Gear Ratio Calculator
Calculate gear ratios and RPM
RPM calculation
Torque output
Speed reduction
Your bike has a 50-tooth front sprocket and an 11-tooth rear. What's the gear ratio? How does that compare to the 34/28 climbing gear? Your robot needs 100 RPM from a 6000 RPM motor—what gear reduction do you need?
Gear ratios determine speed, torque, and mechanical advantage. Whether you're tuning a bicycle, designing a robot, or understanding your car's transmission, gear ratio calculation is fundamental.
What is Gear Ratio?
Gear ratio describes the relationship between two meshing gears or sprockets. It's calculated by dividing the driven gear teeth by the driving gear teeth. This ratio determines how speed and torque are transformed.
The formulas:
Gear Ratio = Driven Teeth / Driving Teeth
Output Speed = Input Speed / Gear Ratio
Output Torque = Input Torque Ă— Gear Ratio
Example: 50T driving, 25T driven
Ratio = 25/50 = 0.5 (speed doubles, torque halves)
Gear ratios trade speed for torque. Higher ratio (greater than 1) means more torque, less speed. Lower ratio (less than 1) means more speed, less torque.
Why People Actually Need This Tool
Bicycles, cars, robots, machinery, watches—any mechanical system with rotational motion likely uses gears to match motor speed to load requirements.
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Bicycle gearing — Calculate and compare gear inches across drivetrain.
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Robotics — Match motor output to wheel or arm requirements.
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Automotive — Understand transmission ratios and final drive.
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3D printing — Calculate extruder gear ratios.
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Industrial design — Size gearboxes for applications.
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RC vehicles — Optimize speed vs acceleration trade-offs.
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Mechanical projects — Any DIY project involving rotation.
How to Use the Gear Ratio Calculator
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Enter driving gear teeth — The gear connected to the power source.
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Enter driven gear teeth — The gear connected to the output.
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Optional: Enter input speed — Motor or input shaft RPM.
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View results — Ratio, output speed, torque multiplier.
| Ratio | Speed Effect | Torque Effect | Example Application |
|---|---|---|---|
| 1:1 | Same speed | Same torque | Direct drive |
| 2:1 | Half speed | Double torque | Reduction for lifting |
| 10:1 | 1/10 speed | 10Ă— torque | Heavy machinery |
| 0.5:1 | Double speed | Half torque | Overdrive, high speed |
| 100:1 | 1/100 speed | 100Ă— torque | Precision positioning |
Multiple gear stages multiply. A 5:1 followed by 4:1 gives 20:1 total reduction.
Real-World Use Cases
1. The Bicycle Comparison
Context: Comparing 50/11 high gear to 34/28 climbing gear.
Problem: How different are these gear ratios?
Solution: 50/11 = 4.55 ratio. 34/28 = 1.21 ratio. High gear is 3.75Ă— harder to pedal but 3.75Ă— faster.
Outcome: Understanding of gear range for cycling.
2. The Robot Arm
Context: Stepper motor gives 200 steps/rev, need precise arm movement.
Problem: Want 0.1° resolution (3600 steps/rev).
Solution: Need 3600/200 = 18:1 reduction. Use gear train or planetary gearbox.
Outcome: Specified reduction for precision requirement.
3. The RC Car Speed
Context: Motor: 25,000 RPM. Want wheel speed of 5000 RPM.
Problem: What gear ratio needed?
Solution: 25000/5000 = 5:1 reduction. Pinion to spur gear setup.
Outcome: Correct gearing for desired wheel speed.
4. The Winch Design
Context: Motor produces 1 Nm torque at 1000 RPM. Need 50 Nm at output.
Problem: Gear reduction for lifting torque?
Solution: 50/1 = 50:1 ratio. Output speed: 1000/50 = 20 RPM.
Outcome: Gearbox specification for winch project.
5. The Car Transmission
Context: Engine at 3000 RPM in 3rd gear (1.4:1). Final drive 3.5:1.
Problem: What's the driveshaft and wheel speed?
Solution: 3000/1.4 = 2143 RPM driveshaft. 2143/3.5 = 612 RPM at wheels.
Outcome: Understanding of transmission multiplication.
6. The 3D Printer Extruder
Context: Direct drive extruder, motor step = 1.8°. Need fine filament control.
Problem: Calculate effective resolution with gear reduction?
Solution: 3:1 geared extruder: effective step = 1.8/3 = 0.6°. 600 steps/rev.
Outcome: Understanding of extruder precision.
7. The Differential
Context: Axle ratio 3.73:1. Tire circumference 78 inches.
Problem: How many driveshaft rotations per mile?
Solution: 63,360"/78" = 812 wheel rotations. Ă—3.73 = 3031 driveshaft rotations per mile.
Outcome: Odometer/speedometer calibration understanding.
Common Mistakes and How to Avoid Them
Driven/Driving vs Driving/Driven changes whether you get reduction or multiplication. Be consistent.
Privacy and Data Handling
This Gear Ratio Calculator operates entirely in your browser.
- No calculations are sent to any server.
- No design data is stored.
- No account required.
- Works completely offline.
Your mechanical designs stay private.
Conclusion
Gear ratios are fundamental to mechanical design. Understanding how speed and torque transform through gear trains enables you to design everything from bicycles to robots to industrial machinery.
This calculator handles the math for simple gear pairs and helps you understand the speed/torque trade-offs in your designs.
Match the motor to the load. Calculate the ratio.