A compound train uses at least one intermediate shaft carrying two gears fixed together: one receives motion from the previous stage and the other drives the next. Those two gears share shaft speed but do not mesh with each other. The total ratio is the product of the actual mesh ratios, not the ratio of whichever two gears happen to be drawn at the ends.
Multiply each stage as a fraction
For a first stage 12→36 and second stage 15→45, write (36/12) × (45/15). Multiplying numerators and denominators gives 1,620/180, which reduces exactly to 9. Do not round 36/12 or 45/15 before combining them. With less convenient tooth counts, keeping one reduced integer fraction prevents small decimal errors from accumulating across stages.
Apply input speed only after the total ratio
The reciprocal speed factor of a 9:1 train is 1/9. Multiplying an exact 1,800 RPM input by 1/9 gives 200 RPM. This is the ideal kinematic speed: it does not include elastic slip, backlash events, losses, deformation, or a motor speed change under load. GearTrain leaves RPM optional so ratio work does not imply a performance forecast.
Count external meshes for direction
Each external mesh reverses rotation. One stage therefore produces the opposite direction; two stages produce the same direction; three are opposite again. The two gears fixed to one intermediate shaft do not create an extra reversal. An idler on its own shaft does add a mesh even though its tooth count cancels from the endpoint speed ratio, so represent only the stage structure that the calculator actually supports.