⚙️ Gear Ratio Calculator
Calculate gear ratios from gear teeth
Number of teeth on the driving (input) gear
Number of teeth on the driven (output) gear
How to Use This Calculator
Enter Driving Gear Teeth
Input the number of teeth on the driving gear (the gear that provides power/input). This is the gear that's connected to the power source. Count the actual teeth or find this information in gear specifications.
Enter Driven Gear Teeth
Enter the number of teeth on the driven gear (the gear that receives power/output). This is the gear that's connected to the load or output device. Count the teeth or check gear specifications.
Calculate Gear Ratio
Click "Calculate Gear Ratio" to get the gear ratio. A ratio greater than 1:1 means speed reduction and torque increase. A ratio less than 1:1 means speed increase and torque reduction.
Formula
Gear Ratio = Driven Gear Teeth / Driving Gear Teeth
Where:
- Gear Ratio = Output speed / Input speed (or Input torque / Output torque)
- Driven Gear Teeth = Number of teeth on the output/driven gear
- Driving Gear Teeth = Number of teeth on the input/driving gear
Example Calculation:
For a driving gear with 20 teeth and driven gear with 40 teeth:
Gear Ratio = 40 / 20
Gear Ratio = 2:1
This means: 2:1 reduction - output rotates half as fast with double the torque
For 30 driving teeth and 15 driven teeth:
Gear Ratio = 15 / 30 = 0.5:1 or 1:2
This means: 1:2 - output rotates twice as fast with half the torque
Note: Gear ratio determines the relationship between input and output speed and torque. When gear ratio is greater than 1, speed decreases and torque increases. When less than 1, speed increases and torque decreases. This is due to conservation of energy - power (speed × torque) remains constant (ignoring friction losses).
About Gear Ratio Calculator
The Gear Ratio Calculator computes the mechanical advantage and speed relationship between two meshing gears based on their number of teeth. Gear ratio is fundamental to understanding how gears transmit power, change speed, and multiply torque. Whether you're working with automotive transmissions, mechanical systems, robotics, or simple machines, understanding gear ratios is essential for proper design and operation.
When to Use This Calculator
- Gear Selection: Choose appropriate gears for mechanical systems and transmissions
- Speed Calculations: Determine output speed when input speed is known
- Torque Analysis: Calculate torque multiplication or reduction in gear systems
- Mechanical Design: Design gear trains and power transmission systems
- Educational Purposes: Learn about gears, mechanical advantage, and power transmission
Why Use Our Calculator?
- ✅ Simple Calculation: Quick gear ratio from tooth counts
- ✅ Accurate Formula: Uses standard gear ratio calculation
- ✅ Clear Results: Shows ratio and indicates speed/torque relationship
- ✅ Step-by-Step Display: Shows the complete calculation process
- ✅ Free Tool: No registration required, works on all devices
Understanding Gear Ratios
Gear ratio expresses the relationship between the rotational speeds of two meshing gears. It's calculated as the ratio of driven gear teeth to driving gear teeth. A 2:1 gear ratio means the driven gear rotates once for every two rotations of the driving gear, providing 2× torque multiplication but half the speed. Conversely, a 1:2 ratio provides 2× speed but half the torque. This trade-off occurs because power (speed × torque) must remain constant (ignoring losses).
Common Applications
Automotive Transmissions: Gear ratios in manual and automatic transmissions determine vehicle speed and torque at different RPM ranges. Lower gears (higher ratios) provide more torque for acceleration, while higher gears (lower ratios) provide more speed at highway cruising.
Industrial Machinery: Gear systems in manufacturing equipment use various ratios to match motor speed to required output speeds while maintaining adequate torque for operations.
Robotics and Mechatronics: Robots and automated systems use gear ratios to match motor characteristics to load requirements, providing precise control of speed and torque.
Tips for Best Results
- Count gear teeth accurately - even small errors affect ratio calculations
- For compound gear trains (multiple gear pairs), multiply individual ratios
- Remember: higher ratio = lower speed, higher torque; lower ratio = higher speed, lower torque
- Gear ratio can be expressed as X:1 (e.g., 2:1) or as a decimal (e.g., 2.0)
- For reverse rotation, the ratio is negative, but magnitude is the same
Frequently Asked Questions
What does a 2:1 gear ratio mean?
A 2:1 gear ratio means the driven gear rotates once for every two rotations of the driving gear. This provides 2× torque multiplication (output torque is twice input torque) but half the speed (output rotates at half the input speed). It's a speed reduction and torque increase setup, commonly used when you need more force but can accept slower speed.
How do I calculate speed from gear ratio?
Output speed = Input speed / Gear Ratio. For example, if input rotates at 1000 RPM with a 2:1 gear ratio, output speed = 1000 / 2 = 500 RPM. If gear ratio is 0.5:1 (1:2), output speed = 1000 / 0.5 = 2000 RPM. Remember: higher ratio = slower output, lower ratio = faster output.
How does gear ratio affect torque?
Output torque = Input torque × Gear Ratio. For a 2:1 gear ratio, output torque is twice the input torque. For a 0.5:1 ratio, output torque is half the input torque. This is the inverse relationship with speed - as speed decreases, torque increases proportionally, maintaining constant power (ignoring friction losses).
What's the difference between gear ratio and final drive ratio?
Gear ratio typically refers to a single gear pair, while final drive ratio is the overall ratio through multiple gear stages (like transmission gear × differential gear). For example, first gear might be 3:1 and the differential 4:1, giving a final drive ratio of 12:1 when both are engaged. To find final drive, multiply all individual gear ratios together.
Can I use diameter instead of teeth to calculate gear ratio?
Yes, for two meshing gears, gear ratio = Driven gear diameter / Driving gear diameter. This works because the number of teeth is proportional to gear diameter when gears have the same pitch (tooth size). However, using tooth count is more precise since gear diameters may vary slightly due to manufacturing tolerances.