TAHA Engineering Toolsby TAHA Knowledge Lab

Machining & Workshop

Lathe Change-Gear Calculator for Thread Cutting

Find or check change gears for cutting a metric or TPI thread on your lathe.

Inputs

Calculate from
Change-gear train: gear A meshes with gear B; gear C, fixed behind B, meshes with gear D on the leadscrew.A (stud)BCDleadscrew
Driver A (on the stud, turning with the spindle) drives B. C is fixed to B on the same shaft and drives D on the leadscrew. Ratio = (A × C) ÷ (B × D). For a simple train, A drives the leadscrew gear directly (an idler may sit between them). Diagram not to scale.

From the machine manual or by measuring the leadscrew.

For a multi-start thread, enter the lead.

Speed of the stud (first change-gear shaft) ÷ spindle speed. 1 if the stud turns at spindle speed. Includes any tumbler, quick-change gearbox or fixed reduction — from your machine manual. Do not guess.

Separate with commas. List a size twice if you have two of it. Up to 40 gears.

Result

Required gear ratio (drivers ÷ driven)
0.472441
Best trains from your gears
1. A 60 → B 127 (simple): 1.5 mm = 16.933 TPI, error +0% 2. A 20 → B 25 | C 75 → D 127 (compound): 1.5 mm = 16.933 TPI, error +0% 3. A 30 → B 20 | C 40 → D 127 (compound): 1.5 mm = 16.933 TPI, error +0% 4. A 30 → B 25 | C 50 → D 127 (compound): 1.5 mm = 16.933 TPI, error +0% 5. A 30 → B 35 | C 70 → D 127 (compound): 1.5 mm = 16.933 TPI, error +0%
Working
Leadscrew pitch = 3.175 mm; thread wanted = 1.5 mm Required ratio = 1.5 ÷ (3.175 × 1) = 0.47244

You need a change-gear ratio of 0.472441. The closest trains from your gears are listed, best first.

  • Check every suggested train on the machine: the gears must physically fit on the banjo (quadrant) and mesh, and an idler may be needed to connect them or to reverse direction. Idlers do not change the ratio.

Educational estimate — check the assumptions below.

About this calculator

On a lathe without a quick-change gearbox, the thread pitch is set by change gears between the spindle and the leadscrew. For each turn of the spindle, the leadscrew must turn by the ratio thread wanted ÷ leadscrew pitch. This calculator works out that ratio and searches the gears you actually own for the simple (A → B) and compound (A → B, C → D) trains that come closest — including the classic 127-tooth gear, which converts exactly between inch and metric (127 = 5 × 25.4).

Every lathe is different. Enter your leadscrew and any fixed internal ratio from your machine’s manual; nothing is assumed about a particular machine.

Formula

Pcut = PLS × k × (A × C) ÷ (B × D)

Required ratio R = Pwanted ÷ (PLS × k)

PLS = leadscrew pitch (for TPI: 25.4 mm ÷ TPI), k = fixed ratio from spindle to the stud gear, A, C = driving gears, B, D = driven gears (B and C share a shaft). For a simple train, C ÷ D = 1. Idler gears do not change the ratio.

Worked example

Cutting a 1.5 mm metric thread on a lathe with an 8 TPI leadscrew (pitch 3.175 mm), stud at spindle speed (k = 1):

  • Required ratio = 1.5 ÷ 3.175 = 0.472 44 = 60 ÷ 127
  • A 60-tooth driver and a 127-tooth driven gear give exactly 3.175 × 60 ÷ 127 = 1.5000 mm.

Cutting 20 TPI on the same lathe: ratio = 1.27 ÷ 3.175 = 0.4 = 20 ÷ 50 (or 40 ÷ 100).

Assumptions and limitations

  • The fixed ratio <var>k</var> must come from your machine (manual, gear labels, or by counting). Reversing tumblers and idlers change direction only.
  • The search uses only the tooth counts you enter, without reusing a gear unless you list it twice. It does not check centre distances, gear module, banjo slots or whether gears clash.
  • An error of a few hundredths of a percent is normally acceptable for short threads; over long threads a small pitch error accumulates. Exact inch–metric conversion needs a 127-tooth gear (or a gearbox designed for it).
  • For multi-start threads, cut the lead and index the work for each start.

Safety note

Isolate the machine before changing gears. Never adjust change gears or the banjo while the spindle can turn.

References

  • Screw-cutting gear train relation: pitch cut = leadscrew pitch × spindle-to-stud ratio × product of drivers ÷ product of driven gears (standard machining texts).
  • Inch–metric translation: 127 teeth = 5 × 25.4.