Gear ratio is similar to
mechanical advantage, in that it describes the ratio of input forces to output forces in a
machine. In a simple
gear arrangement, you can work it out by looking at the number of
teeth on the two
gear wheels. If one has 60 teeth and the other has 15, then the gear ratio is 1:4 (or 4:1, depending on which way around the gears are arranged).
Because matching gear teeth are designed to be the same physical size, then you can also measure the diameters of the gear wheels to get a good estimate of the gear ratio. If you have a 4-inch gear and a 1-inch gear, then again, the ratio is 1:4 (or 4:1).
It gets more tricky with a more complicated gearbox, but in general, the gear ratio is the number of turns it takes on the input shaft to get one turn of the output shaft. Thus in a 100:1 gearbox, you need 100 turns of the input shaft to get a single turn of the output.
As with simple levers,a gearbox converts a small force over a large distance into a larger force over a small distance. That means the 100:1 gear box will, in theory, generate on output torque 100 times as powerful as the input torque. In practice, this rarely happens with high gear ratios, because of friction, but in general, a high gear ratio will give a high output torque multiple.
A special case of gear ratio is the engine speed of a car to the rotation of the drive wheels. In top gear, many cars have a so-called straight-through drive. That is to say one turn of the engine crankshaft results in one turn of the drive wheels. Lower gears require more turns of the engine to produce a single turn of the drive wheels, and therefore produce more torque at the drive wheels.