Calculator
Engineering
MathGear Ratio Calculator
Free online gear ratio calculator to calculate speed ratios, RPM, torque multiplication, and gear teeth for mechanical design. Essential tool for automotive, robotics, and mechanical engineering.
What is Gear Ratio?
Gear ratio is the relationship between the number of teeth (or diameter) of two meshing gears. It determines how rotational speed and torque are transferred from an input gear to an output gear. A gear ratio of 3:1 means the input gear rotates 3 times for every 1 rotation of the output gear. Gear ratios are fundamental in mechanical design, used to reduce speed and increase torque (reduction gearing) or increase speed and reduce torque (overdrive gearing). Understanding gear ratios is essential for automotive transmissions, robotics, industrial machinery, and any mechanical power transmission system.
How to Use the Gear Ratio Calculator
- Enter the number of teeth on the input (driver) gear
- Enter the number of teeth on the output (driven) gear
- Optionally enter the input speed (RPM) to calculate output speed
- Optionally enter input torque to calculate output torque and mechanical advantage
- Click Calculate to see gear ratio, speed ratio, and torque multiplication
- For multi-stage systems, calculate each stage separately and multiply ratios
Gear Ratio Formulas
1. Gear Ratio = Driven Teeth / Driver Teeth = Driver RPM / Driven RPM
2. Output RPM = Input RPM / Gear Ratio
3. Output Torque = Input Torque × Gear Ratio × Efficiency
4. Mechanical Advantage = Output Torque / Input Torque ≈ Gear Ratio
Gear Ratio Examples
Reduction (3:1): 30-tooth driver, 90-tooth driven → Output 1/3 speed, 3× torque
Overdrive (1:3): 90-tooth driver, 30-tooth driven → Output 3× speed, 1/3 torque
Direct drive (1:1): Equal teeth → Same speed, same torque
Multi-stage: (2:1) × (3:1) = 6:1 overall ratio
Types of Gears
Spur Gears: Straight teeth, parallel shafts, most common and efficient
Helical Gears: Angled teeth, smoother/quieter than spur, parallel or crossed shafts
Bevel Gears: Conical shape, intersecting shafts at angles (typically 90°)
Worm Gears: High reduction ratios (10:1 to 100:1), self-locking, 90° shafts
Planetary Gears: Compact, high torque, multiple gear ratios in small space
Applications of Gear Systems
- Automotive: Transmissions, differentials, starter motors, window regulators
- Robotics: Robot joints, drive systems, precision positioning
- Industrial: Conveyors, mixers, pumps, machine tools
- Power tools: Drills, saws, impact wrenches, angle grinders
- Clocks & watches: Precise time keeping, gear train design
- Bicycles: Multi-speed systems, internal hub gears
- Wind turbines: Speed increase from rotor to generator
- Elevators: Traction systems, safety mechanisms
Tips for Gear Design & Selection
- Higher gear ratios provide more torque but reduce speed
- Gear efficiency typically 95-99% per stage (90% for worm gears)
- Use multiple stages for very high ratios (better than single large ratio)
- Ensure proper gear mesh - too tight causes binding, too loose causes backlash
- Consider gear module/pitch for strength and smooth operation
- Lubrication is critical for gear life and efficiency
- Calculate for peak loads, not just average - include safety factor
Gear Design Considerations
When selecting or designing gear systems, consider: (1) Required speed ratio and torque capacity, (2) Space constraints and mounting configuration, (3) Gear type based on shaft arrangement (parallel, intersecting, crossed), (4) Material selection (steel, bronze, plastic) based on load and environment, (5) Noise and vibration requirements, (6) Efficiency and power loss through gear train, (7) Backlash tolerance for precision applications, (8) Lubrication method and maintenance accessibility. Remember that each gear stage reduces efficiency slightly, so minimize the number of stages when possible while achieving the desired ratio.