If you can find a reference as to the weight of weld material in lbs (the web, AWS Welding handbooks, etc-somebody inhere may even have that weight intheir head or ready to hand), and it doesn't have to be specific to 625, carbon steel weight is close enough, (there isn't enough difference to matter), then all you have to do is multiply this weight by the area of the weld surface and the depth of the weld (you give it as 3/16") to give you a volume result. Then you should add whatever factor of additional metal you may add to ensure you have the 3/16". Perhaps 1/4".
If its pipe ID then its ID circumference X length of pipe X depth of weld X weight of weld material. From this you can calculate the number of coils you need to purchase.
There will be some innefficiency factors but quite frankly I think you will end up overpurchasing somewhat anyway since you have to go up to the next stock coil size from your calculation.