Press Fit and Interference Fit Calculator (ISO 286 Fits, Pressure, Stress, Torque)

Method

What it returns. For the chosen fit and geometry the calculator gives the minimum, mean and maximum interference and the contact pressure from Lamé thick-cylinder theory (hollow shafts and dissimilar materials included). It also gives the hub and shaft stresses with safety factors on yield, the axial holding force, the torque capacity and the press fit force. For a shrink fit it gives the hub heating or shaft cooling temperature, and it reports the interference left at the operating temperature.

Units and sharing. 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.

Limits. For a fit code the hole and shaft limit deviations come from ISO 286-1:2010 and ISO 286-2:2010. The grade and size range set the standard tolerance ITn; the letter sets the fundamental deviation. 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: the upper deviation es is fundamental for f, g and h, the lower deviation ei for k to u, and ±IT/2 applies to js and JS.

Interference. 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, and this point 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 fit force needed to push the shaft in is the holding force at maximum interference, the worst case for the press.

Shrink fit and operating temperature. For a shrink fit the hub must grow by the maximum interference plus an assembly clearance c (default 0.001 × d when left blank). With α the coefficient of thermal expansion, the hub is heated by ΔT = (δ_max + c) / (α_hub d), or the shaft is 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.

Hub heating limit. Heating must not change the heat treatment of the hub, so the rule is to stay well below its tempering or ageing temperature. The calculator warns when the hub temperature exceeds the limit for its material. For steel and cast iron it follows the DIN 7190 table of maximum joining temperatures: 350 °C for low-strength structural steel, and 300 °C for quenched and tempered steel and for cast iron. The same table drops to 250 °C for surface-hardened and 200 °C for case-hardened steel.

Age-hardened aluminium alloys such as 6061-T6 and 7075-T6 are limited to 150 °C, near their T6 ageing temperatures, to avoid over-ageing. Stainless steels, titanium and copper alloys use conservative values of 250 to 350 °C, and a custom material 250 °C. If the hub has been surface or case hardened, use the lower DIN 7190 values or cool the shaft instead.

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

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.

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. The limit depends on the hub material. DIN 7190 gives about 350 °C for plain structural steel and 300 °C for quenched and tempered steel and cast iron. Age-hardened aluminium such as 6061-T6 or 7075-T6 is limited to 150 °C, because it over-ages and loses strength if held hotter. The calculator warns above the limit for the chosen hub; 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.

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