Sometimes in gear design (for e.g. in the case of spur gears, i.e. driver and driven) gears are to be designed for a specific velocity ratio and distance between central shafts. For the purpose of understanding this gear design better, let:

x = Distance between the centres of two shafts

N_{1} = Speed of the driver

T_{1} = Number of teeth on the driver

d_{1} = Pitch circle diameter of the driver

N_{2} T_{2} and d_{2} = Corresponding values for the driven or follower, and

P_{c} = Circular pitch

We know that the distance between the centres of two shafts,

x = (d_{1} + d_{2})/2

and speed ratio or velocity ratio,

N_{1}/N_{2} = d_{2}/d_{1} = T_{2}/T_{1}

From the above equations, we can calculate d_{1} and d_{2} (or T_{1} and T_{2}) and the circular pitch (P_{c}). The values of T_{1} and T_{2} as obtained above, may or may not be whole numbers. But in gear design, since the number of teeth is always a whole number, a slight alteration must be made in the values of x, d_{1}, and d_{2}, so that number of teeth in the gear design is a complete number.