Compound Gear Train Calculator
Multiply several gear-pair ratios to get a compound gear train’s overall ratio and output speed.
How to use this calculator
- Represent every actual meshing stage as driver:driven. For example, a 12-tooth gear driving a 36-tooth gear is entered as 12:36.
- Separate stages with commas in the order power passes through them. Gears rigidly mounted on the same compound shaft share shaft RPM and should not be treated as an additional mesh by themselves.
- Enter input RPM to calculate final output speed. The total ratio itself depends only on the stage ratios, not the RPM value.
- Check whether any gears in the train are simple idlers. A single idler that only reverses direction does not change the magnitude of the overall ratio.
- Use the result as ideal kinematics. Bearing losses, mesh efficiency, backlash and compliance are separate design considerations.
Formula and assumptions
Total ratio = product of each stage's (driven teeth ÷ driver teeth). Final output RPM = input RPM ÷ total ratio. Direction of rotation depends on the number and arrangement of external or internal gear meshes and is not reported by this ratio-only tool.
GIIRR calculates idealized geometry and kinematics. Friction, slip, compliance, tire deformation, manufacturing tolerances and control-system behavior can move real measurements away from the theoretical result.
Worked example
A 12-tooth gear driving 36 teeth is 3:1. If that 36-tooth gear shares a shaft with a 15-tooth gear that drives 45 teeth, the second stage is also 3:1. The total reduction is 3 × 3 = 9:1, so 3,000 rpm input becomes about 333 rpm output. Merely inserting an idler between two gears would change direction or spacing, not the 9:1 magnitude.
Frequently asked questions
Do idler gears affect the ratio?
A simple idler that only transfers motion between two gears changes rotation direction and spacing but not the ratio magnitude between the original driver and final driven gear.
Can one gear be shared on a compound shaft?
Yes. Gears rigidly attached to the same shaft rotate at the same RPM. Enter each actual meshing pair as a separate stage.
Should I multiply tooth counts or ratios?
Calculate driven ÷ driver for each mesh and multiply those stage ratios. Multiplying all driven teeth and dividing by all driver teeth is mathematically equivalent when the stages are identified correctly.
Does this work for planetary gearsets?
Not directly. Planetary gearsets depend on which member is input, output or held, so they require a different relationship than a simple series of external gear pairs.
Can the overall ratio be below 1?
Yes. If the product of the stages is below 1.00 in this convention, the train acts as an overall overdrive and output RPM is higher than input RPM.
For safety-critical, legal or fitment decisions, verify the result against manufacturer documentation and physical measurements.
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