Gear Train Calculator
A train of two, three or four stages: the ratio it gives, what friction takes back, and how much play ends up at the output.
Inputs
Each stage is one pair of meshing gears.
Stage 1
The gear the motor side turns.
The gear it turns.
Blank until you measure it. Hang a known weight on the output, find the smallest motor torque that just lifts it, then divide the torque the ratio says you need by the torque it took.
Blank until you measure it. Hold the input still, rock this stage's output shaft back and forth by hand, and read the angle it moves through before the gears bite.
Stage 2
The gear the motor side turns.
The gear it turns.
Blank until you measure it. Hang a known weight on the output, find the smallest motor torque that just lifts it, then divide the torque the ratio says you need by the torque it took.
Blank until you measure it. Hold the input still, rock this stage's output shaft back and forth by hand, and read the angle it moves through before the gears bite.
Stage 3
The gear the motor side turns.
The gear it turns.
Blank until you measure it. Hang a known weight on the output, find the smallest motor torque that just lifts it, then divide the torque the ratio says you need by the torque it took.
Blank until you measure it. Hold the input still, rock this stage's output shaft back and forth by hand, and read the angle it moves through before the gears bite.
Stage 4
The gear the motor side turns.
The gear it turns.
Blank until you measure it. Hang a known weight on the output, find the smallest motor torque that just lifts it, then divide the torque the ratio says you need by the torque it took.
Blank until you measure it. Hold the input still, rock this stage's output shaft back and forth by hand, and read the angle it moves through before the gears bite.
Used for the speed and torque at the output.
Their stall torques add up.
Used to turn the play at the output into a distance at the end of it.
Results
Total reduction
—
Free speed at the output
—rpm
Torque the ratio promises
—N·m
Torque after friction
—N·m
What the train gives back
—%
Play at the output
—°
Play at the end of the arm
—in
Turn the motor
Every gear in your train, sized by its tooth count, with a line on each so you can see it turn. The motor drives the small gear on the left. Each pair meshes, so each stage turns the next shaft the opposite way, and slower by that stage's ratio. Gears sharing a shaft turn together. Turn the motor a few times round and watch how little the last shaft moves.
Show the numbers behind this chart
How this is calculated
A train's reduction is its stages multiplied together, and so is its efficiency. That second one is what surprises teams: four stages that each give back nine tenths do not give back nine tenths.
total reduction = (driven ÷ driving) × … for each stage total efficiency = e₁ × e₂ × … for each stage torque out = motor torque × reduction × total efficiencyWith your numbers
Why the last stage owns the play
Every mesh has a little play in it: the gears have to be able to turn, so the teeth cannot touch on both sides at once. Hold the motor still and the output can be rocked back and forth through the sum of all that play, but not in equal shares.
Play at a stage is divided by whatever reduction comes after it, because that reduction divides every angle passing through, including a wasted one. So the play in the last mesh arrives at the output in full, while the play in the first mesh is divided by the whole rest of the train:
play at output = Σ (stage play ÷ reduction after that stage)That is worth knowing before you spend an afternoon shimming the first stage. On a 15:1 train built as 5:1 then 3:1, a degree of play in the last mesh costs you a whole degree at the output; a degree in the first costs you a third of one.
Measuring the two numbers this page does not know
VEX publishes no efficiency or backlash figure for its gears, and this site ships no number it has not measured, so both boxes start empty and the answers that need them stay blank. Neither measurement needs anything you do not have:
- Efficiency. Hang a weight the train can just lift. Work out the motor torque the ratio says that needs, then find the smallest motor torque that does lift it. The first divided by the second is the efficiency, for that load, on that day.
- Play. Hold the input shaft still. Rock the stage's own output back and forth by hand and read the angle it moves through before it bites. A protractor taped to the frame and a mark on the shaft is enough.
Both change with load, wear and how tightly the stage is mounted, so they are your team's numbers for your build, and worth writing on a notebook page beside the date.
When you would use this
Our four-stage lift is slower and weaker than the ratio says.
Put the four stages in and measure one stage’s efficiency. Four stages at nine tenths each leave about two thirds of the torque, not nine tenths, and that is before the arm.
The arm wobbles at the top even when the motors are holding.
Measure the play in each mesh and read the play at the output. If it is mostly the last stage, shimming the first one will not help.
We are choosing between one big reduction and three small ones.
Enter both and compare the torque after friction. Fewer stages lose less, but they need bigger gears and more room.
Sources & assumptions
Tooth counts and cartridge speeds are VEX's published figures. The efficiency and play are your measurements: nothing on this page assumes a value for either, and every answer that needs one stays blank until you type it.
- VEX Robotics: Gears — checked August 2026
Make a notebook page
Turns this calculation into a dated engineering notebook page: the setup, data, results, figures, working and sources, numbered and cited. You add the goal, the decision and the reflection in your own words, plus photos and sketches. Print it, paste it into Google Docs, or download a Word file or slides.
Where this goes next
Explore further on the full mapWhere the answers on this page can be used, and which tools could have given you the numbers it asks for.
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Gear Train Calculator
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