Gears trade input speed for output torque, but the simple ratio math is only the first screen. A gear reducer also has efficiency loss, thermal limits, service factor, tooth stress, lubrication, shaft, bearing, coupling, guard, and machine-safety requirements that cannot be proven from tooth counts alone.
This guide covers the basic ratio and torque relationships, common gear-type considerations, and compound-train arithmetic. Treat efficiency ranges and service-factor examples as source-gap context until verified against current manufacturer data, AGMA/ISO sources, the machine layout, and qualified review.
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 common in low-speed and moderate-speed drives, but noise, quality, material, lubrication, service factor, and tooth rating still control final suitability. Helical gears engage more gradually and can run smoother, but they add axial thrust that must be handled by the bearing and housing design.
Worm gears can provide high ratios in one stage, but efficiency depends heavily on lead angle, sliding velocity, lubricant, temperature, and manufacturer geometry. Planetary gear sets can be compact and coaxial, but ratio path, carrier/sun/ring arrangement, bearing loads, lubrication, and rating method are configuration-specific. The local ToolGrit screen labels these gear types for arithmetic only; it does not validate the arrangement.
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.
Service Factors and Selection
Gearbox catalogs rate output torque against a specific product family, speed, duty, life basis, lubricant, mounting, ambient condition, and rating method. Service factor, shock loading, start frequency, reversals, overload, thermal capacity, and duty cycle all need source validation for the actual application.
Required gearbox rating is often screened as output torque multiplied by a service factor, but the factor is not universal. Use the current manufacturer catalog, AGMA/ISO rating method, owner specification, and qualified review before selecting a reducer frame size or approving a replacement.