SizingKitMachining · Interference fits
Press fit calculator for force, stress and heat
This works an interference fit as the physical event it is: the contact pressure two parts develop when one is forced into the other, and from that the tonnage a press needs, the torque the joint transmits through friction, the hoop tension that decides whether a hub survives, and the temperature a shrink fit has to reach. Every figure is reported at both ends of the interference band, because the loose end decides whether the joint holds and the tight end decides whether it can be assembled at all. Free, no signup, and the designation itself comes from a separate page rather than being redefined here.
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- Lamé thick-wall solution
- Both ends of the band
- Force in tons
The joint
A designation carries the interference; the geometry decides what that interference costs in pressure. Both are needed before anything below means anything.
Whatever you write after a number wins, so a bore listed in inches and a hub listed in millimeters resolve to one joint without converting either first.
The basic size of the fit, and the diameter of the contact face.
Hole basis. The limits behind it are on the tolerance calculator.
1.67× the joint diameter. Thinner hubs take the same interference at higher stress.
Zero for solid bar. A hollow shaft collapses more and presses on lighter.
How much of the diameter is in contact, not the whole boss.
Deducted from the interference before anything is calculated. Zero is what a measured interference gives before the peaks flatten — see the note below.
E = 200 GPa (29.0 × 10⁶ psi)
E = 200 GPa (29.0 × 10⁶ psi)
Default 0.12 — The static friction coefficient used for dry pressed steel interference joints in the interference-fit section of Machinery's Handbook, where a range of roughly 0.05 to 0.15 is given for pressing force.
Default 0.29 — Poisson's ratio for carbon and alloy steel. Shigley's Mechanical Engineering Design uses 0.292 for steel in its interference-fit worked examples; the AISC Specification for Structural Steel Buildings gives 0.30 for structural steel.
0.33 for the wrought aluminum alloys, 0.21–0.26 for gray cast iron.
Default 11.7 — Coefficient of linear thermal expansion for carbon steel over 20–100 °C, 11.7 µm/m·°C (6.5 µin/in·°F), as published in the thermal-properties tables of ASM Handbook Volume 1 and Machinery's Handbook.
PRESS FORCE, TIGHT END
9.761 tons
86.84 kN
TORQUE HELD, LOOSE END
832.2 N·m
613.8 lbf·ft
HUB HOOP STRESS, TIGHT END
163.2 MPa
23.66 ksi
| Quantity | Tightest interference | Loosest interference |
|---|---|---|
| Interference | 72.0 µm 2.83 thou | 23.0 µm 0.91 thou |
| Contact pressure | 76.78 MPa 11,136 psi | 24.53 MPa 3,557 psi |
| Axial press force | 86.84 kN 9.761 tons-force | 27.74 kN 3.118 tons-force |
| Torque through friction | 2,605 N·m 1,921 lbf·ft | 832.2 N·m 613.8 lbf·ft |
| Hub hoop stress at the bore | 163.2 MPa 23.66 ksi | 52.12 MPa 7.559 ksi |
| Hub temperature rise to assemble | 131.1 °C 235.9 °F | 61.25 °C 110.3 °F |
Two different ends of the band decide two different things. The loosest interference sets what the joint holds — 832.2 N·m here, and a design that needs more than that needs a key rather than a tighter fit. The tightest sets what assembly costs and what the hub survives: 163.2 MPa of tension at the bore, arriving whether the press is big enough or not.
A heavy press, or heat the outer part and chill the inner. On thin-walled or cast outer parts, check the hoop stress before committing: at these interferences it is easy to exceed the material's strength and split the hub on assembly.
Both parts are structural and carbon steel at the same Poisson’s ratio, so ν has dropped out of the contact pressure entirely — it is added to the hub’s term and subtracted from the shaft’s, and at equal moduli the two cancel. Changing it here moves nothing until the two parts are different metals.
Contact pressure is the Lamé thick-walled cylinder solution with both parts elastic. It assumes the joint is long compared with its diameter, which puts the ends — where the pressure genuinely peaks — outside the model, and it takes the interference as fully effective. It is not: the peaks of both surfaces flatten as the parts go together, so a bored hub at Ra 3.2 µm delivers measurably less than it measures. DIN 7190 sets that deduction from the peak-to-valley height of both surfaces; this site does not reproduce that table, which is why the smoothing box above starts at zero. Leaving it at zero overstates the torque the joint holds and overstates the stress in the hub, so it is conservative in one direction and optimistic in the other. Specify a ground finish and the deduction stops mattering.
