Lathe Change Gear & Thread Pitch Calculator
Enter the leadscrew, target thread, and the change gears you actually have. The calculator ranks simple and compound trains by pitch error and shows how much the lead will drift.
Best gear arrangement20 driving 30
- Required leadscrew ratio
- 0.67
- Actual thread pitch
- 1
- Actual threads per inch
- 25.4
- Pitch error
- 0%
- Lead error per 100 mm
- 0
- Lead error per inch
- 0
- Tolerance result
- Exact ratio
Ranked alternative trains
| Arrangement | Train | Actual pitch | Pitch error | Drift per 100 mm | Tolerance |
|---|---|---|---|---|---|
| 20 driving 30 | Simple | 1 | 0% | 0 | Exact ratio |
| 30 driving 45 | Simple | 1 | 0% | 0 | Exact ratio |
| 40 driving 60 | Simple | 1 | 0% | 0 | Exact ratio |
| 45 driving 70 | Simple | 0.96 | -3.57% | -3.57 | Outside 1% limit |
| 40 driving 63 | Simple | 0.95 | -4.76% | -4.76 | Outside 1% limit |
The listed ratio is leadscrew revolutions per spindle revolution; idler gears change direction or spacing but not pitch.
Check the lathe manual for any quick-change gearbox, tumbler, or internal gear ratio that is not 1:1.
How to use this calculator
- Choose whether the leadscrew is marked as millimeters per revolution or threads per inch.
- Enter the target thread pitch, using millimeters or TPI as appropriate.
- List each physical change gear you can use, repeating a tooth count only if you own two of that gear.
- Choose simple, compound, or automatic search and set the pitch-error limit you can accept.
How the gear train is calculated
A threading setup is a speed ratio problem. The spindle turns the work. The leadscrew moves the carriage. If the leadscrew advances L millimeters per revolution and the gear train makes the leadscrew turn R times for each spindle revolution, the thread pitch is:
Pactual = L × R
The calculator first converts the leadscrew and target into millimeters. A TPI value is converted with the exact inch relationship 25.4 ÷ TPI. The required ratio is then:
Rrequired = Ptarget ÷ L
For a simple train, where spindle gear A drives leadscrew gear D, the ratio is A ÷ D. An idler between them reverses direction or bridges distance, but it does not change the numerical ratio. For a compound train, where A drives B, and C is fixed to the same shaft as B and drives D, the ratio is (A ÷ B) × (C ÷ D).
What the ranking means
The search treats each gear slot as one physical gear. If you enter 40 teeth once, that 40-tooth gear can appear in only one position. If you enter 40 in two slots, the calculator can use two separate 40-tooth gears in one compound train. Zero slots are ignored.
Results are ranked by the absolute value of pitch error, then by fewer gears. The pitch error keeps its sign: a positive value means the thread is coarser than requested, and a negative value means it is finer. The lead-error rows show the same error as accumulated distance over 100 mm and over one inch, because a small percentage can matter on a long thread.
What this leaves out
This is a numerical train search, not a banjo layout tool. It does not know shaft spacing, gear diameter clearance, keyed bushings, tumbler direction, or whether a compound pair can physically share a stud. It also assumes the leadscrew path is otherwise 1:1. If the lathe has a quick-change gearbox, fixed internal reduction, or a manufacturer-specific transposing arrangement, include that ratio before relying on the result.
Worked example
With the default entries, a 1.5 mm leadscrew cutting a 1.0 mm thread needs 1.0 ÷ 1.5 = 0.6666667 leadscrew revolutions per spindle revolution. The entered gear set includes 20 and 30 teeth, so a simple train with 20 driving 30 gives 20 ÷ 30 = 0.6666667.
The actual pitch is 1.5 × 20 ÷ 30 = 1.0 mm, or 25.4 TPI. The signed pitch error is 0%, with 0 mm drift per 100 mm and 0 mm drift per inch.
Common questions
Which gear is the driver and which is the driven gear?
In this calculator, A is the spindle-side driver and D is the leadscrew-side driven gear. A larger driver or smaller driven gear makes the leadscrew turn faster, which cuts a coarser thread.
Why does an idler gear not change thread pitch?
A single idler meshes between the driver and driven gear, but its tooth count cancels out of the ratio. It can change rotation direction or let the gears reach each other, but the pitch still depends on the driver and driven gears.
How do compound change gears work?
A compound train has two gear meshes and two gears fixed together on an intermediate shaft. The total ratio is the first mesh multiplied by the second mesh, which gives many more possible ratios from the same inventory.
Why are 63-tooth and 127-tooth gears used for metric and imperial threads?
Metric-imperial threading needs the inch-to-millimeter conversion in the gear ratio. A 127-tooth gear can represent 25.4 exactly because 25.4 equals 127 divided by 5; a 63-tooth gear is a common compact approximation used on smaller lathes.
Can the calculated gears physically fit my lathe?
Not necessarily. The calculation only proves the tooth-count ratio. You still need to check banjo slot travel, gear outside diameters, stud spacing, bore and keyway fit, gear module or diametral pitch, and safe mesh engagement.