Fits & Limits Calculator

📖 New to ISO 286? Read the guide: Interference Fits: ISO 286 Tolerances and Lamé Stresses — a plain-language explainer of the standard behind this calculator.

Contact pressure and stresses use classical Lamé thick-walled-cylinder theory for a shaft (solid or hollow) pressed into a hub of finite outer diameter, following the standard treatment in Shigley's Mechanical Engineering Design ("Press and Shrink Fits"): p = δ / { d/Eo·[(Do²+d²)/(Do²−d²) + νo] + d/Ei·[(d²+di²)/(d²−di²) − νi] }. Stresses assume plane stress (free ends, no additional axial load or torque) and the von Mises criterion; a solid shaft is under uniform hydrostatic compression (σr = σθ = −p) while a hollow shaft's highest stress is at its bore. Axial insertion force uses F = π·f·p·d·L at the assembly-temperature pressure. ISO 286 hole fits (H6–H11 etc.) are computed directly from the standard's formulas; the interference-range shaft fits (k6, m6, n6, p6, r6, s6, t6, u6) are transcribed from the published ANSI B4.2 tolerance-zone tables, which reproduce the ISO 286-1 values for these classes exactly (these letters carry IT-grade-dependent correction terms in the standard's own formulas, so they are looked up rather than computed). Each part's diametral thermal growth is αpart·d·(Tpart−20°C); the shaft and hub can be set to different assembly temperatures for a heat/shrink fit (hub heated and/or shaft chilled to open a sliding clearance before assembly), while the operational and storage points assume both parts have equalised to one shared ambient. The net shift in interference is the difference between the two parts' growth — a genuine failure mode at the operational/ storage points if it drives the worst-case interference to zero or below ("fit lost"), or drives stress beyond yield at the opposite extreme. Material properties (E, ν, yield, CTE) are typical published room-temperature values for each preset and are not varied with temperature; grey cast iron and other brittle materials have no well-defined yield point in compression, so their check is advisory only — compare against the compound's actual compressive strength rating. This is an estimation tool; verify against the application's holding-force, torque, and fatigue requirements before production use.

Validated: a solid steel shaft (50 mm) pressed into a steel hub (100 mm OD) with a clean 0.05 mm diametral interference should give p = δ/{(d/E)·[(Do²+d²)/(Do²−d²) + (1−ν)]} = 75.0 MPa by hand — this calculator returns exactly 75.0 MPa, a hub bore hoop stress of 125.0 MPa (von Mises 175.0 MPa), and a shaft-interface von Mises stress of 75.0 MPa. That last figure checks out analytically too: a solid shaft is under equal radial and hoop compression (σr = σθ = −p), and the von Mises formula reduces exactly to p in that special case — which is exactly what came back. The thermal-shift term was checked separately (aluminium shaft in a steel hub at 80°C) and also matched the hand-calculated interference exactly.