How to use it
- Choose the number of stages: 1 for a simple pair, 2 or 3 for a compound train.
- For each stage enter the teeth on the driving gear (input side) and the driven gear.
- Enter the input speed in rpm, the input torque in N·m and the overall efficiency (100 % ignores losses).
- Read the ratio, output speed, output torque and direction.
Formulas
- Stage ratio: i = driven teeth ÷ driving teeth.
- Train ratio: i = i₁ × i₂ × i₃.
- Output speed: n_out = n_in ÷ i.
- Output torque: T_out = T_in × i × η.
- Direction: each external gear mesh reverses rotation, so an odd number of stages turns the opposite way.
A ratio above 1 is a reduction; below 1 is an overdrive.
Worked example
A 12-tooth gear on a 1,500 rpm motor drives a 36-tooth gear: i = 36 ÷ 12 = 3, output 500 rpm, and 10 N·m in becomes 30 N·m, turning the opposite way.
Two stages, 10→40 and 15→45, with 90 % efficiency: i = 4 × 3 = 12, so 1,200 rpm becomes 100 rpm, and 5 N·m becomes 5 × 12 × 0.9 = 54 N·m, in the same direction as the input.
Tips
- Internal (ring) gears do not reverse direction; adjust the direction result for planetary sets and ring gears.
- Chains and toothed belts follow the same tooth ratio but do not reverse direction.
- Efficiency per mesh of spur gears is high; worm gears lose much more. Multiply stage efficiencies to get the overall figure.