Calculation
iges = i1·i2·i3
For gear stages connected in series, the individual ratios multiply to give the overall ratio.
Dubbel Konstruktionselemente G 8.1.2, Gl. (1): Gesamtübersetzung i = i1·i2·…
Overall ratio of a multi-stage gear train
For gear stages connected in series, the individual ratios multiply to give the overall ratio.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Overall ratio iges — Ratio of input to output speed across all stages.
- Stage 1 ratio i1 — Ratio of the first gear stage.
- Stage 2 ratio i2 — Ratio of the second gear stage.
- Stage 3 ratio i3 — Ratio of an optional third stage; set to 1 if only two stages are present.
Example
i1=4, i2=3 and i3=2 give iges=4·3·2=24.
Assumptions and limits
Lossless, rigid stages with no intermediate branching (no planetary stages); the efficiency of each stage is not accounted for.
Understand Overall ratio of a multi-stage gear train
This calculator determines the overall ratio of a gear train made up of several stages, complementing the existing single-pair gear-ratio calculator with the system-level view.
What does this quantity describe?
For gear stages connected in series, the individual ratios multiply to give the overall ratio: iges=i1·i2·i3.
Formula and variables
iges = i1·i2·i3
iges = i1·i2·i3
| Symbol / input | Meaning |
|---|---|
| Overall ratio iges | Ratio of input to output speed across all stages. |
| Stage 1 ratio i1 | Ratio of the first gear stage. |
| Stage 2 ratio i2 | Ratio of the second gear stage. |
| Stage 3 ratio i3 | Ratio of an optional third stage; set to 1 if only two stages are present. |
Choose the inputs correctly
i1 and i2 are the ratios of the first two stages, i3 that of an optional third stage.
How to use the calculator
Determine each stage's ratio from tooth-count ratio or pulley diameters; set i3=1 if only two stages are present.
Worked example
i1=4, i2=3 and i3=2 give iges=4·3·2=24.
Understand the result and units
Overall ratio grows multiplicatively; even a small additional stage can substantially change the overall ratio.
i1, i2, i3 and iges are dimensionless gear ratios.
Typical applications
Sizing multi-stage gear, belt or mixed drive trains, e.g. in countershaft gearboxes or geared motors.
Assumptions, limits and common mistakes
Lossless, rigid stages with no intermediate branching (no planetary stages); the efficiency of each stage is not accounted for and further reduces actually transmitted power.
Common mistake: Do not set i3 to 0 if only two stages are present; since ratios multiply, this would incorrectly zero the overall ratio. The correct neutral value is 1.
Frequently asked questions
What is “Overall ratio of a multi-stage gear train” used for?
Sizing multi-stage gear, belt or mixed drive trains, e.g. in countershaft gearboxes or geared motors.
Where do the input values come from?
i1 and i2 are the ratios of the first two stages, i3 that of an optional third stage.
What does the result not cover?
Lossless, rigid stages with no intermediate branching (no planetary stages); the efficiency of each stage is not accounted for and further reduces actually transmitted power.