There are two common methods used to calculate a chain ratio, by sprocket tooth count, and by sprocket diameter. Each method works mathematically, but only the diameter method takes into account the physical size that may be important for the application. For instance, the diameter of the front sprocket on a motorcycle cannot be too small or too large, otherwise clearance for the chain will not be present.
When using the sprocket diameter method to calculate chain ratios, it is important to determine the diameter correctly, as it is not the overall diameter at the tips of the teeth, but rather the diameter at the center of the chain link rollers as they engage the sprocket. This diameter can be approximated (close enough for ratio calculations) using this equation: Sprocket Diameter = (pitch x teeth)/'pi'.
So, the diameter of a 14-tooth 630 sprocket is (0.75" x 14) / 3.1416 = 3.34". To change the 630 sprocket to a 530 sprocket, with the intention of retaining the same diameter, perform a reverse calculation starting with a diameter of 3.34", divide by 'pi', then divide by the pitch (0.625" for 530 sprocket) to get a result of 16.8 teeth. This shows that a 530 sprocket with 17 teeth is the closet equivalent to a 630 sprocket with 14 teeth.
This method can also be useful when the chain clearance necessary to accommodate a smaller or larger sprocket needs to be know in advance. For instance, if a 16-tooth 530 front sprocket is currently installed, and there is 0.25" of space between the top of the chain and the engine case, how much larger can the sprocket be? Using the formula above, the 16-tooth sprocket diameter is 3.18", a 17-tooth sprocket would be 3.38", a 18-tooth sprocket would be 3.58", and a 19-tooth would be 3.78".
The difference between the 16-tooth and the 17-tooth sprocket diameters is 0.20", half of which will be on top, so 0.10" is needed, and that will fit without issue. The difference between the 16-tooth and the 18-tooth sprocket diameters is 0.40", half of which is 0.20", so that will also fit, but not by much. The difference between the 16-tooth and the 19-tooth sprocket diameters is 0.60", half of which is 0.30", so that will not fit at all.
So, when the pitch of the chain and sprockets is the same, calculating and comparing ratios by counting sprocket teeth can be easier to do, but when converting from one pitch to another, the diameter method is best to ensure that the replacement sprockets position the chain in the same relative location as before to prevent fitment issues.