPS), ISO code system for tolerances on linear sizes, Part 1: Basis of tolerances, deviations and fits | Standard tolerance grades IT5 to IT11 and fundamental deviations, including the Δ rule for holes. |
| ISO 286-2:2010, Part 2: Tables of standard tolerance classes and limit deviations for holes and shafts | Limit deviation tables used to check the computed limits for sizes up to 500 mm. |
| DIN 7190-1:2017, Interference fits, Part 1: Calculation and design rules for cylindrical self-locking pressure fits | Smoothing loss 0.8 × (Rz_shaft + Rz_hub) and the transmission and assembly equations. |
| Budynas, R. G. and Nisbett, J. K., Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015 | Lamé thick-cylinder stresses and the general press-fit pressure for dissimilar materials, section 3-16. |
| Young, W. C. and Budynas, R. G., Roark’s Formulas for Stress and Strain, 8th ed., McGraw-Hill, 2012 | Thick-walled cylinder formulas under internal and external pressure. |
| ANSI B4.2-1978 (R2020), Preferred metric limits and fits | US adoption of the ISO 286 system; H7/p6 is its locational interference fit. |
Worked example: 50 mm H7/p6 steel shaft in a steel hub
A solid steel shaft of 50 mm nominal diameter is pressed into a steel hub of 100 mm outside diameter with an H7/p6 fit over a 40 mm engagement. E = 210 GPa and ν = 0.3 for both parts, friction coefficient 0.15, no smoothing, assembly clearance 0.02 mm, α = 11.5 × 10⁻⁶ /K, from 20 °C. This is the default case loaded in the calculator.
| Result | Value |
|---|---|
| Hole limits | 0 / +25 µm |
| Shaft limits | +26 / +42 µm |
| Interference min / mean / max | 1 / 21.5 / 42 µm |
| Contact pressure min / mean / max | 1.575 / 33.862 / 66.150 MPa |
| Hub hoop stress at bore, max | 110.250 MPa |
| Hub von Mises at bore, max | 154.350 MPa |
| Shaft hoop and radial stress at surface, max | −66.150 MPa |
| Axial force min / mean / max | 1.48 / 31.91 / 62.34 kN |
| Torque min / mean / max | 37.11 / 797.87 / 1558.62 N·m |
| Hub heating | 107.8 K, hub at 127.8 °C from 20 °C |
Frequently asked questions
Is H7/p6 a press fit?
Yes. H7/p6 is the ISO 286 and ANSI B4.2 locational interference fit. At 50 mm it gives 1 to 42 µm of interference, so the parts go together with a press or a modest temperature difference and the fit locates rigidly. It is not meant to carry torque on its own at the minimum interference; for torque use H7/s6 or H7/u6 and check the stresses.
What friction coefficient should I use?
For a longitudinal press fit, dry steel on steel is typically 0.10 to 0.15 and lubricated 0.07 to 0.10. Shrink fits made by heating the hub are usually higher, about 0.14 for steel on steel dry and up to 0.2 degreased. Steel on cast iron is around 0.10 to 0.14, and steel on aluminium or bronze about 0.05 to 0.10 when pressed. 0.15 is the default here; use a lower value for a conservative torque.
Why is the torque at minimum interference so low?
Pressure is proportional to interference, and the minimum interference of a fit is small. For the default 50 mm H7/p6 it is 1 µm, which gives 1.575 MPa and 37.11 N·m against 1558.62 N·m at the maximum. Design for the minimum case, and check stresses at the maximum case.
How hot does the hub need to be for a shrink fit?
Hot enough to grow by the maximum interference plus an assembly clearance: ΔT = (δ_max + c) / (α d). For the default case with c = 0.02 mm that is 107.8 K, a hub at 127.8 °C. Tempered steels and aluminium alloys can lose strength when heated much above 250 °C, so the calculator warns above that line; cool the shaft instead, or use both.
What does surface smoothing do?
The measured interference is between the roughness peaks. When pressed, the peaks flatten and part of the interference is lost. DIN 7190-1 estimates the loss as 0.8 × (Rz_shaft + Rz_hub); with Rz 4 µm and 6.3 µm it removes 8.24 µm, so the 42 µm maximum of H7/p6 becomes 33.76 µm effective.
Why does an aluminium hub lose its grip when hot?
Aluminium expands about twice as much as steel. At a higher operating temperature the hub bore grows faster than the steel shaft and the interference falls by d (α_shaft − α_hub)(T − T₀). A 50 mm steel shaft in a 6061 hub loses about 60 µm at 120 °C, more than the whole H7/p6 interference. The calculator shows the interference, pressure and torque at the operating temperature and warns when the minimum case reaches zero.
What happens if I choose a clearance fit?
If the maximum interference is zero or negative, for example H7/g6, there is no contact pressure and nothing to transmit torque by friction. The calculator shows the limits and the clearance and says it is not an interference fit instead of stress results. A transition fit such as H7/k6 has a minimum case with clearance, so its minimum pressure and torque are zero.