Press Fit Calculator Formula

Understand the math behind the press fit calculator. Each variable explained with a worked example.

Formulas Used

Interface Pressure

interface_p = interference * e_mpa / (shaft_dia * (1 / (1 - k_ratio)))

Assembly Press Force

assembly_force = pi * shaft_dia * fit_length * (interference * e_mpa / (shaft_dia * (1 / (1 - k_ratio)))) * friction_coeff / 1000

Variables

VariableDescriptionDefault
interferenceDiametral Interference (delta)(mm)0.05
shaft_diaNominal Shaft Diameter (d)(mm)50
hub_odHub Outer Diameter (D)(mm)100
fit_lengthFit Length (L)(mm)40
modulusElastic Modulus (E)(GPa)200
friction_coeffFriction Coefficient0.15
e_mpaDerived value= modulus * 1000calculated
k_ratioDerived value= pow(shaft_dia / hub_od, 2)calculated

How It Works

Press Fit (Interference Fit) Analysis

A press fit creates a joint by assembling a slightly oversized shaft into a slightly undersized hole.

Simplified Formula (solid shaft, same material)

p = delta E (1 - (d/D)^2) / d

where delta is the radial interference (diametral/2), d is shaft diameter, D is hub OD, and E is the elastic modulus.

Assembly Force

F = pi d L p mu

where L is the engagement length and mu is the friction coefficient.

Worked Example

A 50 mm shaft pressed into a hub (OD=100 mm) with 0.05 mm diametral interference, 40 mm long, steel.

interference = 0.05shaft_dia = 50hub_od = 100fit_length = 40modulus = 200friction_coeff = 0.15
  1. 01k = (50/100)^2 = 0.25
  2. 021/(1-0.25) = 1.333
  3. 03p = 0.05 x 200,000 / (50 x 1.333) = 10,000 / 66.67 = 150 MPa
  4. 04F = pi x 50 x 40 x 150 x 0.15 / 1000 = 141.4 kN

Frequently Asked Questions

What interference fits are standard?

ISO specifies H7/p6 for light press fits, H7/r6 for medium, and H7/s6 for heavy. The choice depends on required holding force, assembly method, and whether disassembly is needed.

Can I use heat to assist assembly?

Yes. Heating the hub expands the bore, allowing easy assembly. Alternatively, cooling the shaft with dry ice or liquid nitrogen shrinks it. This avoids the high forces and potential surface damage of mechanical pressing.

What if hub and shaft have different materials?

Use the full Lame equation with separate terms for each material, including their individual moduli and Poisson ratios. The simplified formula shown assumes the same material for both parts.

Ready to run the numbers?

Open Press Fit Calculator