Is this ratio fast enough, and can it still push?

A gearbox is a trade, and only a trade. It cannot create power. It can only convert the power a motor already makes from one shape into another. Reduce by 10:1 and the output shaft turns a tenth as fast and delivers about ten times the torque. That is the whole idea, and almost every drivetrain argument your team will have is really an argument about where on that trade you want to sit.

One reduction is just the driven gear's tooth count over the driving gear's. A 14-tooth pinion turning a 50-tooth gear is 50 ÷ 14, or 3.571:1. Stack stages and you multiply them: the KOP ToughBox Mini that everyone calls “8.45:1” is really a 14T into 50T followed by a 19T into 45T, which works out to 8.459. Chain and belt runs count exactly the same way, sprocket teeth over sprocket teeth, so a 12T to 36T chain run is another 3:1 on top of whatever the gearbox already did.

Free speed is what you get from pure geometry: take the motor's no-load RPM, divide by the reduction, and multiply by the wheel circumference. It is exact, and your robot will never once achieve it. A motor only reaches free speed when it is doing no work at all, and a robot on carpet is always doing work: squashing tread, dragging bearings, scrubbing wheels sideways through every turn.

So the convention is to derate. Multiplying free speed by 80-85% gets you a number that matches what teams actually clock on a field, and that is the figure worth comparing between designs. It is an empirical allowance, not a derivation from first principles, which is exactly why the calculator above puts it in an editable box rather than hiding it inside the result. If your robot only ever travels twenty feet at a stretch, you may not even reach the adjusted number before it is time to brake.

Efficiency is a separate thing, and it is easy to double-count. Gear losses take torque, not speed. A 90%-efficient gearbox still spins its output at very nearly the full free speed with nothing attached; what it loses is roughly a tenth of the force you can get out of it. That is why the calculator applies efficiency to torque and pushing force but leaves free speed alone. Budget about 95% per gear mesh and 97% per chain or belt run: two stages lands near 90%, a three-stage swerve module near 86%.

Rookie teams tend to ask “what ratio should we use?” when the useful question is “what is currently limiting us?” There are only two answers. If your gearing can generate more force at the wheel than friction with the carpet can hold, you are traction-limited: the wheels break loose and spin, and adding reduction makes you slower without making you push any harder. If the carpet could hold more than your motors can deliver, you are torque-limited: the wheels grip, the motors bog down, and more reduction genuinely does help.

The calculator tells you which one you are, because the fix is completely different in each case. Traction-limited robots need grippier tread, more weight over the driven wheels, or simply a lower current limit to stop wasting energy spinning wheels. Torque-limited robots need more reduction, more motors, or a higher current limit, if the breakers can stand it. Which wheels are even driven matters here too, and that depends on the layout you chose; our guide to FRC drivetrain types walks through how tank, swerve and mecanum differ on this point.

One caution on the traction number: the coefficient of friction is not a specification anybody publishes. Community measurements put smooth and Colson wheels somewhere around 0.8-1.0 and nitrile or roughtop tread around 1.1-1.4 on FRC carpet, but that swings with tread wear, dust, and how the test was run. If grip is deciding your design, drag your actual robot across actual carpet with a luggage scale and use your own number.

Arms, elevators and turrets get designed backwards from drivetrains. With a drivetrain you usually start from a target speed; with a mechanism you start from the torque you need and let speed fall out of it. For an arm, the worst case is horizontal: torque equals the weight of the arm plus whatever it is carrying, times the distance from the pivot to the combined centre of mass. Size the reduction so you can produce that at a current the motor can hold continuously, not at its stall current: a motor held near stall turns almost all of its power into heat and will fade or trip within a match.

Then sanity-check the speed you got. A 100:1 reduction on a NEO gives you about 57 RPM at the output, which is roughly a second for a quarter turn: fine for an arm, hopeless for a shooter. And check back-drive: a low reduction lets gravity spin the mechanism down when the robot is disabled, while a high reduction (especially a worm or a planetary) may hold it in place on its own. Switch the calculator to Mechanism mode, enter your lever radius, and read the force at the end of the arm directly.

Torque is proportional to current, so your smart-current limit sets a ceiling on force just as firmly as your gear ratio does. A CIM at a 40 A limit produces only about 29% of its stall torque; a Kraken X60 at the same limit produces about 10% of its. Doubling your reduction and halving your current limit can land in the same place, except one of those changes also halves your top speed and the other keeps it.

Then there is the ceiling above all of that. Four drive motors at 40 A is 160 A, already beyond the 120 A main breaker, and that is before the intake or the elevator moves. The breaker is thermal, so a momentary spike while you shove someone is fine; a sustained draw is not. Meanwhile every amp pulls the bus voltage down by roughly the battery's internal resistance times the current, and at about 6.75 V the roboRIO starts shutting your outputs off. Add up the rest of the robot in the current & brownout calculator, and if you are already browning out at events, work through our brownout troubleshooting lesson.

If any of this was new, the long-form version, with worked examples and diagrams, is in FRC gear ratios explained.