If you know the number of sprocket grooves and the belt pitch (distance from the center of one belt tooth to the center of the next), you can easily calculate sprocket (or pulley) pitch diameter:
Metric Pitch Belts / Sprockets:
sprocket pitch diameter (in) = 0.012532 × pitch (mm) × # grooves
Timing Belts / Pulleys:
pulley pitch diameter (in) = 0.31831 × pitch (in) × # grooves
Pitch and number of grooves can typically be identified using the part number:
Metric Pitch Example - 14MX-40S-68:
sprocket pitch diameter (in) = 0.012532 × 14 mm × 40 grooves = 7.018 in
Timing Example - TL40H150:
pulley pitch diameter (in) = 0.31831 × 0.50 in × 40 grooves = 6.366 in
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