Moves with everything: surface finish, whether the joint was oiled to assemble (which lowers it, sometimes by half), the materials in contact, and whether the joint has been apart before. Shrink-fitted joints hold better than pressed ones because the peaks are not sheared off going in — the same geometry can show a coefficient half again as high when heated on rather than pressed. Use the low end when calculating whether a joint holds and the high end when calculating whether the press can push it together; using one figure for both is optimistic in both directions. The temperature figure adds 0.02 mm of working clearance on top of the interference so the parts drop together before the heat equalises, and it is a rise above whatever the shaft is sitting at. Chilling the shaft instead reaches −78 °C with dry ice and −196 °C with liquid nitrogen, which is the whole budget cooling has.
A hoop stress is a number, not a verdict. Comparing it to the hub material takes a yield or tensile figure this site does not carry for castings and bar stock — an ASTM A48 Class 30 gray iron hub, for instance, is specified at 30,000 psi minimum tensile, the class number being the strength in ksi, and gray iron has no useful yield point in tension at all. Take the figure from the material specification or the mill certificate, decide the margin, and have somebody qualified sign the joint off.
How to work an interference fit
Three inputs decide everything: the overlap, the wall around it and the length of contact.
Say where the overlap comes from
Either name an ISO fit and its basic size, in which case the interference band is looked up rather than typed, or switch to the measured mode and enter four numbers: the smallest and largest the bore may be, and the smallest and largest the shaft may be. The four combine crosswise — largest shaft against smallest bore is the tight end, smallest shaft against largest bore is the loose end — which is how a drawing that reads as one fit produces a range of behavior across a batch.
Give the outer part a wall and the joint a length
Contact pressure depends far more on how much metal surrounds the bore than on the interference itself. A hub outside diameter of twice the joint diameter and a solid shaft is the ordinary case; halve the wall and the same overlap produces a much larger stress. Engagement length is the part of the diameter actually in contact, not the width of the boss — force and torque are both directly proportional to it, so an over-generous figure here inflates every result on the page.
Read the two columns as two different questions
The loose column answers whether the joint does its job: that is the torque a batch is guaranteed to hold, and it is often zero for a transition fit. The tight column answers whether the joint can be built: that is the tonnage the press has to have, the tension the hub has to survive and the temperature it has to reach. A single mid-band number would hide both, which is why nothing on this page is reported as one figure.
Technical specifications
| Pressure model | Lamé thick-walled cylinder solution with both parts elastic — contact pressure from diametral interference, joint diameter, hub outside diameter, shaft bore and both moduli |
|---|---|
| Fits offered | H7/g6, H7/h6, H7/k6, H7/p6 and H7/s6, the preferred hole-basis set of ISO 286-1 Annex B. Only p6 and s6 interfere throughout; g6 and h6 are refused as having no overlap to press |
| Friction coefficient | 0.12 dry steel on steel by default, editable. Machinery's Handbook gives roughly 0.05 to 0.15 for pressing force, and a shrunk joint holds better than a pressed one because the peaks are not sheared off going in |
| Poisson's ratio | 0.29 by default and entered per part, editable. Published values run 0.21 for gray cast iron to 0.34 for titanium and brass, and a joint made of one metal throughout is completely insensitive to the figure — the hub and shaft terms cancel it exactly |
| Thermal expansion | 11.7 µm/m·°C for carbon steel by default, editable — 10.8 gray iron, 17.3 austenitic stainless, 23.6 wrought aluminum, all rising with temperature |
| Assembly allowance in the heat figure | 0.02 mm of working clearance added to the interference, so the parts drop together before the heat equalises rather than seizing halfway on |
| Chilling budget | −78 °C on dry ice and −196 °C in liquid nitrogen, which is the whole range cooling the shaft can contribute instead of heating the hub |
| Worked example | 60 mm H7/s6, 100 mm hub outside diameter, solid shaft, 50 mm engagement, steel on steel: 23 to 72 µm interference, 25 to 77 MPa contact pressure, 9.8 tons-force to press together, 832 N·m held at the loose end, 163 MPa hoop tension and a 131 °C rise to shrink it on |
Frequently asked questions
Do I design to the minimum or the maximum interference?
Both, for different checks. The minimum is what the joint is guaranteed to have, so the torque capacity, the axial holding force and any slip check are all read from it — design to the maximum there and a fraction of the batch will spin on the shaft. The maximum is what assembly has to survive, so press tonnage, hub hoop stress and the shrink temperature all come from that end. A calculation that uses one interference for everything is optimistic in one direction and unconservative in the other at the same time.
Will an H7/p6 joint hold torque on its own without a key?
It transmits some, and designing on that alone means relying on a friction coefficient nobody measured on your parts. The published range for dry pressed steel is roughly 0.05 to 0.15 — a factor of three, and the low end applies to exactly the case you cannot rule out, a joint that was oiled to get it together or has been apart once already. Where the torque is the point rather than a bonus, key it or pin it and treat the interference as what stops the part wandering, which is what the locational interference class is named for.
How hot does the hub have to get, and will a torch do it?
