How is gear ratio calculated?

For a single mesh the ratio is the driven tooth count divided by the driver tooth count. A 40-tooth gear driving a 10-tooth gear gives a ratio of 10 / 40 = 0.25, a speed-up; the reverse gives 4, a reduction.

How do compound gear trains multiply?

In a compound train the stage ratios multiply together. Two stages each reducing by 4 to 1 give an overall reduction of 16 to 1. This tool multiplies the driven-over-driver ratio of every stage to get the total.

What is the relationship between speed and torque?

Speed and torque trade off inversely, ignoring friction. A reduction ratio that slows the output by a factor of N multiplies the torque by the same factor N. Output RPM equals input RPM divided by the ratio, and output torque equals input torque times the ratio.

What does a ratio greater than one mean?

A ratio greater than one is a reduction: the output turns slower than the input and produces more torque. A ratio less than one is an overdrive or speed increase: the output turns faster but with less torque. A ratio of one means equal speed.

Do idler gears change the ratio?

A single idler gear between driver and driven changes the direction of rotation but not the overall ratio, because its tooth count cancels out. This calculator models meshing stages directly, so simply omit pure idlers from the stage list.

Gear Ratio & Speed Calculator

A gear train trades speed for torque, and the exact trade is set entirely by the tooth counts. This calculator multiplies the stages of a simple or compound train to give you the overall ratio, the output speed, and the torque multiplication in one place.

How it works

For a single meshing pair the ratio is the driven gear’s teeth over the driver’s teeth. Compound trains simply multiply the stage ratios:

stage ratio   = driven teeth / driver teeth
overall ratio = stage1 × stage2 × ... × stageN
output RPM    = input RPM / overall ratio
torque factor = overall ratio

A ratio greater than one is a reduction — slower output, more torque. A ratio less than one is an overdrive — faster output, less torque. The fraction is shown in lowest terms by dividing numerator and denominator by their greatest common divisor.

Compound trains and idlers

To get a large reduction in a small space, gears are stacked into stages on shared shafts: two 4:1 stages give 16:1 overall. A lone idler gear inserted between a driver and driven only reverses rotation direction — its tooth count cancels and the ratio is unchanged — so leave pure idlers out of the stage list.

Example and tips

A driver of 12 teeth meshing a driven of 60 teeth gives a 5:1 reduction: at 1800 input RPM the output turns 360 RPM and torque is multiplied by 5. Add a second stage of 15 driving 45 (3:1) and the overall becomes 15:1, dropping the output to 120 RPM with 15 times the torque. Remember the torque gain ignores friction; real trains lose a few percent per mesh.