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How to Calculate Press Fit Pressure and Pressing Force

Guide · Updated October 28, 2026

A press fit holds because the hub is stretched and the shaft is squeezed. The interference sets the contact pressure between them, the pressure sets how much load the joint can carry and how hard the hub is stressed, and pressure times friction times area sets the force you need on the press. A quick calculation tells you whether your arbor press can do the job and whether the hub will crack.

Measure the interference first

The calculation is only as good as the measured sizes. Set your micrometer and bore gage on gage blocks. The free Gage Block Calculator builds the gage block stack for any size you need to set.

Step by step

  1. Measure both parts: Measure the shaft and bore at the press area. Diametral interference δ = shaft diameter − bore diameter.
  2. Note the hub size: Measure the hub outside diameter D at the fit and the fit length L.
  3. Find the contact pressure: For a solid steel shaft in a steel hub: p = (E × δ ÷ 2d) × (1 − (d/D)²), with E = 200,000 MPa (about 29,000,000 psi).
  4. Check hub stress: Hoop stress at the hub bore: σ = p × (D² + d²) ÷ (D² − d²). Keep it well below the hub material yield strength.
  5. Estimate the pressing force: F = μ × p × π × d × L, with μ about 0.1 to 0.2 for dry or lightly oiled steel.
  6. Compare with your press: Convert to tons and make sure the press has margin; a 3-ton arbor press should not be run at its limit.
  7. Press straight and steady: Chamfer the shaft, lubricate if allowed, and press in one smooth stroke with the parts square.

Worked example: 25 mm shaft in a 50 mm hub

A solid steel shaft d = 25 mm goes into a steel hub with D = 50 mm, L = 30 mm, and measured interference δ = 0.025 mm (about 0.001 in). Pressure: p = (200,000 × 0.025 ÷ 50) × (1 − 0.25) = 100 × 0.75 = 75 MPa (about 10,900 psi). Hub hoop stress: σ = 75 × (2,500 + 625) ÷ (2,500 − 625) = 75 × 1.667 = 125 MPa (about 18,100 psi), comfortably below the roughly 250 MPa yield of mild steel. Force with μ = 0.15: F = 0.15 × 75 × π × 25 × 30 = 0.15 × 75 × 2,356 = about 26,500 N, or about 5,960 lbf, close to 3 US tons.

How interference changes the answer

Pressure and force rise in direct proportion to interference. Doubling δ to 0.050 mm doubles the pressure to 150 MPa and the hoop stress to 250 MPa, right at mild steel yield, and the force to about 53,000 N (about 6 tons). That is why a fit that is only a thousandth of an inch tighter than planned can crack a cast iron hub or stall a small press. Thin hubs are worse: if D drops to 35 mm, (d/D)² rises to 0.51 and the hoop stress factor climbs to about 3.1.

Holding torque

The same numbers give the torque the joint can carry before slipping: T = F × d ÷ 2. In the example, T = 26,500 × 0.0125 m ≈ 330 N·m (about 245 lbf·ft). Use a safety factor, because surface finish, lubricant and actual interference all vary. Smooth ground surfaces lose some interference when the peaks are flattened during pressing, so very fine fits may hold less than calculated.

Limits of the formula

The formula assumes both parts are the same elastic material, the shaft is solid, and the hub is long compared with the fit and stays elastic. For a hollow shaft, aluminum hub, or a hub stressed near yield, use the full thick-walled cylinder (Lamé) equations with each material's modulus and Poisson's ratio, or ask the designer. Treat the friction value as an estimate; it is the largest uncertainty in the pressing force.

Tips

FAQ

How do I calculate press fit pressure?

For a solid steel shaft in a steel hub, p = (E × δ ÷ 2d) × (1 − (d/D)²).

How much force to press a 25 mm shaft?

With 0.025 mm interference, a 50 mm hub and 30 mm length, about 26,500 N (6,000 lbf) at μ = 0.15.

What friction coefficient should I use?

About 0.1 to 0.2 for steel on steel; it is the biggest uncertainty.

Can a press fit crack the hub?

Yes, if hoop stress approaches the hub material strength, especially with cast iron or thin hubs.

Does lubricant matter?

Yes. It lowers pressing force and holding torque and helps prevent galling.

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