Gear Ratio Basics
A gear ratio describes how much a gear pair changes rotational speed and torque. High ratio = more torque, less speed. Low ratio = less torque, more speed.
Core Formulas
Gear Ratio: GR = T_driven / T_driving
= ω_input / ω_output (speed ratio)
Output Speed: ω_out = ω_in / GR
Output Torque: τ_out = τ_in × GR × η
η = efficiency (typically 0.95-0.98)Worked Example
Drive gear: 20 teeth | Driven gear: 60 teeth
GR = 60/20 = 3:1
Input: 1500 RPM, 50 N·m
Output speed: 1500/3 = 500 RPM
Output torque: 50 × 3 × 0.97 = 145.5 N·mGear Train (Multiple Stages)
Overall ratio = GR1 × GR2 × GR3
3:1 × 4:1 = 12:1 overall
Input 3600 RPM → Output 300 RPM
Torque multiplied 12× (minus losses)Common Applications
- Car 1st gear ~3.8:1 — maximum torque for acceleration
- Car 6th gear ~0.6:1 — overdrive, fuel efficiency
- Bicycle chainring 52T / cassette 11T = 4.7:1
- Wind turbine gearbox: ~100:1 (slow rotor → fast generator)
Calculate gear ratios: Free Gear Ratio Calculator
Gear Ratio Formula
Gear ratio = driven teeth / driver teeth = input RPM / output RPM = output torque / input torque (ignoring losses). Example: a 20-tooth pinion driving a 60-tooth gear has ratio 60/20 = 3:1. The output shaft rotates at 1/3 the input speed but with 3× the torque. Efficiency losses (friction) mean actual output torque = input torque × ratio × efficiency (typically 95–99% per gear mesh for spur/helical gears; lower for worm gears at high ratios).
Applications Across Industries
- Automotive: Gearboxes convert engine speed (600–7,000 RPM) to wheel speed with appropriate torque. First gear has highest ratio (most torque multiplication); 6th or 7th gear is near 1:1 for motorway cruising.
- Industrial: Speed reducers convert high-speed motor output to low-speed high-torque drives for conveyors, mixers, and winches. Ratios of 10:1 to 100:1 are common.
- Bicycles: Derailleur systems provide ratios from ~1.5:1 (low gear, climbing) to ~5:1 (high gear, descending). Chainring and sprocket tooth counts are chosen to give even ratio steps.
- Clocks: Watch gear trains achieve ratios of thousands:1 to reduce the mainspring's energy over 24–48 hours.
Frequently Asked Questions
What is the difference between spur, helical, and bevel gears?
Spur gears have straight teeth parallel to the shaft axis — simple, low cost, moderate noise. Helical gears have angled teeth — quieter and stronger but introduce axial thrust loads requiring thrust bearings. Bevel gears transmit drive between intersecting shafts (at 90° for miter gears). Worm gears can achieve very high ratios (up to 300:1) in a compact package but have lower efficiency (50–90%) due to sliding contact.
How do I achieve a specific output speed from a fixed input?
Target ratio = input RPM / desired output RPM. Choose gear tooth counts to match. If a single stage gives too large a gear (space constraint), use a compound gear train: two stages in series. Compound ratio = ratio₁ × ratio₂. For a 9:1 total from a 3:1 and 3:1 stage: both stages use manageable gear sizes.
What is backlash and why does it matter?
Backlash is the play (clearance) between mating gear teeth, necessary to prevent binding due to thermal expansion and manufacturing tolerances. Standard backlash: 0.05–0.25 mm depending on module. Excessive backlash causes position error in servo drives and CNC machines; insufficient backlash causes overheating and tooth damage. Anti-backlash gears (spring-loaded split gears) minimise positional error in precision applications.