# Press Fit Interference Calculator (Contact Pressure, Force and Torque)

> Source: https://netray.co/tools/press-fit-interference-pressure-force-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Estimate contact pressure, hub hoop stress, press-in force and slip torque for a solid shaft pressed into a hub.

## Category

engineering-plm

## Industry

Discrete Manufacturing

## Audience

- Design engineer
- Manufacturing engineer
- Assembly engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Nominal fit diameter

**Key:** d

**Type:** number

**Default:** 40

**Min:** 1

**Step:** 0.5

**Unit:** mm

#### Hub outside diameter

**Key:** od

**Type:** number

**Default:** 80

**Min:** 2

**Step:** 0.5

**Unit:** mm

**Help:** Must be larger than the fit diameter.

#### Engagement length

**Key:** len

**Type:** number

**Default:** 50

**Min:** 1

**Step:** 0.5

**Unit:** mm

#### Diametral interference (before smoothing)

**Key:** delta

**Type:** number

**Default:** 40

**Min:** 0

**Step:** 1

**Unit:** um

**Help:** Largest shaft limit minus smallest hole limit gives maximum interference.

#### Roughness smoothing loss

**Key:** loss

**Type:** number

**Default:** 4

**Min:** 0

**Step:** 0.5

**Unit:** um

**Help:** Surface peaks flatten on assembly and reduce effective interference.

#### Hub material modulus

**Key:** e_hub

**Type:** select

**Default:** 207

**Options:**

##### Steel (207 GPa)

**Value:** 207

##### Cast iron (100 GPa)

**Value:** 100

##### Bronze (105 GPa)

**Value:** 105

##### Aluminium (69 GPa)

**Value:** 69

#### Shaft material modulus

**Key:** e_shaft

**Type:** select

**Default:** 207

**Options:**

##### Steel (207 GPa)

**Value:** 207

##### Stainless 304 (193 GPa)

**Value:** 193

##### Titanium (114 GPa)

**Value:** 114

#### Coefficient of friction

**Key:** mu

**Type:** number

**Default:** 0.12

**Min:** 0

**Max:** 0.5

**Step:** 0.01

**Help:** Typical 0.08 to 0.15 for steel on steel, lubricated to dry.

#### Hub yield strength

**Key:** yield

**Type:** number

**Default:** 350

**Min:** 1

**Step:** 10

**Unit:** MPa

**Outputs:**

#### Effective interference (um)

**Key:** de

**Expr:** max(0, delta - loss)

**Format:** decimal

#### Contact pressure (MPa)

**Key:** p

**Expr:** de / (d * (((od*od + d*d)/(od*od - d*d) + 0.3) / e_hub + 0.7 / e_shaft))

**Format:** decimal

**Primary:** true

**Description:** Lame solution for a solid shaft and a thick-walled hub, Poisson ratio 0.3 for both.

#### Hub bore hoop stress (MPa)

**Key:** hoop

**Expr:** p * (od*od + d*d) / (od*od - d*d)

**Format:** decimal

**Description:** Peak tensile stress in the hub at the bore.

#### Safety factor on hub yield

**Key:** sf

**Expr:** if(gt(hoop, 0), yield / hoop, 0)

**Format:** decimal

**Primary:** true

#### Press-in or slip force (N)

**Key:** force

**Expr:** p * pi * d * len * mu

**Format:** integer

**Primary:** true

**Description:** Axial force to move the joint, assuming uniform pressure.

#### Torque capacity (N.m)

**Key:** torque

**Expr:** p * pi * d * len * mu * d / 2 / 1000

**Format:** decimal

**Chart:**

#### Contact pressure and hub stress versus interference

**Type:** line

**X:** delta

**From:** 5

**To:** 100

**Steps:** 20

**Series:**

- p
- hoop

**Disclaimer:** Elastic thick-wall equations for a solid shaft and a uniform hub, with a Poisson ratio of 0.3. Real joints vary with roughness, edge effects, temperature and assembly method. Validate critical joints by test.

## Content

**Intro:** A press fit holds two parts together by friction from radial interference between the shaft and hub. This calculator applies the classical Lame thick-wall equations to estimate the contact pressure, the stress in the hub, the force to press the parts together and the torque the joint can transmit.

**Sections:**

#### How to use it

**Body:** Enter the fit diameter, hub outside diameter, engagement length and the diametral interference, which is the shaft diameter minus the hole diameter. For limits, use the maximum interference to check hub stress and the minimum interference to check holding capacity. Subtract a small roughness smoothing loss, then choose the materials and friction coefficient. The default 40 mm joint with 40 um interference gives about 80 MPa contact pressure and a press force near 60 kN. Run the min and max cases separately.

#### The method

**Body:** For a solid shaft in a hub with the same modulus and a Poisson ratio of 0.3, contact pressure equals the radial interference per unit diameter divided by the sum of two compliance terms: the hub term with the diameter ratio factor, and the shaft term. Hub hoop stress at the bore is pressure times the sum of the squared outside and fit diameters over their difference. Force equals pressure times contact area times friction. Torque capacity is that force times half the fit diameter.

#### Reading the result

**Body:** Check the safety factor on hub yield with the maximum interference and typical dimension and material extremes, and check slip torque against the load with the minimum interference. A safety factor under about 1.5 on yield is a warning, since heavy hubs may crack, and thin hubs flare. The press force is a guide for choosing a press, but use the larger of the pressing and withdrawal forces, and expect scatter of 30 percent or more from friction alone. Heated or cooled assembly removes the pressing force but not the hoop stress.

**Bullets:**

- Use the maximum interference for stress, the minimum for holding
- Lead-in chamfers and lubrication reduce galling
- Fatigue of the hub bore, not static yield, often governs

#### Common mistakes

**Body:** Common mistakes are entering a radial interference as diametral, which halves the result, forgetting the roughness loss on rough finishes, using the nominal instead of the tolerance extremes, and assuming a joint with a keyway or step behaves as a plain cylinder. Also check that the hub outside diameter is realistic: the thin-walled hub case shows high stress and the formula does not capture end effects at the hub faces.

**Cta:** If fit calculations and tolerance data sit in spreadsheets, separate from your ERP item and routing records, we can help connect them.

**Faq:**

#### How do you calculate press fit force?

**Answer:** Compute contact pressure from the interference using the Lame equations, then multiply by contact area and the friction coefficient. Area is pi times diameter times engagement length. This gives the force to press in or to start slipping, with a large scatter from friction.

#### How much interference is needed for a press fit?

**Answer:** A common guide for steel is H7 hole with p6 or s6 shaft, roughly 0.5 to 1.5 thousandths of the diameter in interference. The right amount depends on the load: enough to transmit torque with a margin, but not enough to yield or crack the hub.

#### What is the difference between press fit and shrink fit?

**Answer:** Both rely on interference. A press fit is assembled by force at room temperature, while a shrink fit uses heating or cooling to change the size temporarily so no pressing force is needed. The resulting pressure and stresses at room temperature follow the same equations.

#### Why is the diametral interference used?

**Answer:** Drawings and gauges work in diameters, so interference is given as shaft diameter minus hole diameter. The Lame equation then divides by the diameter to get strain. Entering a radial value by mistake would halve the pressure and give a misleading result.

## Search terms

press fit calculator, interference fit calculator, press fit force calculator, press fit pressure lame, interference fit torque capacity, shaft hub press fit stress, how much interference for press fit, interference fit hoop stress

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