Threading Formulas and Definitions

This section covers threading formulas and definitions for how to calculate cutting speed, feed rate, or any other parameter for your thread turning, thread milling, or tapping operations. You will also find the designation for different thread forms according to international standards.

Thread Turning Formulas and Definitions

Infeed

By dividing the full cutting depth of the thread into smaller cuts, the sensitive nose radius of the insert is not overloaded.

Example: By taking 0.23–0.10 mm (0.009–0.004 inch) in cutting depth per pass (radial infeed), the full cutting depth (a_p) and the profile depth of the thread (0.94 mm (0.037 inch)) are turned on a 1.5 mm (0.06 inch) pitch metric thread in 6 passes (nap).

1st pass, infeed
0.23 mm

= 0.009 inch

2nd pass, infeed
0.42–0.23 = 0.19 mm

0.017–0.009 = 0.008 inch

3rd pass, infeed
0.59–0.42 = 0.17 mm

0.023–0.017 = 0.006 inch

4th pass, infeed
0.73–0.59 = 0.14 mm

0.029–0.023 = 0.006 inch

5th pass, infeed
0.84–0.73 = 0.11 mm

0.033–0.029 = 0.004 inch

6th pass, infeed
0.94–0.84 = 0.10 mm

0.037–0.033 = 0.004 inch

The infeed can be calculated according to the formula:

Δa_p = radial infeed, cutting depth per pass

X = actual pass (in a series from 1 to nap)

a_p = Total depth of thread + extra stock

nap = number of passes

Y = 1st pass = 0.3

2nd pass = 1

3rd and higher = x-1

Pitch 1.5 mm (0.06 inch)
a_p = 0.94 mm (0.037 inch)
nap = 6

γ₁ = 0.3
γ₂ = 1
γ_n = x-1

1. Root/bottom
   The bottom surface joining the two adjacent flanks of the thread
2. Flank/side
   The side of a thread surface connecting the crest and root
3. Crest/top
   The top surface joining the two sides, or flanks.

P = Pitch, mm, or threads per inch (t.p.i.)

The distance from a point on the screw thread to a corresponding point on the next thread measured parallel to the axis.

β = The thread profile angle

The angle between the flanks of the thread measured in an axial plane.

φ = Lead angle (helix angle) of the thread

The angle of the thread at a pitch diameter with a plane perpendicular to the axis.

Diameter parameters

d = Major diameter, external

D = Major diameter, internal

d₁ = Minor diameter, external

D₁ = Minor diameter, internal

d₂ = Pitch diameter, external

D₂ = Pitch diameter, internal

The effective diameter of the screw thread; approximately half way between the major and minor diameters.

Lead angle (helix angle)

The lead angle, φ, (helix angle) is dependent on and related to the diameter and the pitch of the thread. This measurement can be represented by a triangle being unwound from the component. The lead angle is calculated according to the formula below.

Thread Milling Formulas and Definitions

Cutting speed (v_c)

Metric (m/min)

Imperial (ft/min)

Formulas for internal thread milling

Calculated version

Peripheral feed (mm/min) (inch/min)

Radial depth of cut (mm) (inch)

Tool center feed (mm/min) (inch/min)

Feed per tooth (mm) (inch)

Thread milling with a roll into cut tool path, D_vf1

Formulas for external thread milling

Calculated version

Tapping Formulas and Definitions

How to calculate thread height in percentage, %

Thread height in %, is the ratio between actual height and maximum height of the internal thread. The example below applies to ISO & UTS standard – 60° threads.

Example, M8 × 1.25

Maximum thread height according to standard is 6/8 H.

H = 0.866 × P

(H = Basic triangle height)

(P = thread pitch)

Maximum thread height is:

6/8 * (0.866 × 1.25) = 0.811 mm

Actual thread height at a core hole of Ø 6.9 mm:

(8–6.9) / 2 = 0.55 mm

Thread height is then (0.55 / 0.81) × 100 = 68%