Gear Ratio, Speed & Torque Calculator
Compute mechanical gear ratios, output rotational speed, and torque multipliers.
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How to Use the Gear Ratio Calculator: Speed, RPM & Torque Output
- 1Enter the tooth count of the driving gear (pinion / input gear).
- 2Enter the tooth count of the driven gear (output gear).
- 3Input the input motor rotational speed in RPM.
- 4Input input torque in ft-lbs or N·m to review output speed and mechanical torque advantage.
Formula & How It Works
Gear Transmission Equations
Calculates rotational speed reduction and inverse torque multiplication.
Worked Examples
20-Tooth Pinion Driving a 60-Tooth Gear at 1,750 RPM
Input: Driving: 20 teeth, Driven: 60 teeth, Input: 1,750 RPM, Torque: 80 ft-lb
Explanation: A 3:1 reduction ratio cuts rotational speed by two-thirds while tripling available output shaft torque to 240 ft-lb.
Frequently Asked Questions
What is the difference between gear reduction and overdrive?▼
Gear reduction (ratio > 1) reduces speed to increase torque; overdrive (ratio < 1) increases rotational speed at the expense of output torque.
Do idler gears in between change the overall gear ratio?▼
No. Idler gears placed between driving and driven gears change only the direction of rotation, leaving the overall gear ratio unchanged.
What does a 4.10 differential ratio mean in a truck?▼
The driveshaft must turn 4.10 revolutions for the rear wheels and tires to complete one single full rotation.
What is mechanical efficiency in gear transmissions?▼
Spur gears typically deliver 97% to 99% mechanical efficiency, while worm gears may operate between 50% and 85% efficiency due to sliding friction.
Quick Reference & Conversion Table
| Driving Teeth | Driven Teeth | Gear Ratio | Speed Reduction / Torque Gain |
|---|---|---|---|
| 15 teeth | 45 teeth | 3.00:1 | 1/3 Speed, 3x Torque |
| 12 teeth | 48 teeth | 4.00:1 | 1/4 Speed, 4x Torque |
| 10 teeth | 50 teeth | 5.00:1 | 1/5 Speed, 5x Torque |
| 40 teeth | 20 teeth | 0.50:1 (Overdrive) | 2x Speed, 0.5x Torque |
⚠️ Common Pitfalls to Avoid
- •Inverting driving and driven gears (a driven gear smaller than the driving gear creates an overdrive speed increase with reduced torque).
- •Ignoring friction transmission efficiency losses across multi-stage planetary gear sets.
💡 Practical Real-World Uses
- •Selecting automotive rear differential gear ratios (e.g. 3.73 vs 4.10 for towing acceleration vs highway fuel economy).
- •Sizing electric motor reduction gearboxes for robotics and conveyor belts.
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