All gears (and sprockets) have a pitch diameter, and all gears should mesh at this pitch diameter.
To find the pitch diameter for gears, take the total number of teeth on the gear and divide by the diametrical pitch (DP). For example, the 50t gear in an AndyMark Toughbox gearbox has a pitch diameter of 2.5". (50 teeth / 20 DP) = 2.5 inch
To find the
theoretical center-to-center (CTC) distance between two gears, divide the two pitch diameters by half (to get the radius) and add together. For an AndyMark 50:14 reduction in a Toughbox, this is ((14/20) / 2) + ((50/20) / 2) = 1.6".
But in reality, you should add a small value onto this theoretical CTC distance; I usually add 0.003" to all calculated CTC values. This serves two purposes: 1) it adds in a small buffer to account for manufacturing tolerances, and 2) it's better for gears to "run loose" than it is to "run tight".