Gear Ratio Calculator | The Mech Elite

The Gear Ratio Calculator calculates the basic ratio, output speed and ideal output torque for a simple pair of gears. It is intended for preliminary mechanical design and does not include gear losses, tooth strength or detailed gearbox dynamics.

Gear ratio formula

For a driver gear with Z₁ teeth and a driven gear with Z₂ teeth:

Ratio = Z₂ / Z₁

The ideal driven speed is approximately n₂ = n₁ × Z₁/Z₂. Ignoring losses, ideal output torque is approximately T₂ = T₁ × Z₂/Z₁.

Worked example

Consider a 20-tooth driver at 1500 rpm driving a 60-tooth gear. The ratio is 3:1, so the driven speed is about 500 rpm. If input torque is 10 N·m, the ideal output torque is 30 N·m. Real output torque will be lower because of gear-mesh, bearing, seal and other losses.

What the calculator does not check

Gear ratio alone does not prove that a gear pair is safe. Final design should check transmitted power, tooth bending strength, contact stress, module or diametral pitch, face width, material, lubrication, backlash, shaft loads, bearing life, alignment and manufacturing tolerances.

Why gear ratio matters in machine design

A reduction ratio trades rotational speed for torque. This is useful when a motor operates efficiently at a higher speed but the machine requires lower speed and higher torque. The ratio also changes gear tooth loads and shaft reactions, so it must be considered together with shaft and bearing design.

Common mistakes

Using ideal torque as if it were actual output torque.
Ignoring gearbox efficiency.
Checking ratio but not tooth strength.
Forgetting that gear forces create radial and sometimes axial shaft loads.
Choosing a ratio without checking motor operating speed and machine duty cycle.

Engineering note

Use this calculator for preliminary sizing. For a production gearbox, verify the design against the relevant gear standard, manufacturer data, duty cycle, lubrication requirements and safety factors.