Calculate helix angle or thread lead angle from diameter and lead, pitch or TPI, solve for lead or diameter, and get the helix length per turn.

Use the pitch or reference diameter; major diameter is only an approximation.

Usually 1. Lead = axial pitch × number of starts.

Thread lead angle is measured from the plane normal to the axis; gear helix angle from the axis. The two add up to 90°.

Helix length
Optional. The helix’s overall height along the axis, for total helix length and number of turns.

Helix Angle Formula

The following formula calculates a screw lead angle from a plane normal to the cylinder axis. Use C = πD at the pitch or reference cylinder, with C and lead L in the same units. The gear helix angle measured from the axis is the complementary angle, 90° minus this lead angle.

HA = atan(L / C)
  • Where HA is the thread lead angle in degrees, measured from the normal plane
  • L is the lead of the screw
  • C is the circumference at the pitch or mean cylinder, Ï€ times its diameter

To calculate the thread lead angle, take atan(L / (πD)); for the gear angle measured from the axis use atan(πD / L). Inverse thread formulas are L = πD tan(HA) and D = L / (π tan(HA)); the gear convention uses the complementary angle. Lead equals axial pitch times the number of starts, and axial pitch in mm equals 25.4 / TPI. Do not substitute gear normal or circular pitch. Changing a length unit converts the entered quantity.

Helix Angle Definition

A helix angle is an angle formed by the shape of a screw, which is governed by its overall circumference and its lead.

The lead is a measure of the linear distance a nut will travel with one revolution around the screw.

Example Problem

How to calculate helix angle?

The following example outlines the steps and information needed to calculate the angle of a helix.

First, determine the lead of the screw. The lead of the screw in this example is .25 inches.

Next, determine the circumference of the screw. The pitch-cylinder circumference is 3 inches, so enter pitch diameter D = 3 / π ≈ 0.95493 inches in the calculator.

Finally, calculate the helix angle using the formula above:

HA = atan(L / C)

HA = atan(.25/ 3)

HA ≈ 4.763642 degrees (thread lead angle); the complementary axial angle is about 85.236358 degrees