Productive ToolboxGear Ratio Calculator
Calculate gear ratio instantly using gear teeth count. Determine output speed, torque multiplication, and RPM for automotive, bicycle, robotics, and mechanical systems.
Gear Ratio Calculator
Enter driver and driven gear teeth to instantly calculate gear ratio, output RPM, and torque multiplication. Works for automotive, bicycle, robotics, and industrial systems.
Gear Ratio
Actions
Gear Teeth
Optional InputsUsed for RPM and torque output
Quick Presets
What is a Gear Ratio Calculator?
A Gear Ratio Calculator determines the mechanical relationship between two meshing gears by dividing the number of teeth on the driven gear by the number of teeth on the driver gear. The result tells you how many times the driven gear rotates for every single rotation of the driver gear.
Gear ratios are fundamental in mechanical engineering, automotive design, bicycle drivetrains, robotics, and industrial machinery. A ratio greater than 1 means the driven gear rotates slower but with more torque (torque multiplication). A ratio less than 1 means the driven gear rotates faster with less torque (speed multiplication).
This calculator also computes output RPM, output torque, and supports unit conversion between RPM and rad/s, making it useful for both quick estimates and precise engineering calculations.
How to Use the Gear Ratio Calculator
Step-by-Step Guide
- 1Enter the number of teeth on the driving (input) gear
- 2Enter the number of teeth on the driven (output) gear
- 3Optionally enter input speed in RPM or rad/s
- 4Optionally enter input torque in Nm, lb-ft, or lb-in
- 5View the gear ratio, output speed, and torque instantly
- 6Use presets for bicycle, automotive, or robotics setups
Key Features
- ✓Real-time calculation as you type
- ✓Animated gear visualization diagram
- ✓Simplified ratio (e.g., 40:20 → 2:1)
- ✓Output RPM and rad/s conversion
- ✓Torque multiplication with unit support
- ✓Compare two gear setups side by side
- ✓Presets for bicycle, automotive, robotics
- ✓Calculation history with localStorage
Gear Ratio Formula
| Formula | Expression | Description |
|---|---|---|
| Gear Ratio | GR = Driven Teeth ÷ Driver Teeth | Core ratio formula |
| Output RPM | N_out = N_in ÷ GR | Speed at output shaft |
| Output Torque | T_out = T_in × GR | Torque at output shaft |
| Output rad/s | ω_out = ω_in ÷ GR | Angular velocity output |
Example Calculations
| Driver Teeth | Driven Teeth | Gear Ratio | Effect |
|---|---|---|---|
| 20 | 40 | 2:1 | Torque doubles, speed halves |
| 15 | 45 | 3:1 | Torque triples, speed is 1/3 |
| 50 | 25 | 0.5:1 | Speed doubles, torque halves |
| 30 | 30 | 1:1 | Direct drive, no change |
| 22 | 34 | 1.55:1 | Bicycle low gear — climbing |
| 50 | 11 | 0.22:1 | Bicycle high gear — speed |
Who Uses This Calculator?
Automotive Engineers
Design transmission systems and optimize gear ratios for performance and fuel efficiency.
Bicycle Enthusiasts
Select the right gear combination for climbing, sprinting, or touring.
Robotics Developers
Calculate motor-to-wheel ratios for precise speed and torque control.
Industrial Engineers
Design gearboxes and power transmission systems for machinery.
Students & Teachers
Learn and teach mechanical advantage, torque, and rotational motion concepts.
DIY Mechanics
Troubleshoot and modify gear systems in vehicles, tools, and machines.
Frequently Asked Questions
How is gear ratio calculated?
Gear Ratio = Driven Gear Teeth ÷ Driver Gear Teeth. For example, if the driver has 20 teeth and the driven has 40 teeth, the gear ratio is 40 ÷ 20 = 2:1.
What does a 2:1 gear ratio mean?
A 2:1 ratio means the driven gear completes one full rotation for every two rotations of the driver gear. The output speed is halved, but the output torque is doubled.
What is the difference between gear ratio and speed ratio?
They are inversely related. A gear ratio of 2:1 means the speed ratio is 1:2 — the output shaft rotates at half the input speed.
How do I calculate output RPM?
Output RPM = Input RPM ÷ Gear Ratio. If input is 1000 RPM and gear ratio is 2:1, output RPM = 1000 ÷ 2 = 500 RPM.
Does gear ratio affect torque?
Yes. Output Torque = Input Torque × Gear Ratio. A higher gear ratio increases torque at the output shaft while reducing speed proportionally.
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