Gears are mechanical advantage in rotary form. A gear reducer trades input speed for output torque. Double the ratio and you roughly double the torque while halving the speed. Every conveyor drive, mixer gearbox, hoist, and machine tool spindle depends on getting this tradeoff right, and the losses through the gear train determine how much motor power actually reaches the load.
This guide covers the fundamental ratio and torque relationships, the characteristics of common gear types, efficiency losses you need to account for, and how compound gear trains multiply ratios without requiring enormous gears.
Ratio, Speed, and Torque Relationships
Gear ratio equals the number of teeth on the driven gear divided by the number of teeth on the driving gear. A 60-tooth gear driven by a 20-tooth pinion gives a 3:1 ratio. Output speed equals input speed divided by the ratio, and output torque equals input torque multiplied by the ratio (before efficiency losses). A 1,750 RPM motor through a 3:1 reducer produces 583 RPM at roughly 3 times the motor torque.
Power (HP or kW) stays constant through an ideal gear train. You cannot create energy with gears. In practice, friction consumes 1–15 % per stage depending on gear type. The torque formula including efficiency is: Output Torque = Input Torque × Ratio × Efficiency. Always work with power at the motor and torque at the output shaft, accounting for losses along the way.
Gear Ratio & Torque Calculator
Calculate compound gear train ratios, output speed, torque multiplication, and power loss.
Gear Types and Their Characteristics
Spur gears are the simplest: straight-cut teeth on parallel shafts. They are inexpensive, easy to manufacture, and 94–98 % efficient per mesh. The downside is noise at high speeds because teeth engage suddenly along their full face width. Use them for low-speed, high-load applications like conveyors and hoists.
Helical gears have angled teeth that engage gradually, running quieter and smoother than spur gears. They handle higher speeds and loads but generate axial thrust that requires thrust bearings. Worm gears provide high ratios (5:1 to 100:1) in a single stage and are inherently self-locking at ratios above about 40:1, making them useful for hoists. However, efficiency is only 50–90 % due to sliding contact. Planetary (epicyclic) gear sets are compact, coaxial, and handle very high torque density. They are common in slewing drives, winches, and servo gearboxes.
Compound Gear Trains
When you need a ratio higher than about 6:1 with spur or helical gears, a single pair becomes impractical because the driven gear gets too large. Compound trains stack two or more gear pairs in series. The overall ratio is the product of the individual stage ratios. Two 4:1 stages in series give 16:1 overall. Three 3:1 stages give 27:1.
Each stage multiplies the ratio but also multiplies the efficiency loss. A two-stage helical reducer at 97 % per stage delivers 94 % overall. A three-stage worm at 70 % per stage delivers only 34 % overall. Two-thirds of your motor power becomes heat. This is why multi-stage worm reducers are rare; the industry uses worm-helical combinations or planetary sets for high ratios instead.
Gear Ratio & Torque Calculator
Calculate compound gear train ratios, output speed, torque multiplication, and power loss.
Service Factors and Selection
Gearbox catalogs rate output torque for a nominal service life (usually 20,000–40,000 hours for industrial reducers). Apply a service factor to account for shock loading, duty cycle, and application severity. Uniform loads like fans and pumps use a factor of 1.0–1.25. Moderate shock loads like conveyors and mixers use 1.25–1.75. Heavy shock like crushers and stamping presses use 1.75–2.5 or higher.
Required gearbox rating = output torque × service factor. Under-sizing a gearbox is the most common cause of premature gear failure in the field. When in doubt, go one frame size up. The cost difference is small compared to a gearbox replacement and the associated downtime.