The last place I worked used round cement forms made of very thick cardboard. They are about 1/2" thick and won't collapse. The ones I saw had a plastic coating on both sides so the water won't soak in and weaken it. Many companies make them. They are available at places like Home Depot and Ace Hardware. The price for a section 10" dia x 48" long seems to be about $8. Some of them are made to peel away in layers once the cement has set. Here's the sizes that one company makes.
http://www.sonotube.com/sonotube_round_size_chart.html
For big furnaces, a friend of mine used fiber drums for a mold, although you have to put wooden stretchers in them to prevent them from collapsing and it's a bear to remove that metal ring at the bottom (I am thinking that he burned out the fiber drum and left the ring in there). For very, very small furnaces, I have used large coffee cans as a mold. Stove pipe works and is easier to remove because it has a collapsible seam. A small coffee can, or other type can, depending on the size you want, works well for the hole in the lid.
In building a furnace, I always start with the dimensions of the maximum crucible size I want to use and go from there. I prefer the "bilge" shape with a spout. I also prefer silicon carbide although clay/graphite is good also, especially for certain things. This link gives the dimensions of the various sizes. Looking at their prices, though, their name, "Budget", doesn't seem to fit too well.
http://www.budgetcastingsupply.com/Crucibles.php
According to the chart, a #10 crucible is about 6.5" wide at the bilge x 8" tall. For that size, I like about a 2" spacing between the crucible and the furnace walls, and 2.5" - 3" (I prefer 3") thick refractory for the floor, walls, and lid. The cardboard tube mold would, therefore, be about 10" diameter. Probably, those tubes are measured by the I.D. The metal shell would be about 15" - 16" dia. The height of the shell (not counting the lid) would be about 8" (crucible height) + about 1.5" (pedestal thickness) + 2.5" (floor refractory thickness) + 2" to 3" (space between top of crucible and top of furnace) = 14" - 15". With this size furnace, you could use a #10 crucible, or smaller. All these figures are ballpark. Measure everything before you build. If you go an inch or so bigger, it will be OK. You might be able to squeeze a #16 in there if you go about an inch taller and wider. For the dimensions I gave above, with 2.5" refractory and a 15" furnace diameter and height, it will take about 1.5 cubic feet of refractory, including the lid. For 3" thick refractory, it will take about 1.75 cu.ft. Use 3000F refractory. The cubic feet are marked on the bag. All manufacturer's bags are not the same.
For just melting karat gold scrap, a #4 or #6 would probably be adequate. Just remember that you can use a small crucible in a big furnace, but not the other way around. I've even seen people fire 30 gram assay crucibles (when doing assay fusions) in a #20 furnace. When I was pouring 10 oz and 100 oz pure silver bars, in a graphite book mold, I used a #6 or a #8 crucible in a #20 furnace.
NOTE: Do not accept my figures on anything, since I figured it hurriedly. Calculate everything yourself. I am just trying to give you some general design size ideas.
