Lead Angle (Threads)

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Screw Lead Angle Helix

Definition of Screw Lead Angle

The lead angle (φ) measures the inclination of a screw helix from a plane that is perpendicular to the screw’s axis. In more simple words, it is the proportion between the screw’s lead and its diameter.

Screw lead angles per diameter and pitch

Lead/Diameter Chart

As seen in this chart, a screw with a fine pitch and a large diameter will have a small lead angle, whereas a screw with a coarse pitch and a small diameter will have a large lead angle.

The above chart is for single start threads where the lead equals the pitch (L=D). The lead of the screw equals its pitch times the number of starts (L=nXP). Therefore Multi start threads have large lead angles.

Screw Lead Angle Formula

The lead angle is measured at the pitch diameter. It can be represented by a right triangle whose base is the circumference of the screw, and its height is the lead of the screw.

Thread Lead Angle Triangle
\( \large\begin{array}{l} L = n\,\times\,P \\ C = \pi\,\times\,d_2 \\ \varphi = \arctan \left ( \frac{L}{C} \right ) \end{array} \)

Formula symbols:

  • n – Number of starts
  • P – Pitch of the thread (Inch / mm)
  • d2Pitch Diameter of the thread (Inch / mm)

Lead Angle Calculator

For easier thread selection and higher accuracy, use the ThreaDoctor calculator.

Machining Considerations

Lead Angle Insert Tilting

As machining people, why do we care about the lead angle?
When turning a thread with a typical laydown insert, the best practice is to tilt it by the lead angle size. It ensures symmetrical relief on both sides of the insert flanks.

All threading tools suppliers provide an assortment of shims to tilt the inserts to all the needed angles. They will also publish charts that specify the correct shim for each thread.

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