| Stage | Driver T | Driven T | Ratio | Direction flip |
|---|
A gear mesh trades speed for torque, not power — ignoring friction, power in ≈ power out (P = τω), so whatever ratio slows the output speed down by, it multiplies torque up by the same factor. Each stage's ratio is simply driven teeth ÷ driver teeth; chain multiple stages together and the overall ratio is just the product of each stage's ratio. Every external mesh also flips rotation direction, which is exactly why an even number of stages ends up spinning the same way as the input, and an odd number reverses it.
A motor at 1750 RPM and 10 N·m feeds two 3:1 reduction stages (20→60 teeth, then 15→45 teeth) for a 9:1 overall ratio: output speed drops to 194 RPM while ideal torque rises to 90 N·m — two direction flips mean the output shaft turns the same way as the input.
Because the driven gear has more teeth meshing over the same distance, each tooth on the smaller driver has to push harder to keep the tangential mesh force consistent — more teeth sharing that force means more total leverage, which shows up as torque.
A gear inserted between driver and driven purely to reverse direction or bridge a gap — its own tooth count cancels out of the ratio math entirely (it appears once as a "driven" and once as a "driver"), but it does add one more direction flip.
Practical tooth counts and centre distances get unwieldy fast — a single 50:1 spur stage needs a driven gear 50× the driver's diameter. Splitting the same overall ratio across two or three stages keeps every gear a sane, manufacturable size.
Sliding friction between meshing teeth, plus some churning loss from lubricant, bleeds off a few percent of power at every mesh — well-cut spur and helical gears typically manage 96–99% per stage; worm gear meshes can be far lower, sometimes 50–90%.