Gear Ratio Calculator - Single & Compound Gear Trains

How to Calculate Gear Ratio

Gear ratio compares the number of teeth on the driven gear to the number of teeth on the driving gear: Ratio = Driven Teeth ÷ Driving Teeth. A ratio greater than 1 means the driven gear turns slower than the driving gear but with more torque (a speed reduction); a ratio less than 1 means it spins faster with less torque. For a gear train with multiple pairs in sequence, the overall compound ratio is the product of each stage's individual ratio.

Example

A driving gear with 12 teeth meshed with a driven gear with 36 teeth gives a ratio of 36 ÷ 12 = 3, often written 3:1 — the driven gear turns once for every 3 turns of the driving gear. Add a second stage (say, 10 teeth driving 40 teeth, a 4:1 ratio) and the compound ratio becomes 3 × 4 = 12:1 overall.

Common Use Cases

FAQs

Which gear is the "driving" gear?

The driving gear is the one connected to the power source (like a motor shaft or pedal crank), and the driven gear is the one that receives motion from it. Torque and speed both scale with the ratio between them, in opposite directions.

How does compound ratio work for multiple gear stages?

Each pair of meshing gears forms one stage. In a gear train, the driven gear of one stage is typically connected to the driving gear of the next stage, so the overall reduction is the product of every individual stage ratio, not their sum.

Does gear ratio depend on gear diameter instead of teeth count?

Teeth count and diameter are proportional for gears of the same tooth pitch (tooth size), so using teeth counts gives the same ratio as using diameters, and is usually easier to count accurately.