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.

What is the Lathe Thread-Cutting Gear Train Calculator?

For a lathe without a quick-change gearbox, calculate the change-gear combination needed to cut a target thread TPI from the leadscrew TPI. The tool searches a standard gear set for the exact or closest single-pair or compound-pair ratio. It runs free in your browser on Gera Tools, with nothing uploaded.

Lathe Thread-Cutting Gear Train Calculator

Name: Lathe Thread-Cutting Gear Train Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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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.

Single pair vs compound train

A single-pair setup is the simplest arrangement: one driver on the spindle stud and one driven on the leadscrew, often with an idler in between to bridge the gap. The ratio is just driver ÷ driven.

A compound train stacks two pairs. For example, if you need a ratio of 2/5, a single pair requires a 40-tooth driver and a 100-tooth driven — if a 100-tooth gear is not in your set, you might instead stack 20/50 × 40/40, which multiplies to 2/5 using teeth you have. The tool finds these combinations automatically when no single pair matches.

Worked example

Say your lathe has an 8 TPI leadscrew and you want to cut a 20 TPI thread:

Required ratio = 8 ÷ 20 = 0.4 = 2/5
Single pair: a 40-tooth driver with a 100-tooth driven would work if available
Compound option: 20/40 × 40/50 = 0.5 × 0.8 = 0.4 — same ratio using common gears

Now suppose you want to cut an M1.25 metric thread on the same 8 TPI leadscrew. M1.25 pitch is 1.25 mm. Converting: 1 inch = 25.4 mm, so 25.4 ÷ 1.25 = 20.32 TPI — not a clean integer. The exact ratio requires the 127-tooth gear (because 127 = 5 × 25.4), which allows exact inch-to-metric translation. The tool searches for combinations that include 127 when needed.

Setting up the gears

Compute the ratio from the tool output.
Mount the driver on the spindle stud (gear nearest the headstock).
Mount the driven on the leadscrew end.
Add an idler only to bridge centre-to-centre distance or to reverse thread hand — it does not change the ratio.
Set backlash so the gears mesh smoothly without binding.
Cut a short test thread (5–10 mm) and check it with a thread gauge or a mating nut before machining the full length.

Any percentage error in the ratio accumulates along the thread. For a true thread the ratio must be exact; small approximations are only acceptable for decorative or self-mating threads where no mating part is involved.