For a 60 mm steel joint at 72 µm the rise is about 130 °C, so a hub starting at 20 °C has to reach roughly 150 °C — an oven, an induction heater or a hot plate, not a torch. A torch heats a patch rather than a ring, and a bore that expands unevenly will not go on straight or will grip halfway; that is the usual reason a shrink fit ends up stuck in the wrong position with no way back. Heating also has a ceiling that has nothing to do with expansion: past about 200 °C a hardened or tempered part starts losing the condition it was heat treated to.
Why did my press read a different force from this?
Three effects, and all three push the same way. The equation assumes the interference is fully effective, but the surface peaks flatten as the parts go together, so a rough bore behaves as though it were made smaller than it measures. It also assumes a long joint with uniform pressure, whereas the real pressure peaks sharply at each end of the engagement. And the friction coefficient it uses is a static figure for a dry steel pair — an oiled assembly can push on at half the force. Expect the calculated figure to be the right order and to be the ceiling rather than the reading.
What actually splits a cast-iron hub?
Hoop tension at the bore, which is always larger than the contact pressure that caused it and on a thin hub is several times larger. The relation is the same thick-cylinder solution: a hub outside diameter of 1.5 times the joint diameter multiplies the pressure by 2.6, and it takes twice the joint diameter to bring that down to 1.67. Gray iron is the material that finds this out, because it is strong in compression and weak in tension — an ASTM A48 Class 30 casting is specified at only 30,000 psi minimum tensile — and it fails without warning, on the bench, during assembly rather than in service.
Can I size a rolling bearing fit with this?
No — use the bearing maker's own tables. A bearing is not two plain cylinders: the interference passes through the ring and eats into the internal clearance the bearing was built with, so the same overlap that would be harmless on a plain bush can preload the raceways and shorten the life of the bearing dramatically. SKF, Timken and NSK all publish shaft and housing tolerance recommendations by bore size, load class and whether the ring rotates relative to the load, and those recommendations already account for the ring expansion this page does not model.
Does a hollow shaft change the answer much?
Yes, and always downward. A solid shaft resists compression almost entirely through its own stiffness, while a bored one collapses inward as well, so more of the interference is absorbed by the shaft and less of it goes into pressing the two surfaces together. On the 60 mm example in the specification table, boring the shaft to 30 mm gives up 18 percent of the contact pressure — and with it 18 percent of the torque the joint holds and 18 percent of the tonnage needed to assemble it. Enter the real bore rather than leaving the box at zero; the error runs the unsafe way for a joint that has to transmit anything.
About interference, and what it does to two parts
An interference fit is a controlled elastic failure of geometry: two diameters are specified so that one cannot fit inside the other, and the assembly is what reconciles them. The hub stretches, the shaft compresses, and the pressure at which the two agree is given by the thick-walled cylinder solution Gabriel Lamé published in 1852. That pressure is the only quantity on this page that is calculated directly — press force is the pressure times the contact area times a friction coefficient, torque is the same force acting at the interface radius, and hub stress is the pressure amplified by the wall ratio. Which means all four move together, and the sensitivity worth remembering is that they are proportional to the interference: ten percent more overlap is ten percent more of everything, including the tension that breaks the hub.
The overlap itself is not defined here. A designation such as H7/s6 is a statement about limits, and the tolerance calculator is where a basic size and a class become four numbers; this page takes the range between them and asks what it costs. Two things about that range are worth stating plainly. It is a range and not a value, so a production batch spans it — at H7/k6 part of the batch has clearance and transmits nothing at all. And it is nominal rather than effective: roughness on either surface is crushed flat during assembly, so a bore that measures a given interference delivers less of it, and how much less depends on the peak height of both surfaces. DIN 7190 is the standard that quantifies that deduction; this site does not reproduce its table, which is why the smoothing box is an input rather than an assumption. Specifying a finish that a grinder can hold is the practical answer — the smoother the pair, the smaller the correction and the less it matters that nobody applied it.
The check most calculators skip is the hub. Hoop stress at the bore is always larger than the pressure that produced it, and the amplification is set by wall thickness alone: 1.67 at a hub outside diameter of twice the joint diameter, 2.13 at 1.67 times and 2.6 at 1.5 times, with a thin ring being stretched rather than expanded. Steel takes this easily and gray cast iron does not, which is why the failure is nearly always a split casting on the bench rather than a joint that loosened in service. Comparing the stress to a strength takes a figure from the material specification or the mill certificate, and where the part in your hand is an unmarked casting, a hardness test is the cheapest way to find out whether it is the grade the drawing assumed. None of this is a stamped design: it is the arithmetic that tells you which questions to ask, and a qualified engineer signs off the joint, the material and the assembly method.
What happens to the joint you type in
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
Diameters, limits, materials and the coefficients you overwrite exist only in this tab and are discarded when it closes — nothing is stored between visits, so a fit worked out here leaves no trace to be found later.