How Change Gears Set the Thread Pitch
On a manual lathe the leadscrew moves the carriage one leadscrew pitch for every turn it makes. The change gears between the spindle and the leadscrew decide how many turns that is per turn of the work, so they decide the pitch of the thread you cut.
The calculator tries every train it can build from the gears you list, using each physical gear only once, and ranks them by how close the pitch comes to the one you want. It also works backwards: type in a train already on the lathe and it tells you what thread it will cut.
The Formulas
Finding Your Stud Ratio
Many lathes, including most 7x mini lathes, drive the first change gear shaft at spindle speed through the tumbler or fixed gears, so the stud ratio is 1. Some older lathes and many quick-change set-ups do not. To check, put a chalk mark on the chuck and on the gear A shaft, turn the spindle exactly one revolution by hand and count how far the shaft turns. Half a turn is a ratio of 0.5, two turns is 2. If you can see the fixed gears, the ratio is the product of their driver teeth divided by the product of their driven teeth.
Worked Examples
- Leadscrew pitch: 25.4 ÷ 16 = 1.5875 mm. Ratio needed: 1.25 ÷ 1.5875 = 0.787402 (exactly 100 ÷ 127).
- There is no 127T gear, so no exact train. The closest is A 45, B 40, C 35, D 50: (45 ÷ 40) × (35 ÷ 50) = 1575 ÷ 2000 = 0.7875.
- Pitch cut: 1.5875 × 0.7875 = 1.250156 mm, which is 0.0125 % long. Over 25 mm (20 threads) that adds up to 20 × 0.000156 = 0.003 mm, far less than the clearance in a normal nut.
- Fit: C + 2 + 8 = 45 ≤ A + B = 85, and B + 2 + 8 = 50 ≤ C + D = 85, so it passes the rule of thumb.
- 1.5 mm leadscrew, 1.0 mm thread: ratio 1.0 ÷ 1.5 = 2/3, so A 40 → idler → D 60 is exact (1.5 × 40 ÷ 60 = 1.000 mm). 20/30 and 30/45 work too.
- 8 TPI leadscrew with a 127T gear, 1.0 mm thread: leadscrew pitch 3.175 mm, ratio 1.0 ÷ 3.175 = 40 ÷ 127, so A 40 → idler → D 127 is exact: 3.175 × 40 ÷ 127 = 127/40 × 40/127 = 1.000 mm.
Mini Lathe Change Gear Charts
These charts list the closest change gears for common metric and imperial threads on a typical 7x mini lathe (7x10, 7x12, 7x14 and similar), worked out by this calculator with the gear set 20, 20, 30, 35, 40, 40, 45, 50, 55, 57, 60, 65, 80 and a stud ratio of 1. Gear sets differ between makers and years, so check yours, or enter it above for trains that match your own gears. A and C are drivers, B and D are driven; trains that need more clearance than the gears allow are left out.
Metric Leadscrew (1.5 mm Pitch)
For mini lathes sold with a metric leadscrew. Imperial threads come out within about 0.06 % using ratios such as 55/65 and the 57T gear, close enough for short threads.
| Thread | Gears (A/B × C/D) | Pitch cut | Error |
|---|---|---|---|
| 0.4 mm | 20/30 × 20/50 | 0.4 mm | exact |
| 0.5 mm | 20 → idler → 60 | 0.5 mm | exact |
| 0.6 mm | 20 → idler → 50 | 0.6 mm | exact |
| 0.7 mm | 35/30 × 20/50 | 0.7 mm | exact |
| 0.75 mm | 20 → idler → 40 | 0.75 mm | exact |
| 0.8 mm | 40/30 × 20/50 | 0.8 mm | exact |
| 1 mm | 20 → idler → 30 | 1 mm | exact |
| 1.25 mm | 50 → idler → 60 | 1.25 mm | exact |
| 1.5 mm | 20 → idler → 20 | 1.5 mm | exact |
| 1.75 mm | 35 → idler → 30 | 1.75 mm | exact |
| 2 mm | 40 → idler → 30 | 2 mm | exact |
| 2.5 mm | 50 → idler → 30 | 2.5 mm | exact |
| 40 TPI | 55/40 × 20/65 | 0.6346 mm | -0.061 % |
| 32 TPI | 55/65 × 50/80 | 0.7933 mm | -0.061 % |
| 28 TPI | 57/55 × 35/60 | 0.9068 mm | -0.036 % |
| 26 TPI | 57/35 × 20/50 | 0.9771 mm | +0.022 % |
| 24 TPI | 50/60 × 55/65 | 1.0577 mm | -0.061 % |
| 20 TPI | 55 → idler → 65 | 1.2692 mm | -0.061 % |
| 19 TPI | 60/57 × 55/65 | 1.336 mm | -0.061 % |
| 18 TPI | 55/45 × 50/65 | 1.4103 mm | -0.061 % |
| 16 TPI | 55/40 × 50/65 | 1.5865 mm | -0.061 % |
| 14 TPI | 57/30 × 35/55 | 1.8136 mm | -0.036 % |
| 13 TPI | 57/35 × 40/50 | 1.9543 mm | +0.022 % |
| 12 TPI | 55/30 × 50/65 | 2.1154 mm | -0.061 % |
| 11 TPI | 50/20 × 40/65 | 2.3077 mm | -0.061 % |
| 10 TPI | 55/20 × 40/65 | 2.5385 mm | -0.061 % |
Imperial Leadscrew (16 TPI)
For mini lathes sold with an imperial leadscrew. Metric threads are approximations without a 127T gear; the error column shows how far off each one is.
