Gear Ratio Calculator
Gear ratio
2:1
Mechanical advantage
2
How it works
Gear ratio is the ratio of the number of teeth on the output gear to the number of teeth on the input (driver) gear: Gear Ratio = N_output / N_input. A gear ratio of 4:1 means the output shaft rotates once for every four input shaft rotations — speed is reduced by 4× and torque is increased by 4×.
**Speed vs. torque trade-off** Increasing gear ratio (reduction): output speed decreases, output torque increases proportionally. A motor producing 10 N·m at 1000 RPM through a 5:1 gearbox outputs 50 N·m at 200 RPM (minus friction losses). This is why vehicle transmissions use lower gears to multiply torque for acceleration and higher gears for efficient highway cruising.
**Compound gear trains** Multiple gear pairs in series multiply: total ratio = ratio₁ × ratio₂ × ratio₃... A two-stage gearbox with 3:1 and 4:1 stages produces a total ratio of 12:1. Compound systems achieve high ratios in compact packaging. Planetary gear sets achieve very high ratios in small packages.
**Gear efficiency** Each gear mesh loses 1–3% to friction. A 4-stage compound gearbox (each at 98% efficiency) has overall efficiency = 0.98⁴ = 92.2%. Worm gear drives (high reduction in single stage) have low efficiency (30–90% depending on lead angle) — unsuitable for back-driving (the output cannot back-drive the input).
**Pitch circle and tooth geometry** The pitch circle is the effective radius at which gears engage. For correct meshing, mating gears must have the same module (SI: M = D/N, where D is pitch diameter, N is tooth count) or diametral pitch (US: P = N/D). Mismatched tooth profiles prevent proper engagement.
Frequently Asked Questions
- For a two-gear system: speed ratio = N_driver/N_driven (inverse of tooth count ratio). Torque ratio = N_driven/N_driver (inverse of speed ratio). Example: 20-tooth driver at 1000 RPM → 80-tooth driven: output speed = 1000 × 20/80 = 250 RPM; torque multiplied by 80/20 = 4×. For a compound gear train: total speed ratio = product of all individual ratios. If gear 1→2 is 3:1 and gear 3→4 is 4:1 (with gears 2 and 3 on the same shaft): total ratio = 12:1. Torque at output = input torque × 12 × overall efficiency.
- Backlash is the play between meshing gear teeth — the gap between the trailing face of one tooth and the leading face of the mating tooth. It's necessary to prevent binding from thermal expansion and manufacturing tolerances. Backlash causes positioning error when motion direction reverses — CNC machines use anti-backlash mechanisms (spring-loaded split gears, preloaded ball screws) to eliminate this. For precision positioning: use minimal-backlash gears (ground teeth, tight tolerances). For power transmission where direction doesn't reverse frequently (conveyor drives, pumps): standard backlash is acceptable.
- Worm gears: very high reduction in a single stage (10:1 to 100:1+), right-angle output, compact, self-locking (input can drive output, but output cannot back-drive input in many designs). Low efficiency (30–90% depending on lead angle). Use for: lifts, elevators, conveyor drives, instrument drives where self-locking is needed. Spur/helical gears: higher efficiency (96–99% per stage), but each stage gives modest ratio (3:1 to 10:1). Multiple stages for high ratios. Use for: high-efficiency power transmission (automotive transmissions, industrial gearboxes, robotics).
- Gear ratio = (Motor RPM at desired wheel RPM) = Motor_RPM / (Vehicle_speed / Wheel_circumference × 60). Example: motor at 3000 RPM, desired 50 km/h, wheel diameter 0.5 m (circumference = 1.57 m): Wheel RPM = 50,000 m/hr / (1.57 m × 60 min/hr) = 531 RPM. Gear ratio = 3000/531 = 5.65:1. Also check torque: required wheel torque = (Drive force × wheel radius). Required motor torque = wheel torque / gear ratio. Choose a motor with sufficient torque at the operating RPM — motor torque curves show how torque varies with speed.