Basic Guide to Gear Ratio Calculation

Gear ratio determines the speed and torque relationship between two meshing gears. It’s crucial in designing gear systems for vehicles, machinery, and robotics.

1. What is Gear Ratio?

• Definition: The ratio of the number of teeth (or rotational speed) between two gears.

• Purpose:

  • Increase torque (by reducing speed).

  • Increase speed (by reducing torque).

  • Change direction of rotation.

Formula:

Gear Ratio=Number of Teeth on Driven GearNumber of Teeth on Driving Gear=RPM of Driving GearRPM of Driven GearGear Ratio=Number of Teeth on Driving GearNumber of Teeth on Driven Gear​=RPM of Driven GearRPM of Driving Gear​

2. Simple Gear Pair Calculation

Example:

• Driving Gear (Pinion): 20 teeth

• Driven Gear: 40 teeth

Gear Ratio=4020=2:1Gear Ratio=2040​=2:1

Interpretation:

• The driven gear rotates half as fast but with double the torque.

• If the driving gear spins at 100 RPM, the driven gear spins at 50 RPM.

3. Compound Gears (Multiple Gears)

For systems with multiple gears, calculate the total gear ratio by multiplying individual ratios.

Example:

• Gear 1 (Driver): 10 teeth → Gear 2: 30 teeth

• Gear 2 is attached to Gear 3: 20 teeth → Gear 4 (Driven): 50 teeth

Step 1: First pair (Gear 1 & Gear 2)

Ratio1=3010=3:1Ratio1​=1030​=3:1

Step 2: Second pair (Gear 3 & Gear 4)

Ratio2=5020=2.5:1Ratio2​=2050​=2.5:1

Total Gear Ratio:

$$3\times 2.5=7.5:1$$

Result:

• Driven gear (Gear 4) rotates 7.5 times slower than the driver (Gear 1).

• Torque is 7.5 times higher.

4. Gear Ratio vs. Speed & Torque

5. Practical Applications

A. Automotive Transmissions

• Low gear (e.g., 3:1) → More torque for climbing hills.

• High gear (e.g., 0.8:1) → Higher speed, less torque for cruising.

B. Bicycle Gearing

• Small front gear + large rear gear = Easy pedaling (high torque).

• Large front gear + small rear gear = Faster speed (low torque).

C. Industrial Machinery

• Conveyors, cranes, and robots use gear ratios to control speed and power.

6. Common Mistakes to Avoid

❌ Ignoring Efficiency Loss (real-world gears lose ~5-10% energy).
❌ Mismatching Gear Sizes (leads to excessive wear).
❌ Overlooking Backlash (play between gears affects precision).

7. Quick Reference Formulas

Gear Ratio=TeethDrivenTeethDriver=RPMDriverRPMDrivenGear Ratio=TeethDriver​TeethDriven​​=RPMDriven​RPMDriver​​$$\text{Output Torque}=\text{Input Torque}\times \text{Gear Ratio}\times \text{Efficiency}$$

Summary

• Gear ratio = Teeth (Driven) / Teeth (Driver).

• Higher ratio = More torque, less speed.

• Lower ratio = More speed, less torque.