What Is a Gear Ratio?
The gear ratio is the ratio of the number of teeth (or diameter) of the output (driven) gear to the number of teeth (or diameter) of the input (driver) gear in a gear train. It tells you how much an output gear is sped up or slowed down — and how torque is gained or lost — relative to the input gear.
Gear Ratio Formula
You can calculate the gear ratio using any of these equivalent approaches:
- Using number of teeth: Gear Ratio = Driven Teeth / Driver Teeth
- Using diameter: Gear Ratio = Driven Diameter / Driver Diameter
- Using radius: Gear Ratio = Driven Radius / Driver Radius
All three methods give the same result because the diameter (and therefore the circumference) of a gear is proportional to its tooth count.
How to Read the Gear Ratio
- Gear Ratio > 1 (Gear Reduction): The output gear rotates slower than the input, but produces more torque. Example: a ratio of 4:1 means the output turns once for every 4 turns of the input.
- Gear Ratio < 1 (Gear Overdrive): The output gear rotates faster than the input, but produces less torque. Example: a ratio of 0.5 means the output turns twice for every 1 turn of the input.
- Gear Ratio = 1 (1:1): Both gears rotate at the same speed and the same torque is transmitted.
Output Speed and Output Torque
If you know the input speed (in RPM) and/or input torque, the calculator will also compute:
- Output Speed (RPM) = Input Speed / Gear Ratio
- Output Torque = Input Torque × Gear Ratio (assuming 100% mechanical efficiency)
Mechanical Advantage
For a simple two-gear system, the mechanical advantage equals the gear ratio. A gear ratio of 4 means you gain 4× torque at the cost of 4× reduction in speed. This trade-off is fundamental to all gear-based machines — from bicycles and car transmissions to industrial machinery and clocks.
Teeth vs. Diameter Input
Both methods are mathematically equivalent. Use number of teeth when you have gear specs from a manufacturer or blueprint. Use diameter when you are measuring physical gears directly. For diameter input, specify whether you are working in millimeters (metric) or inches (imperial).
Real-World Examples
- Bicycle: A chainring with 40 teeth driving a sprocket with 10 teeth gives a ratio of 10/40 = 0.25 (overdrive — the wheel spins 4× faster than your pedaling).
- Car low gear: A ratio of 3.5:1 provides strong acceleration with high torque multiplication.
- Clock gears: Precise gear ratios translate motor rotation into hours, minutes, and seconds.
- Industrial conveyor: A reducer with a 20:1 ratio converts a high-speed motor into slow, powerful belt movement.
Note on Idler Gears
An idler gear placed between two gears does not change the overall gear ratio — it only reverses the direction of rotation of the output gear. The gear ratio is still determined solely by the driver and driven gear teeth counts.
Measurement Systems
- Metric: Diameters in millimeters (mm), torque in Newton-meters (N·m)
- Imperial/US: Diameters in inches (in), torque in foot-pounds-force (ft·lbf)