How to Calculate Gear Ratio
Gear ratio (i) defines the relationship between the input and output speed and torque of a gear pair. It is one of the most fundamental calculations in gear system design.
Basic Gear Ratio Formula
For a simple gear pair:
i = z₂ / z₁ = n₁ / n₂
Where z₁ = number of teeth on the driver gear, z₂ = number of teeth on the driven gear, n₁ = input speed (RPM), n₂ = output speed (RPM).
Example Calculation
If a driving spur gear has 20 teeth and the driven gear has 60 teeth:
i = 60 / 20 = 3:1
This means the output shaft rotates at one-third the speed of the input shaft, with three times the torque (minus efficiency losses).
Compound Gear Trains
For compound gear trains (multiple stages), multiply the individual stage ratios:
i_total = i₁ × i₂ × i₃ …
Torque and Speed Relationship
The output torque increases proportionally with gear ratio (minus friction losses): T₂ = T₁ × i × η where η is the gear mesh efficiency (typically 0.97–0.99 for well-lubricated spur gears).