Gear Ratio Explained: Driven Teeth Over Drive Teeth, and the Speed-for-Torque Trade

A gear ratio is the cleanest piece of mechanical math you will ever use, and almost everyone gets the direction backwards at least once. The whole idea fits in a single fraction: count the teeth on the gear that gets turned, count the teeth on the gear that does the turning, and divide. That number tells you whether you are buying speed or buying torque, because a pair of gears can trade one for the other but never make both at once.

I work this out constantly — sizing a reduction for a small motor one day, arguing with a friend about whether a 53-tooth chainring is worth it the next. The fraction is the same fraction every time. Once it clicks, you stop guessing and start reading the answer straight off the teeth.

The Formula: Driven Over Drive

Here is the one equation worth memorizing:

gear ratio = driven teeth / drive teeth

The drive gear is the one connected to your power source — the motor, the crank, the thing you turn. The driven gear is on the receiving end, the output. So if a small gear spins a big gear, the big number sits on top and the ratio comes out greater than one. If a big gear spins a small one, the ratio drops below one.

A ratio above one is a reduction: the output turns slower than the input, and torque goes up by the same factor. A ratio below one is an overdrive: the output spins faster, and torque drops. The reason is conservation of power. Power equals torque times rotational speed, and a gearbox cannot conjure power from nowhere, so whatever you take off the speed side gets added to the torque side, minus a sliver lost to friction. That is the entire trade, and it never breaks.

People mix up drive and driven all the time. On a bicycle the drive gear is the chainring up front (what your legs turn) and the driven gear is the cog at the rear wheel. Flip them and a sensible road gear reads as a fraction, which is your signal that the numerator and denominator swapped seats.

A Worked Example: 36 Driven on 12 Drive

Take a 12-tooth drive gear turning a 36-tooth driven gear. Plug it in:

gear ratio = 36 / 12 = 3

That is a 3:1 reduction. The output shaft makes one full turn for every three turns of the input, so it spins at one-third the speed. In exchange, torque triples. Feed the drive gear 3,000 RPM and the output settles at 1,000 RPM with three times the twisting force. Feed it 30 newton-metres and you get roughly 90 out the far side.

This is exactly the trade you want when a motor is happiest at high RPM but the load is slow and stubborn — a winch, a conveyor, a robot wheel that has to start under weight. You let the motor spin where it is efficient and let the 3:1 reduction turn that spin into grunt. Run the numbers yourself in the gear ratio calculator: enter 12 and 36, add an input RPM, and it confirms the output speed and the torque multiplier before you commit to a single tooth.

Bikes: Why Cyclists Talk in Gear Inches

Bicycles are a gear-ratio classroom on two wheels, but raw ratios hide one variable: wheel size. A 40-tooth chainring on a 29-inch wheel covers far more ground per pedal stroke than the same 40 on a 26-inch wheel, even though the chainring-to-cog ratio is identical. So cyclists fold wheel diameter into the number and call it gear inches:

gear inches = wheel diameter (in) × (chainring / cog)

Bigger gear inches means a harder, faster gear; smaller means an easier climbing gear. It is the oldest comparison metric in cycling and still the most useful, because it lets you rank a 2x road setup against a 1x gravel build directly instead of squinting at four tooth counts. When you compare two drivetrains, line up their highest and lowest gear inches: the high number is your top-end, the low number is your bailout climbing gear.

There is a real first-person lesson buried here. The first time I swapped a 50-tooth chainring for a 53 chasing flat-road speed, the gain at a 95 RPM cadence was about two km/h — and I lost the easy spin I relied on for hills. The math told me that before I touched a wrench; I just did not believe it until I felt my knees on the next climb.

Cadence Turns Ratio Into Speed

A ratio on its own does not give you a speed. You need to know how fast you are turning the input. For a fixed gear, road speed is directly proportional to cadence:

speed = ratio × wheel circumference × cadence

Double your cadence and you double your speed, right up to the point you spin out. This is why pro riders hold a steady 90 to 100 RPM and change gears to change pace rather than mashing one big gear slowly — spinning a moderate gear fast is more efficient and far kinder to your knees than grinding. If you want to convert the result between km/h, mph, and other units cleanly, the unit converter handles the arithmetic without rounding drift.

The practical move: before reading a speed, set a cadence you can actually sustain. A gear that feels perfect at 80 RPM is over-geared if your real climbing cadence is 60, and the speed readout will quietly lie to you if you forget.

Multi-Stage Ratios: Just Multiply

Cars and gearboxes rarely use a single pair of gears. A car drivetrain stacks the transmission ratio and the final drive (differential) ratio, and you find the overall ratio by multiplying the stages:

overall ratio = stage 1 × stage 2 × stage 3 ...

Say first gear in the transmission is 3.5:1 and the final drive is 4.1:1. The total reduction from engine to wheel is 3.5 × 4.1 = 14.35:1. The engine turns more than fourteen times for every wheel revolution, which is exactly the torque multiplication you need to launch a heavy car from a standstill. Top gear might be an overdrive at 0.8:1, which multiplied by the same 4.1 final drive gives 3.28:1 — far taller, letting the engine loaf at low RPM while you cruise.

The same logic runs through any compound gear train: a worm-and-wheel feeding a spur stage feeding a planetary set. Each stage trades speed for torque (or back), and the stages compound. Work them one pair at a time, multiply the results, and a daunting gearbox reduces to one number you can reason about.

The One Rule Behind All of It

Whether it is a 12-tooth pinion driving a 36-tooth gear, a chainring spinning a cog, or a transmission stacked on a differential, the rule never changes: divide driven teeth by drive teeth, and accept that speed and torque move in opposite directions. A reduction buys force at the cost of speed; an overdrive buys speed at the cost of force. Pick the side of the trade your job needs, multiply your stages, and let the teeth do the talking.

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Made by Toolora · Updated 2026-06-13