Calculate the gear ratio between a drive gear and a driven gear from their number of teeth, and find the resulting output speed and torque multiplier.
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The gear ratio between two meshed gears is simply the number of teeth on the driven (output) gear divided by the number of teeth on the drive (input) gear, and it determines exactly how speed and torque are traded off between them, since gears conserve mechanical power (ignoring small friction losses) while redistributing how that power splits between rotational speed and rotational force. A ratio greater than 1:1 — a reduction gear set, such as 60 teeth driven by 20 teeth, giving a 3:1 ratio — reduces output speed but multiplies output torque by the same factor, which is exactly why a car's final drive and lower gears use reduction ratios, deliberately trading engine RPM for wheel torque to get a heavy vehicle moving or to climb a grade. A ratio less than 1:1, called an overdrive gear set, does the opposite: it increases output speed while proportionally reducing torque, which is exactly how a car's top overdrive gear works to keep engine RPM low and fuel-efficient at steady highway cruising speed, where high torque is no longer needed.
Every geared machine, from a bicycle to a car transmission to an industrial winch, relies on the same fundamental physical trade-off: gears cannot create power out of nothing, but they can redistribute a fixed amount of mechanical power between rotational speed and rotational force (torque) in a predictable, calculable ratio.
This trade-off follows directly from the physics of conservation of energy: power equals torque multiplied by rotational speed, and since a gear pair (ignoring small friction losses) transmits the same power from input to output, any change in speed through the gear pair must be accompanied by an inverse change in torque, and vice versa. Double the speed through a gear reduction, and torque roughly halves; halve the speed, and torque roughly doubles.
This is precisely why a car's lower gears (first and second) use large reduction ratios — the engine spins quickly, but that speed gets converted into high torque at the wheels, which is exactly what's needed to overcome the vehicle's inertia and get it moving from a stop or to climb a steep grade. As the car picks up speed and less torque is needed to maintain motion, the transmission shifts to progressively higher gears with smaller reduction ratios, trading torque back for speed.
At highway cruising speed, many modern transmissions use an overdrive gear — a ratio below 1:1 — specifically to let the engine spin slower than the wheels' effective rotation would otherwise require, since maintaining steady speed on flat ground needs relatively little torque. Running the engine at a lower RPM for the same road speed directly improves fuel economy and reduces engine wear, which is exactly why overdrive gears became standard once fuel economy became a major design priority.
Understanding this speed-torque relationship also explains why modified vehicles (like off-road trucks with larger, heavier tires) often benefit from re-gearing the final drive to a lower (numerically higher) ratio: larger tires effectively act like an extra gear reduction stage of their own, and without compensating gearing, the vehicle loses the torque multiplication it needs at the wheels, resulting in sluggish acceleration despite an unchanged engine.
Because gears conserve total power (ignoring friction losses), so anything that reduces rotational speed by a certain factor must increase torque by that same factor to keep power constant — this is the fundamental trade-off in all gear systems.
A reduction gear set (ratio greater than 1:1) decreases output speed while increasing torque, useful for climbing or accelerating; an overdrive gear set (ratio less than 1:1) increases output speed while decreasing torque, useful for efficient high-speed cruising.
A car's overall drivetrain ratio in any given gear is the transmission gear ratio for that gear multiplied by the final drive (differential) ratio — first gear typically has a high reduction ratio for strong acceleration, while a higher gear has a much lower ratio (sometimes below 1:1) for efficient highway cruising.