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Compound Gear Train Calculator

Calculate the overall ratio, output speed, and output torque of a two-stage compound gear train from each stage's driver and driven tooth counts.

Overall gear ratio
12 : 1
Output speed
100 RPM
Output torque
60 N·m
Stage 1 ratio
4 : 1
Stage 2 ratio
3 : 1

How it works

A compound gear train chains two ordinary gear pairs together — the driven gear of stage 1 shares a shaft with the driver gear of stage 2 — so the overall ratio is the product of each stage's own ratio: ratio = driven teeth ÷ driver teeth for each pair, overall ratio = stage 1 ratio × stage 2 ratio. Verified via web search against SMLease Design's and Precision Microdrives' own gear-train reference pages rather than relied on from memory.

Output speed = input speed ÷ overall ratio, and — assuming an ideal, lossless mesh with no friction losses — output torque = input torque × overall ratio. This follows directly from conservation of power: power is proportional to speed × torque, so whatever factor speed is divided by, torque must be multiplied by the same factor to keep power constant. Real gear trains lose a few percent to friction, so actual output torque runs slightly below this ideal figure.

To model a single gear stage instead of two, set stage 2's driver and driven teeth equal (e.g. both 20) — a 1:1 ratio that doesn't change the result, leaving the overall ratio equal to stage 1's alone.

FAQ

Why does output torque go up as output speed goes down?

Power (proportional to speed × torque) has nowhere to go in an ideal gear mesh other than staying constant, since gears don't add or remove energy on their own. A gear train that reduces speed by a factor of 12 must multiply torque by that same factor of 12 to conserve power — that trade-off is the entire reason gear reduction exists, from bicycle low gears to power-tool gearboxes.

Does this account for friction or efficiency losses?

No — this calculates the ideal, 100%-efficient case, which is the standard starting point for gear train design. Real gear trains typically run 85-95% efficient per stage depending on gear type, lubrication, and load, so a real compound train's actual output torque will be somewhat below the ideal figure shown here; multiply by your gearbox's rated efficiency to estimate the real-world value.

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