Gear Ratio Calculator Formula

Understand the math behind the gear ratio calculator. Each variable explained with a worked example.

Formulas Used

Gear Ratio

gear_ratio = ratio

Output Speed

output_speed = input_speed / ratio

Output Torque (ideal)

output_torque = input_torque * ratio

Variable	Description	Default
`teeth_driver`	Driver Gear Teeth (N1)	20
`teeth_driven`	Driven Gear Teeth (N2)	60
`input_speed`	Input Speed(RPM)	1800
`input_torque`	Input Torque(N-m)	50
`ratio`	Derived value`= teeth_driven / teeth_driver`	calculated

Gears trade speed for torque (or vice versa) while transmitting rotational power.

Gear Ratio = N2 / N1 (driven teeth / driver teeth)

Output Speed = Input Speed / Gear Ratio

Output Torque = Input Torque x Gear Ratio (assuming no losses)

A ratio greater than 1 is a speed reduction (torque multiplication). A ratio less than 1 is a speed increase (torque reduction).

A 20-tooth driver meshing with a 60-tooth driven gear, input 1800 RPM at 50 N-m.

teeth_driver = 20teeth_driven = 60input_speed = 1800input_torque = 50

01Gear ratio = 60 / 20 = 3.0 (speed reduction)
02Output speed = 1800 / 3.0 = 600 RPM
03Output torque = 50 x 3.0 = 150 N-m (ideal)
04Actual torque is slightly less due to mesh efficiency (typically 95-99% per stage).

Ready to run the numbers?