| Thread | Gears (A/B × C/D) | Pitch cut | Error |
|---|---|---|---|
| 0.4 mm | 20/65 × 45/55 | 0.3997 mm | -0.087 % |
| 0.5 mm | 20/57 × 45/50 | 0.5013 mm | +0.263 % |
| 0.6 mm | 35/57 × 40/65 | 0.5999 mm | -0.022 % |
| 0.7 mm | 35/55 × 45/65 | 0.6994 mm | -0.087 % |
| 0.75 mm | 50/57 × 35/65 | 0.7498 mm | -0.022 % |
| 0.8 mm | 40/55 × 45/65 | 0.7993 mm | -0.087 % |
| 1 mm | 50/55 × 45/65 | 0.9991 mm | -0.087 % |
| 1.25 mm | 45/40 × 35/50 | 1.2502 mm | +0.012 % |
| 1.5 mm | 65/50 × 40/55 | 1.5009 mm | +0.061 % |
| 1.75 mm | 55/35 × 40/57 | 1.7506 mm | +0.036 % |
| 2 mm | 55/35 × 40/50 | 1.9957 mm | -0.214 % |
| 2.5 mm | 45/20 × 35/50 | 2.5003 mm | +0.012 % |
| 40 TPI | 20 → idler → 50 | 0.635 mm | exact |
| 32 TPI | 20 → idler → 40 | 0.7937 mm | exact |
| 28 TPI | 20 → idler → 35 | 0.9071 mm | exact |
| 26 TPI | 40 → idler → 65 | 0.9769 mm | exact |
| 24 TPI | 20 → idler → 30 | 1.0583 mm | exact |
| 20 TPI | 40 → idler → 50 | 1.27 mm | exact |
| 19 TPI | 60/50 × 40/57 | 1.3368 mm | exact |
| 18 TPI | 40 → idler → 45 | 1.4111 mm | exact |
| 16 TPI | 20 → idler → 20 | 1.5875 mm | exact |
| 14 TPI | 40 → idler → 35 | 1.8143 mm | exact |
| 13 TPI | 80 → idler → 65 | 1.9538 mm | exact |
| 12 TPI | 40 → idler → 30 | 2.1167 mm | exact |
| 11 TPI | 80 → idler → 55 | 2.3091 mm | exact |
| 10 TPI | 80 → idler → 50 | 2.54 mm | exact |
Error is the pitch cut against the nominal pitch. Over a 25 mm length of thread, 0.05 % adds up to about 0.0125 mm, which a short nut or bolt will take up; long threads need a smaller error.
Practical Tips
- Metric on an imperial leadscrew, or imperial on a metric one: keep the half nuts closed. The threading dial cannot find the start of the thread again, so at the end of each pass stop, withdraw the tool, run the spindle in reverse back past the start, then put on the next cut. Use the dial only for threads in the same system as the leadscrew, and only as its own chart says.
- Test the train before cutting deep. Take a scratch pass and check it with a thread gauge, or measure across 10 threads with a rule or calipers. A wrong gear shows up straight away.
- Set the mesh with paper. Wind a strip of paper between gears as you tighten the banjo, then remove it. Too tight wears the gears and loads the motor; too loose rattles.
- Pick the size and depth first. Look up the pitch and major diameter in the thread size chart, then measure the finished thread with the 3-wire thread measurement calculator.
- The lathe threading pass calculator is a different job: it sets the depth of each pass and G76/G92 code on a CNC lathe, where no change gears are needed. Cutting gears or splines on a dividing head instead? Use the dividing head calculator.
Frequently Asked Questions
Presets are typical set-ups, not data for your machine: gear sets, leadscrews and stud ratios vary by maker and year, so count your own. The fit check is a rule of thumb. Always confirm the pitch with a scratch pass before cutting to full depth.