Thread Engagement Length

Calculate thread engagement length, number of engaged threads and contact surface stress.

Inputs

W

Load

p

Pitch

d_2

Pitch Dia.

h'

Height

q

Stress

MPa

Formula Interpretation

Thread Engagement Length

h = \dfrac{W \cdot p}{\pi \, d_2 \, h' \, q}

$h$ is the thread engagement length (mm); $W$ is the axial load (N); $p$ is the thread pitch (mm); $d_2$ is the pitch diameter (mm); $h'$ is the contact height on the thread flank (mm); $q$ is the allowable contact stress (MPa).

Number of Engaged Threads

n = \dfrac{h}{p} = \dfrac{W}{\pi \, d_2 \, h' \, q}

$n$ is the number of engaged threads; equals the engagement length $h$ divided by the pitch $p$ .

Contact Stress on Thread Flanks

q = \dfrac{W}{\pi \, d_2 \, h' \, n}

$q$ is the actual contact stress (MPa) on thread flanks; $W$ is the axial load; $d_2$ is the pitch diameter; $h'$ is the contact height; $n$ is the number of engaged threads.

Allowable Contact Stress Reference (MPa)

External Thread	Internal Thread	Connection	Transmission
Low-carbon steel	Low-carbon steel or bronze	30	10
High-carbon steel	High-carbon steel or bronze	40	13
High-carbon steel	Cast iron	15	5

Knowledge: Thread Engagement

•The thread engagement length must ensure that the thread teeth of both external and internal threads cannot be sheared off at the root during engagement.
•When the allowable shear stresses of external and internal threads are equal, the strength of the external thread should be considered first.
•The nut height is determined by the contact stress on thread flanks and the shear stress on thread teeth.

Example

An eyebolt lifts a load of $W = 6000 \text{ N}$ . The tensile strength of the thread is $\sigma = 40 \text{ MPa}$ , and the allowable contact stress is $q = 15 \text{ MPa}$ . Find the major diameter and the internal thread length (plate thickness).

Step 1 — Calculate major diameter

The eyebolt is used for lifting, so it is subject to axial load only. The formula is as follows.

d = \sqrt{\dfrac{2W}{\sigma}} = \sqrt{\dfrac{2 \times 6000}{40}} = 17.3 \text{ (mm)}

Therefore, the eyebolt major diameter is M20 (per standard thread tables).

Step 2 — Calculate engagement length

M20 thread has $p = 2.5 \text{ mm}$ , $d_2 = 18.376 \text{ mm}$ , $h' = 1.353 \text{ mm}$ . Substituting into formula:

h = \dfrac{W \cdot p}{\pi \, d_2 \, h' \, q} = \dfrac{6000 \times 2.5}{\pi \times 18.376 \times 1.353 \times 15} = 12.8 \text{ (mm)}

Therefore, the internal thread length (plate thickness) is 13 mm.

Extended Knowledge

•The pitch diameter is an imaginary circle where the distance to the thread crest equals the distance to the thread root.
•The engagement length must ensure that the contact stress on both external and internal thread flanks exceeds the allowable value.
•For low-carbon steel bolts and nuts, nut height is typically 0.8 to 1.0 times the bolt major diameter. For low-carbon steel bolts with cast iron nuts, nut height is 1.3 to 1.5 times the major diameter.

Related Standards & Articles

Authoritative references for the formulas used in this calculator

Standard

Metric Coarse Thread Standards: ISO and National Equivalents (CN/DE/FR/JP/RU/US/UK)

A cross-reference table of metric coarse thread standards covering thread form, diameter-pitch series, basic dimensions, tolerances, limit deviations, preferred thread limits, and gauging — aligned across ISO, China GB/T, Germany DIN, France NF, Japan JIS, Russia GOST, USA ASME, and UK BS.

External Thread

Internal Thread

Connection

Transmission

Low-carbon steel

Low-carbon steel or bronze

High-carbon steel

High-carbon steel or bronze

High-carbon steel

Cast iron