How it works
The gear tooth ratio of one mesh is the driven tooth count divided by the driving
tooth count:
i = z₂ / z₁
A ratio above 1:1 is a reduction — the output turns slower than the
input. For a gear train of several meshes in series, the overall
(compound) ratio is the product of the stage ratios:
i = (z₂/z₁) · (z₄/z₃). The output speed is the input speed divided by the
total ratio, n₂ = n₁ / i.
An idler gear placed between two gears only reverses the direction of rotation — it cancels out of the ratio and does not change it. Each external spur mesh reverses rotation, so the output of a two-stage train turns the same way as the input.
Worked example
A 12-tooth gear driving a 36-tooth gear is 36 ÷ 12 = 3, a
3:1 reduction; at 1,500 RPM in, the output turns 500 RPM. Add a second
stage of a 15-tooth gear driving a 45-tooth gear (another 3:1) and the train becomes
3 × 3 = 9, a 9:1 overall ratio, dropping 1,500 RPM to
≈ 167 RPM. Those are the numbers the calculator returns for these inputs.
Frequently asked questions
- How do you calculate gear tooth ratio?
- Divide the driven (output) tooth count by the driving (input) tooth count for each mesh: ratio = z₂ / z₁. For 12 driving teeth and 36 driven teeth that is 36 ÷ 12 = 3, a 3:1 reduction.
- What is a gear train and how do I find the compound ratio?
- A gear train is two or more meshes in series. Find each stage ratio (driven ÷ driving), then multiply the stages for the overall (compound) ratio: i = i₁ · i₂. A 3:1 stage followed by another 3:1 stage gives 9:1 overall.
- Does an idler gear change the gear ratio?
- No. An idler gear sits between the driving and driven gears and only reverses the direction of rotation — it cancels out of the ratio, so the overall ratio depends only on the first driving and last driven gears.
- What is the difference between a reduction and an overdrive ratio?
- A reduction (ratio > 1, e.g. 3:1) turns the output slower than the input but with proportionally more torque. An overdrive (ratio < 1) turns the output faster with less torque. The total ratio sets the output speed: n_out = n_in ÷ total ratio.
- How is this different from a gear ratio calculator?
- This solves the pure tooth-count ratio of a single or compound gear train and the output speed. If you need the resulting torque and vehicle (road) speed from tire size, use the gear ratio calculator instead.
- Does the gear tooth ratio depend on metric or imperial units?
- No — the tooth ratio is just a count divided by a count, so it is unit-independent and the same in any system. Only the speed result carries a unit (RPM).
Method & assumptions
- External spur meshes — each stage reverses the direction of rotation.
- Idler gears are omitted from the ratio; they affect direction only.
- The tooth ratio is exact and unit-independent; this ignores efficiency (mesh) losses.
Related calculators
- Involute Gear Calculator — Tooth geometry from module/DP and pressure angle, with a tooth-profile render and DXF export.
- Gear Ratio Calculator — Gear ratio with output RPM, torque and vehicle speed from tire size.
- Gear Module Calculator — Module from pitch diameter and teeth, with diametral and circular pitch.
- Planetary Gear Calculator — Epicyclic gear ratio for ring-, sun- or carrier-fixed arrangements.
- Worm Gear Calculator — Worm drive ratio, center distance, lead angle and self-locking check.