How do I work out the change-gear ratio for a thread?

The carriage must advance one thread pitch per spindle revolution. That makes the required ratio of driver to driven gears equal to the leadscrew TPI divided by the target TPI. For an 8 TPI leadscrew cutting a 20 TPI thread, the ratio is 8 over 20, or 0.4.

Which gear is the driver and which is the driven?

The driver gear is on the spindle or stud side, driven by the chuck rotation. The driven gear is on the leadscrew side. Any idler gears in between simply bridge the centre distance and reverse direction; they do not change the overall ratio, only the pair on the ends matters.

When do I need a compound gear train?

A single pair can only reach ratios available from two gears in your set. Some threads need a ratio no single pair provides, so you stack two pairs on a shared stud, multiplying their ratios. The tool falls back to a compound train and shows it when no single pair gives an exact match.

Can I cut metric threads on an imperial leadscrew?

Yes, but it requires the 127-tooth translation gear because 127 is half of 254, and there are 25.4 millimetres per inch. The tool includes 127 in its standard set, so when a metric-equivalent ratio needs it the search can find a combination using that gear.

How close does the ratio need to be?

For a true thread it must be exact, since any error accumulates along the length and the thread will not fit a mating part. The tool marks exact matches clearly and shows the percent error for approximations, which are only acceptable for non-critical work like decorative or self-mating threads.

Lathe Thread-Cutting Gear Train Calculator

Older lathes and many small bench lathes lack a quick-change gearbox, so to cut a given thread you physically fit a set of change gears between the spindle and the leadscrew. Picking the right gears is a ratio problem, and this calculator solves it against a standard gear set so you can find the combination on your bench.

How it works

The governing rule is simple: the carriage must move exactly one thread pitch for every turn of the spindle. With a leadscrew of a known TPI, that fixes the gear ratio.

advance per rev = (driver / driven) x (1 / leadscrew_TPI)
must equal       = 1 / target_TPI
=> driver / driven = leadscrew_TPI / target_TPI

So the required ratio of the driver gear to the driven gear is just the leadscrew TPI divided by the target TPI. The tool computes that number, then searches a standard set of change gears for a single pair that matches it. When no single pair is exact, it looks for a compound train, two gear pairs on one stud whose ratios multiply to the target.

Tips and notes

The driver gear goes on the spindle or stud side and the driven on the leadscrew side. Idler gears between them only bridge the distance and set rotation direction, so they never enter the ratio. If the calculated thread runs the wrong hand, add or remove an idler.

For metric threads cut on an imperial leadscrew, the 127-tooth gear is essential because it translates inches to millimetres exactly, and the search includes it. Always cut a short test thread and check it with a thread gauge or a known nut before committing to the full length, since an approximate ratio drifts noticeably over distance.