The **gear ratio** is the relationship between the number of teeth
on two gears that are meshed or two sprockets connected with a common roller chain, or the circumferences
of two pulleys connected with a drive belt. It is usually expressed as a
decimal fraction, representing how many turns of the input shaft cause
one revolution of the output shaft. It applies to transmission, power
take off, power dividers and rear axles. It can be defined as the ratio
between numbers of teeth on the meshing gears. If the input gear is
turning faster than the output gear, the system is said to have power
ratio. If the input gear is turning slower than the output gear then the
system is said to have a speed ratio.

The first number in the ratio is usually the gear that power is applied to.
In an automobile the first number is the gear receiving power from the
engine.

We use two gears (sometimes more) of different diameters to have a
particular gearing ratio. In any pair of gears, the larger gear will move more
slowly than the smaller gear, but it will move with more torque. Thus, the
bigger the size difference (or gearing ratio) between two gears, the greater the
difference in speed and torque.

The gearing ratio is the value at which we change our velocity and torque.
Again, it has a very simple equation. The gearing ratio is just a fraction in which
we multiple velocity and torque by.
Suppose your gearing ratio is 3/1. This would mean you would multiple your
torque by 3 and your velocity by the inverse, or 1/3

**Example** Torque Old = 10 lb-in, Velocity Old = 100rps

Gearing ratio = 2/3

Torque * 2/3 = 6.7 lb-in

Velocity * 3/2
= 150rps

In simple gear arrangement, the gear ratio can be simple calculated by looking
at the number of teeth on the two gear wheels. It can also be calculated by
dividing the tooth count of ring gear to the tooth count of pinion gear, carry
out to 2 decimal point. The diameter of the gear wheel can also be calculated. A
high gear ratio implies a high torque.

The special case of gear ratios are the engine speed of the car to the rotation
of the drive wheels. In top gears, one turn of the engine crankshaft results in
one turn of the drive wheels. Lower gears require more turns of the engine to
provide single turn of the drive wheels, producing more torque at the drive
wheel. Several gearboxes use the drive ratio of 15/46.